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. 2020 Dec 28;15(12):e0242363. doi: 10.1371/journal.pone.0242363

Cooperation in the face of thresholds, risk, and uncertainty: Experimental evidence in fisher communities from Colombia

Juan C Rocha 1,2,3,4,*, Caroline Schill 1,2, Lina M Saavedra-Díaz 5, Rocío del Pilar Moreno 6, Jorge Higinio Maldonado 6
Editor: The Anh Han7
PMCID: PMC7769437  PMID: 33370255

Abstract

Cooperation is thought to be a necessary condition to solve collective action dilemmas such as climate change or the sustainable use of common pool resources. Yet, it is poorly understood how situations pervaded by thresholds shape the behaviour of people facing collective dilemmas. Here we provide empirical evidence that resource users facing thresholds maintain on average cooperative behaviours in the sense of maximising their individual earnings while ensuring future group opportunities. A framed field experiment in the form of a dynamic game with 256 Colombian fishers helped us investigate individual behavioural responses to the existence of thresholds, risk and uncertainty. Thresholds made fishers extract less fish compared to situation without thresholds, but risk had a stronger effect on reducing individual fishing effort. Contrary to previous expectations, cooperation did not break down. If cooperation can be maintained in the face of thresholds, then communicating uncertainty is more policy-relevant than estimating precisely where tipping points lay in social-ecological systems.

Introduction

Sustainability challenges are often characterised by situations pervaded by thresholds [1]. Achieving sustainable development goals such as eradicating poverty, dealing with climate change, and preventing the tragedy of the commons in using natural resources, require all cooperation to deal with situations characterised by non-linear dynamics with tipping points [25]. Under current development trajectories, ecosystems worldwide are at risk of undergoing more frequent and severe regime shifts –abrupt transitions in their function and structure– changing the flow of ecosystem services on which societies rely upon, and the source of livelihoods for many communities [6, 7]. Examples include bush encroachment, a regime shift that reduces the ability of ranchers to maintain cattle; soil salinisation which compromises the ability of farmers to produce food; or the collapse of fisheries which could compromise the livelihoods of ∼ 51 million people who today depend on them, most of them from developing countries [8]. Over 30 different types of regime shifts have been documented in social-ecological systems, and their frequency and intensity are expected to increase [7, 9]. This raises the questions: how do people behave in situations pervaded by thresholds? How do thresholds affect individual decisions regarding the extraction from a shared resource? Do people race to the bottom and collapse their resources, or do they find strategies for dealing with threshold uncertainty?

Traditionally these questions have been studied from a rather theoretical point of view [4, 1014] with a strong focus on public goods [5, 1517]. Theoretical and empirical evidence suggests that the relationship between collective action and uncertainty is negative: the higher the uncertainty, the higher the likelihood of cooperation to break down [11, 12, 16, 18, 19]. Only under very specific circumstances in public good models, uncertainty was predicted to increase cooperation [5, 15]. However, most of these empirical results have been largely obtained in lab settings with “weird” subjects: western, educated, industrialised, rich, and democratic [17, 20, 21]. Whether these results hold when tested with people whose livelihoods depend on natural resources is still an open question.

To fill that gap, we designed a framed field experiment to investigate how resource users deal with different degrees of uncertainty regarding the existence of thresholds below which common pool resources can collapse [22]. Using group-level analysis focusing on sustainable resource use, we found that uncertainty around critical climate-induced thresholds is not necessarily bad but can in fact protect common pool resources [22]. The purpose of this paper is to test how individual resource users behave in situations pervaded by thresholds when facing collective action dilemmas. This allows us to investigate closely cooperative behaviour and the role of context for individual behaviour—both within the game and the fishers’ everyday realities. This in turn allows us to test whether our previous results hold and identify critical factors and dynamics for managing common pool resources in situations pervaded by thresholds, risk and ambiguity.

Methods

We played a dynamic common pool resource game with 256 fishers in 4 coastal communities of the Colombian Caribbean (see Appendix 1 in S1 File for instructions, and [22] for details about the communities). The game is inspired on previous lab experiments tested at Stockholm University [17, 21]. The game was framed as a fishery with the potential of a climate event to abruptly reduce the recovery rate of the fish stock on which the fishers’ earnings depended.

At the time of the fieldwork and fieldwork preparation (2015/2016) there was not a formal ethical review process established at our institution. However, we made sure to follow relevant ethical requirements and practice for researchers in Sweden at the time e.g. as stipulated by the Act concerning the Ethical review of research involving humans (2003:460) and the Personal Data Act (1998:204). This means for example that we provided the participants with an informed consent containing information about the purpose of the study, how the data collected would be used and that the participants’ anonymity would be guaranteed. We then only included participants that gave written consent (all did). We also only make an anonymised version of the game data and survey available, including only the variables used in this study for replication purposes.

Fishing game

In the game, fishers made individual decisions each round of how much they wanted to fish from a common pool with 50 fish in the beginning. Communication was allowed and the social dilemma was faced in groups of four. The game lasted 16 rounds (unknown to the players), of which the last ten were run under one of three treatments or the control group (baseline). 64 fishers (16 groups) were randomly assigned to the threshold treatment, in which at the beginning of round seven a climate event occurred reducing the recovery rate of the fish below a stock size of 28 (threshold, Fig 1). For all other stock sizes the recovery rate remained the same. This framing is similar to hypoxia events –low water oxygen– which could follow times of drought or extreme rain, and have been recorded in the region for decades [23]. In times of hypoxia fish die creating death zones [24]. The second treatment was risk, where fishers (n = 64) knew that a climate event could occur in any following round reducing the fish stock’s ability to reproduce with a 50% chance below the threshold. In the uncertainty treatment (n = 64) the same framing was used, but the probability of the climate event was between 0.1-0.9. The remaining fishers played the control condition (baseline, n = 64), which continued playing as in the first six rounds. The fish stock was restored to 50 fish at the beginning of round seven for all groups.

Fig 1. Reproduction rate as function of stock size.

Fig 1

Treatments where the climate event triggers the threshold effect (threshold, risk, and uncertainty) can have a lower reproduction rate if the stock size is below 28 fish.

The climate event reduced the capacity of the fish stock to reproduce below a threshold. In the baseline the reproduction rate was 5 fish if the remaining fish stock was 5-19 or 35-45 fish, and 10 fish if the remaining fish stock was 20-34 (Fig 1). There was no reproduction in neither treatment for fish stocks below 5 or above 45, which was justified in the game as Allee effects. In too low densities, or highly populated ponds, fish have it harder to reproduce due to lack of partners or competition for resources. If the climate event occurred in the game, the reproduction rate changed to 1 fish for a remaining fish stock of 5-27, 10 fish for a remaining fish stock of 28-34, and 5 fish for a remaining fish stock of 35-45 (Fig 1). Once the climate event occurred, the reproduction rate changed for the rest of the game mimicking a long-lasting effect on the function and structure of the ecosystem—a regime shift.

We communicated risk and uncertainty with a ballot system to avoid deception. For risk, five green and five red stones were shown at the beginning of the round. We drew one stone in private. If it was red the climate event occurred and we calculated the reproduction rate at the end of the round accordingly. If the stone was green, we kept the reproduction scheme of the baseline (Fig 1). Since we drew the stone in private, fishers could not know if the climate event happened if the remaining stock was above the threshold θ = 28 since both reproduction schemes are identical for St ≥ 28. For the uncertainty treatment, we showed them ten red and ten green stones. We first took one stone of each colour and put them into an urn. The remaining 18 stones were mixed in another urn. Once mixed, 8 stones were moved to the first urn without revealing their colour, so neither experimenters or fishers knew the exact distribution of stones of the urn we later used to draw the climate event. All we knew was that the probability could be between 0.1 and 0.9 since for sure there was one green and one red stone in the urn. For the risk and uncertainty treatments, we drew a stone every round regardless if the climate event occurred or not, and the stone was returned to the urn so each round had exactly the same odds.

The fishing game was part of a 3 hour workshop that was carried out in four Colombian fishing communities in the Caribbean coast in February 2016. Participants knew that the total duration of the workshop was 3 hours but they did not know how long the fishing game would last. This was to avoid so-called end of game effects—people depleting the resource to maximise their individual earnings. Each workshop consisted of the fishing game (including two to three practice rounds), a post-experimental survey, and a risk/ambiguity elicitation task. Before starting, each participant signed a consent form agreeing to participate in all three activities and authorising us to use the anonymised data for research purposes.

To make decisions in the game more realistic, each fisher earned $COL500 (USD$0.14) for each fish caught, in addition to a show-up fee (COL$15000, USD$4.3) meant to compensate for the time invested in the workshop. A day spent in the workshop meant for them a day without fishing, so their average earnings were adjusted in a way that represented a typical working wage. The full instructions of the game (English version) are available in Appendix 1 in S1 File (Appendix 3 in Spanish of S2 File). For a more detailed explanation of the experiment and how it relates to similar experimental designs, please see [22]. Our selection of sample in terms of the number of groups per treatment (64) was informed by a previous study with a similar experimental design performed in the lab with students at Stockholm University [17, 21]. The within and between group variances, however, were higher in the field, resulting on a slightly lower power in our field data (0.74 versus 0.8).

Surveys

After the game, each fisher participated in a 56-question survey. Such post-experimental surveys commonly complement behavioural economic experiments both in the lab and in the field [25]. Our survey is inspired by surveys we, the author team, used for previous studies [17, 19] but adapted to our research question. The purpose of the survey was to better investigate the context in which individual decisions are taken—both with respect to the fishers’ perceptions about the game and its dynamics as well as to the fishers’ everyday reality. The survey was divided into five sections. The first section was about the game and their perceptions about the activity, for example, whether they expected the game to end when it did. The second section was about their fishing habits: how much effort they put on fishing (time per day or year), how much earnings they get in a good or bad day, whether they own and share the fishing gear, whether they fish in groups, or what are the targeted species. The third section was about traditional ecological knowledge focused on questions about abrupt changes in their fishing grounds in the past and the type of strategies they have used to cope with it. The fourth section was about cooperative activities and associations in the community. The last section included questions about demographics, socioeconomic information, and sense of place. The full questionnaire is available in Appendix 2 in S1 File.

Risk and ambiguity elicitation task

After the survey fishers were asked to do a risk and ambiguity elicitation task [26]. To measure risk and ambiguity aversion we asked fishers to choose two times between six binary lotteries: $13000|$13000; $10000|$19000; $7000|$25000; $4000|$31000; and $0|$38000. For risk, the chances of getting the high payoff was 0.5, while for ambiguity it was an unknown probability between 0.1-0.9. Half of the fishers started with the risk task and the other half with the ambiguity task in order to control for order effects. Their choices were transformed to a discrete variable used in our regressions that takes one if the fisher is risk or ambiguity averse (when the $13000|$13000 lottery was chosen), and six when the fisher is risk or ambiguity keen (when the $0|$38000 lottery was chosen). The payoffs from the risk and ambiguity elicitation task were paid to only one fisher per group (decided by lottery).

Regressions

We fitted a random effects panel model to our full game dataset (N = 4096) to disentangle treatment effects with a difference-in-difference regression. It follows the form:

Yi,t,g=μi,t,g+γGi,t,g+δTi,t,g+τGi,t,gTi,t,g+ϵi+ϵt+ϵg (1)

where γ is the effect of being assigned to a group with a treatment, δ is the effect of the treatment (before-after), and τ is the interaction term that captures the average treatment effect on the treated. As response variables Yi,t,g we used individual extraction, proportion of stock extracted, and cooperation (defined below). The average treatment effect on the treated (ATT, Fig 2) in the difference-in-difference framework was calculated according to the following definitions (Table 1):

Fig 2. Fishers fish less and cooperation does not break down.

Fig 2

Effects of treatments (threshold, risk, uncertainty) on individual extraction (top), proportion of stock (middle) and cooperation (bottom) compared to baseline (no potential for thresholds). Treatment effects are tested with a difference-in-difference random effects model with (respect to individual extraction, the proportion of the stock extracted, and cooperation (N = 4096) per response variable. Before refers to rounds before the introduction of the treatments (round 1-6) and after refers to the rounds after introduction of the treatments (round 7-16). The counterfactual is the expected response of fishers in the treatment if they would have played the baseline instead. S1-S3 Tables in S1 File complement this figure with a sensitivity analysis of robust standard error estimations.

Table 1. Difference-in-difference specifications.

Terms After (Ti = 1) Before (Ti = 0) After-Before
Treated Gi = 1 μ^+γ^+δ^+τ^ μ^+γ^ δ^+τ^
Control Gi = 0 μ^+δ^ μ^ δ^
Treated-Control γ^+τ^ γ^ τ^

Cooperation: Individual behaviour in context

To gain a better understanding of the interplay between group-level dynamics, and the context in which each individual decision was made [27], we designed two additional response variables: cooperation and coordination. Broadly speaking cooperation is working together towards a shared goal. Cooperation can also be defined as “a form of working together in which one individual pays a cost (in terms of fitness, whether genetic or cultural) and another gains a benefit as a result” [28]. In the context of common pool dilemmas (and non-dyadic games) cooperation can be interpreted as favouring the common good over individual benefits [29, 30]. An important distinction in the literature is that of cooperators versus defectors, while cooperators pay a cost for other(s) to benefit, defectors have no cost and do not deal out benefits [31, 32]. Here we operationalise these definitions by measuring cooperation as the ratio of the individual extraction xi,t with respect to the optimal level for the group. Thus, cooperation happens when (i) individuals take a number of fishes that maintain the fish stock at the optimal level (i.e. above the threshold in the treatments), or when (ii) take no fishes when the fish stock is below the optimal level (i.e. below the threshold in the treatments). Cooperation C is measured assuming fairness or equal sharing of the stock available for fishing St (above θ = 28 in treatments and θ = 20 in baseline):

Ci,t=xi,tSt-θN (2)

where N is the number of players in the group (always four in our experimental design). To avoid division by zero or negative values, when the fish stock is below the optimal level (20 or 28 depending on treatment, denominator < 1) and fishers do not take any fish (xi,t = 0), we consider that they cooperate C = 1 (212/4096 observations), and if the denominator is zero and they take one fish (xi,t = 1) cooperation is set C = 1.5 (17/4096 observations). Thus, cooperation is at its maximum when C = 1 meaning that the individual took 100% of what was fair to take while maintaining the optimal stock level and avoiding crossing the threshold in the treatments. If cooperation C < 1 the fisher did cooperate in order to avoid the threshold but was not efficient at maximising her/his personal utility; if C > 1 the fisher did not cooperate and preferred maximising her/his utility over the common good in the long run. If C = 2 the individual took twice as much as it was fair to take, and by doing so the group could have crossed the threshold. Cooperation in this interpretation is not understood as a point in time but by the distribution it forms over time. However, in any given round, the value of cooperation can be > 1 because a fisher can take one or two extra fish by agreement (e.g. a rotation scheme), by having weak agreements that do not specify quotas (e.g. “let’s fish less”), or by mistake. Crossing the threshold is, however, the aggregated effect of individual decisions. For that reason, we also introduced coordination as the average (Bray-Curtis) similarity distance to other group members’ decisions through the game. Thus, if coordination is close to one the individual extraction xi,t is very similar to the other group members, while if coordination is close to zero, xi,t is very dissimilar to the rest of the group (S1 Fig in S1 File).

Results

Fishers fish less and cooperation does not break down

Fishers facing thresholds tend to fish less compared to the baseline both in absolute terms as well as in proportion to the availability of the resource. We also find that contrary to theoretical expectations, cooperation does not break down. We studied the individual behaviour of fishers by looking at their individual extraction xi,t, the proportion of the stock they appropriated per round (xi,t/St), and their levels of cooperation C. A difference-in-difference panel model with random effects reveals that treatment effects for individual extraction and proportion of stock extracted are significant and negative (Fig 2). The model also shows that treatment effects on cooperation are not significant. A Hausman test suggests that our choice for random effects is preferred for the proportion of stock available and cooperation (p > 0.05), but it supports fixed effects for individual extraction (p < 0.05). However, since our panel is nested, we fitted a random-effects model clustered around individuals, groups, and time following our hierarchical design. A fixed-effects model would have not allowed us to control for the different levels of nestedness. A Breusch-Pagan Lagrange multiplier test further supported our choice of a random model when compared with a pooled regression with any of the response variables (p << 0.05).

The reduction of fishing effort is stronger for risk than for threshold or uncertainty treatments. Our results are robust to different choices of clustering standard errors (see S1-S3 Tables in S1 File) which were clustered simultaneously around individuals, groups and time. Given the nested structure of our design and that decisions in the past affect the stock size in the future, we expected that our dynamic game data presented cross-sectional dependence. We confirmed these expectations with a Breusch-Pagan LM test for cross-sectional dependence (p << 0.05 for all response variables) and a Breusch-Godfrey/Wooldridge test for serial correlation (p << 0.05 for all response variables). In addition, a Breusch-Pagan test reveals that our models are heteroskedastic (p < 0.05), meaning that the variances change over time. To correct for heteroskedasticity, cross-sectional dependence, and serial correlation, we calculated robust standard errors by estimating the variance-covariance matrix with heteroskedasticity and autocorrelation consistent estimators (S1-S3 Tables in S1 File). We also performed a F-test to the joint linear hypothesis H0: γ + τ = 0, this is that the difference in the coefficients before and after treatments (threshold, risk, and uncertainty) are indeed different from zero. We found that our differences are significant for individual extraction (F = 5.95, p << 0.05, df = 3), weakly significant for proportion of stock extracted (F = 2.23, p = 0.08), and non-significant for cooperation (F = 0.3, p = 0.8). When tested individually for each treatment in the case of proportion of stock extracted, the weakly significant treatment was risk (p = 0.08), while threshold and uncertainty were both significant (p = 0.02, 0.01 respectively; Fig 2).

Besides the effects of treatments on the reduction of fishing effort, we find that cooperation does not break down (Fig 2). While these results already contradict the premise that uncertainty breaks down cooperation, our response variables thus far do not allow us to investigate the context in which each decision was taken. For example, agreements or the emergence of rules are ignored, and an amount of fish caught worth the same in the above regression if they are caught before or after crossing potential thresholds. In the game and real life they are not the same thing. The same amount of fish extracted can have substantially different impacts on the stock size and the potential earnings of fishers if non-linear thresholds are crossed (Fig 1).

Fishing decisions in context

To better understand what explains the behaviour of individuals in terms of cooperation and coordination, we regressed variables that summarize individual behaviour from the second part of the game against explanatory variables that were individual attributes. As dependent variables we used median cooperation, coordination, the mean extraction, the mean proportion of the stock extracted, and their variances (Fig 3, see S1 Fig in S1 File for correlations between response variables). Decrease in variances and increase in coordination can be seen as empirical proxies of the emergence and compliance of agreements. As explanatory variables, we used our treatments, after controlling for socioeconomic variables (e.g. education, income), risk and ambiguity aversion (See Methods), the percentage of rounds in which individuals made agreements (a proxy of the intention but not necessarily of agreement compliance), and place to account for fixed effects that were not necessarily controlled for with our socioeconomic terms. Since our experimental design focuses on the impacts of tipping points in natural resource dynamics, we approximated income not as the amount of money people make per month, but rather as the frequency of bad days (i.e. returning from a fishing trip without any earnings). The latter although collinear with reported income, is a better proxy of exposure to regime shifts. We also include a response variable about the expectation of the fisher’s children to depend on fishing as livelihood to deal with the long term perspective of sustaining the resource, as well as group fishing and sharing of fishing arts to control for aspects of the fishing activity that can prime individuals to be more cooperative (shown in S4 and S5 Tables in S1 File).

Fig 3. Relationships between response variables of individual behaviour.

Fig 3

Figure A) shows the relationship between cooperation and coordination, figure B) shows the relationship of mean extraction and the mean proportion of the extraction. Each point represent an individual player (N = 256) and the summary statistic calculated over the second part of the game (rounds 7-16, N = 2560).

We find that all treatments significantly reduced the proportion of stock that fishers extracted (Fig 4). Individuals who played the uncertainty treatment decreased coordination, yet coordination increased in groups that reached agreements. The proportion of rounds with agreements (intentions) had a negative effect on the proportion of stock extracted, the variance of extraction, and the median and variance of cooperation suggesting that agreements were in average followed. Fishers who reached agreements were better at maximising their individual earnings while maintaining sustainable stock levels (Fig 4). Median cooperation and its variance were only affected by the proportion of rounds people reached agreements, showing that it responds more to in-group dynamics rather than treatments or socioeconomic effects. We also found place effects that were not accounted for by our socioeconomic controls, showing that place B had on average less coordination and higher variance of extraction, while place D had higher extraction and higher cooperation (C ≤ 1), both when compared to place A. People with higher levels of education reduced their variance of extraction, while people with a higher frequency of zero income days tend to fish more, but these effects are relatively small. Controlling for fishing art sharing, risk or ambiguity aversion render weakly significant coefficients (p < 0.1) and their effect sizes are relatively small together with other socioeconomic controls (S4 Table in S1 File). Controlling for individual behaviour in the first part of the game is significant for most of our response variables (except variances S4 Table in S1 File), suggesting that individuals bring cooperative preferences to the game that are independent of our treatments and other socio-economic factors. Some of our socio-economic factors are partially correlated with place (S1 Fig in S1 File), thus S5 and S6 Tables in S1 File reproduce the regression without place and only place terms respectively.

Fig 4. Individual behaviour as function of treatments and different contextual factors.

Fig 4

The panel summarises results from an OLS regression for each of the response variables. Treatment effects are shown by taking into account place (A-D), group dynamics (e.g. reaching agreements), and several socioeconomic aspects. S4 Table in S1 File complement this figure with precise estimates and summary statistics. Error bars denote 95% confidence intervals calculated with a CR2 robust standard errors estimator.

Discussion

Fishers under uncertain thresholds showed lower levels of extraction than when the threshold was known. Risk had a stronger effect at reducing individual fishing effort than uncertainty. Cooperation was not affected by thresholds, risk or uncertainty. This result supports and complements previous findings that uncertainty around critical climate-induced thresholds is not necessarily bad but can in fact protect common pool resources [22], and expand our understanding of individual-level dynamics that were not accessible in group-level studies [22, 33]. Our central result contradicts previous theoretical and empirical findings that predicted break down of cooperation under situations with threshold uncertainty [11, 12, 16, 19]. Our findings support the hypothesis that uncertainty can increase cooperative behaviour in public goods settings when the value of the public good is sufficiently high [5, 15], by means of reducing exploitation effort. Our experiment is not a public good setting, but it can be translated to a common pool resource when the dependency of the resource is sufficiently high. Previous work has concentrated their efforts on settings with western, educated, industrialized, rich and democratic individuals [20]. Here we empirically show that the negative relationship between cooperation and uncertainty does not hold for common pool resource games, played with resource users whose livelihoods largely depend on natural resources. On the contrary, our study supports a small but growing body of empirical evidence suggesting that uncertainty can help protect the commons when ecosystems are susceptible to thresholds such as climate-induced regime shifts [22, 33].

One potential explanation for the deviation from theoretical expectations can be personality traits [34, 35]. We expected that risk and ambiguity aversion could be key personal traits affecting individual behaviour. Our results suggest however that group dynamics seem to override personal preferences regarding risk and ambiguity aversion. Some resource users tend to have pro-social and pro-environmental behaviour, others have more individualistic or short term preferences (Fig 3); but as observed by a previous study in the same region, pro-social fishers are less likely of changing their behaviour than non-cooperators [19]. This in turn scales up to the group level, where groups with higher proportions of cooperative individuals maintain higher levels of fish stock despite an occasional free-rider [19]. Our results suggest that fishers were responding more to in-group dynamics (e.g. increasing coordination) and personal preferences regarding pro-social behavior, rather than risk or ambiguity aversion.

Our study shows that reaching agreements decreases fishing efforts and increases cooperation. It suggests that a common strategy that evolved in the game was approaching the threshold without crossing it, thus maximising both social and individual benefits. By reducing fishing effort or keeping close to the social optimal people do cooperate. However, cooperation–as measured in our study–was not affected by our treatments. Cooperative behaviour then seems to be driven more by personal preferences and group dynamics than levels of uncertainty. This observation agrees with previous experiments studying internal Nash solutions on common pool resources [19], and highlights the important and well established role of communication in providing groups an arena for agreement negotiations, rule making, social pressure, and coordinating actions [17, 22, 30, 36]. Previous participatory research in the communities studied supports with different methods our findings [37, 38]

Fishers do reduce fishing in presence of thresholds, but the effect occurs to a lesser extent when uncertainty is high. As shown in [22], this is partly due to our experimental design where uncertainty can mask free-riding behaviour and slow down the erosion of trust. In that sense, the uncertainty about thresholds also induces social uncertainty about adhering to agreements. An alternative explanation is that under higher levels of uncertainty fishers adopt a more exploratory mode (higher variance) with less strict agreements. Reduced variance of decisions over time and increased coordination across group members suggest that people with strong agreements (e.g. strict quotas) were more successful on maintaining the stock above the threshold than groups with soft agreements (e.g. “let’s fish less”). Further research efforts could target disentangling the effects of the different forms of uncertainty regarding the dynamics of the natural resources with potential thresholds, the social uncertainty about free-riding, or the effects of norms ambiguity. As this type of experiments scale up to more realistic settings, noise induced by social network structures needs to be taken into consideration realising that humans have limits to social interactions [39], and that social relationships are heterogeneous in number and quality.

Conclusion

If the existence of thresholds already triggers pro-environmental behaviour reducing fishing effort in natural resource users, then communicating their potential effects on ecosystems and society is more important than quantifying the precise point at which ecosystems tip over. Tipping points are difficult to observe and quantify in nature, they are not unique and they are expected to interact with other tipping points [7, 40, 41], meaning that their exact points change over time. While precise measurements can be out of reach specially in settings where monitoring programs are weak or not in place (e.g. developing countries), knowledge about the circumstances under which an ecosystem can tip over can already trigger behavioural change for maintaining natural resources in configuration that provide crucial ecosystem services for livelihoods. In our case study, these circumstances are related with high concentrations of nutrients in water often correlated with use of fertilizers in agricultural activities, or periods of high sediment input following droughts and strong rainy seasons such as ENSO events [23, 24, 42]. Identifying such circumstances and communicating uncertain but potential regime shifts can mobilise social action towards sustainable behaviour in natural resource users.

Supporting information

S1 File

(PDF)

S2 File

(PDF)

Acknowledgments

We would like to thank the fishing communities that participated in our experiments. This work received valuable feedback on early stages of its design by Anne-Sophie Crépin, Therese Lindahl, Juan Camilo Cárdenas, Maria Alejandra Velez, and Sandra Vilardy. The field work would have not been possible without the support of Nidia Vanegas, Alisson Soche, Darlin Botto, María de los Ángeles González, Cristhian Marrugo, Gloria de León, Jaime González, and Jesús Jiménez. JCR benefit from technical advise by Joshua Abbott. The research was supported by Formas grant 211-2013-1120 and 942-2015-731.

Data Availability

The experimental data necessary for replication is available in a public repository (10.6084/m9.figshare.12563549). Game data and survey data used in this study has been anonymised. The code used for the analysis is publicly available at: https://github.com/juanrocha/BEST.

Funding Statement

The research was supported by Formas (https://formas.se) grant 211-2013-1120 and 942-2015-731. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

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Decision Letter 0

The Anh Han

20 Aug 2020

PONE-D-20-19709

Cooperation in the face of thresholds, risk, and uncertainty

PLOS ONE

Dear Dr. Rocha,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

==============================

ACADEMIC EDITOR: The two reviewers have provided constructive and detailed comments. They both agreed that the work is intersting, relevant and would provide a strong contribution in terms of real-world evidence to support theoretical findings in behavioural modelling research. However, there are several aspects of the paper that need improvements, for which the reviewers have provided constructive suggestions. Please carefully consider them in the revision of your manuscript.

==============================

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We look forward to receiving your revised manuscript.

Kind regards,

The Anh Han, Ph.D.

Academic Editor

PLOS ONE

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6. We noted in your submission details that a portion of your manuscript may have been presented or published elsewhere. [We are also submitting another manuscript based on the same data entitled “Uncertainty can help protect the local commons in the face of climate change” also available as a preprint at https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3468677. ] Please clarify whether this [conference proceeding or publication] was peer-reviewed and formally published. If this work was previously peer-reviewed and published, in the cover letter please provide the reason that this work does not constitute dual publication and should be included in the current manuscript.

Additional Editor Comments (if provided):

The two reviewers have provided constructive and detailed comments. They both agreed that the work is intersting, relevant and would provide a strong contribution in terms of real-world evidence to support theoretical findings in behavioural modelling research. However, there are several aspects of the paper that need improvements, for which the reviewers have provided constructive suggestions.

[Note: HTML markup is below. Please do not edit.]

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Partly

Reviewer #2: Yes

**********

2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: Yes

**********

3. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

**********

4. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

**********

5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: The authors present and discuss empirical results of an experiment with fisherman in Columbia, conducted to study individuals’ decision in a common-pool resource dilemma. Particularly, the authors design treatments to better understand how cooperation depends on shocks in the resource growth, thresholds that determine that resource growth, uncertainty and risk. The authors show that, in all the conditions tested, fisherman cooperate more after the resource growth regime shifts. Notwithstanding, the risk condition is the one presenting a higher increase in cooperation. The authors conclude that uncertain thresholds increase the level of cooperation.

This work has several positive aspects: 1) first of all, it is noteworthy that the common-pool resource game is actually played by individuals that deal with such dilemmas in their daily lives; this makes, in my opinion, the collected data extremely valuable. 2) second, it is also remarkable that the experiments were conducted with “non-weird” subjects. 3) last but not least, the results are interesting in that they point out that uncertain thresholds increase cooperation. The analysis performed appears to be sound and the results are, as far as I know, original.

Despite several worthy features, I also found some unclear points in the manuscript:

1) to start with, the authors use a very specific growth structure, characterized by (not one, but) four thresholds defining different fish stock growth rates. What was the reason behind such specific thresholds and growth rates?

2) related with the previous point: what are the general characteristics of the interaction that results from such thresholds, growth rates and number of players per group? (e.g., what would be a pareto optimal set of strategies? or fair? or Nash equilibria?). The authors provide metrics of cooperation and coordination to characterize their results, but would be relevant to, beforehand, state what is the expected/efficient behaviour of individuals in this interaction.

3) it is hard to grasp the meaning of several expressions used in the text, namely “Uncertain thresholds” or “risk of thresholds”. The threshold seems to be defined on the stock size, below which fish stock growth rate is reduced. Events can occur and reduce fish stock growth rate below the threshold. It seems that there can be risk and uncertainty on the future growth rate, but the threshold is always defined at 28 or 20. How come the threshold is said to be uncertainty or risky?

4) one key conclusion of the paper is that “Fishers do reduce fishing in presence of thresholds”. But no scenario without thresholds was tested, as far as I understood. With or without event, the fish reproduction rate is always defined by thresholds defined on the stock size; lower growth rates when the stock approaches depletion is a feature present in all control and treatment scenarios. How can then be argued that “thresholds” increase cooperation? Compared with what?

5) seems rather strange that cooperation increases even in the baseline condition, where the second-stage is exactly the same as the first one. Actually, from the first to the second stage, the stock is replaced, which would imply that users are free to extract more without consequences. Any hypothesis for cooperation increasing also in the baseline condition?

6) if all treatments have threshold, why is a specific one called “threshold”? It seems that the distinctive feature of that treatment is for the event to occur deterministically.

Overall, I believe that this work can become a good contribution to PLOS ONE. In my opinion, it should be revised to clarify, at least, the points mentioned above.

Minor details:

Line 80, page 2: Fishers facing thresholds tend to fish less -> compared with what?

Page 3, line 114: cooperation is maximized when C = 1 -> seems that efficiency is maximized when C=1. As the authors mention, C<1 means cooperation as well.

Fig. 1 caption: When the difference were -> was?

Fig. 1 caption: contorl

Line 130, page 3: e regressed variables that summarizes -> summarize?

Line 180, page 5: Our findings supports -> support?

Page 5: wihtout crossing

Fig. 3 caption: starndard

SI: Page 1 line 26 -> sing up

Reviewer #2: This manuscript presents experimental evidence on the cooperative behaviours of individuals when faced to the risk of environmental crisis. Its main contribution is to provide insights on the behaviours of individuals used to manage resources, in contrast to previous work mostly focusing on individuals from WEIRD societies.

On the positive side, the manuscript provides a valuable contribution because (i) experimental evidence is always relevant (and this is particularly true in the field of evolution of cooperation dominated by theoretical work), and (ii) because the results of this study challenge previous conclusions mostly based on WEIRD societies. The introduction and the discussion are well written and referenced. The goal of the manuscript is well motivated. Previous work on the topic are cited and the authors do a good work at contextualising their study, either to motivate the study as in the introduction, or to connect their results in the discussion. The experimental design is solid. The authors show an expertise in statistics and data analysis, even if the complexity of the statistical analysis can sometimes limit the understanding of a reader.

The negative point is mainly the results section and the analysis (besides the statistical analysis) presented. First, some choices in the experimental design and the analysis lack justification (or alternatively, discussion of the consequences of these choices). For instance, the index created to measure cooperation appears arbitrary (arbitrary value in some cases, replenishment rate not taken in account, …). The rationale behind the effects of the climate event is not clear. Authors sometimes use median and sometimes use the mean. Altogether, this can lead readers to doubt the robustness of the conclusion of the study. Second, the results section strongly needs rewriting. On the one hand, a large part of the results section is not result but the description of the method. On the other hand, the space dedicated to the actual results and analysis is limited with for instance, the main result on cooperation appears to be missing. Moreover, the plots are too complex and often not clear. Ultimately, this results in readers having to trust the conclusions and interpretations of the authors rather than reaching the same conclusions than the authors throughout the analysis.

To conclude, I favour publication, but at the condition of rewriting the results section. The detailed comments are in the attachment.

**********

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Reviewer #1: No

Reviewer #2: Yes: Cedric Perret

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Attachment

Submitted filename: Review - PONE-D-20-19709.pdf

PLoS One. 2020 Dec 28;15(12):e0242363. doi: 10.1371/journal.pone.0242363.r002

Author response to Decision Letter 0


16 Oct 2020

## Detailed responses to editorial requests:

1. Please ensure that your manuscript meets PLOS ONE's style requirements, including those for file naming. The PLOS ONE style templates can be found at

https://journals.plos.org/plosone/s/file?id=wjVg/PLOSOne_formatting_sample_main_body.pdf and

https://journals.plos.org/plosone/s/file?id=ba62/PLOSOne_formatting_sample_title_authors_affiliations.pdf

We have followed the suggested templates

2. Please include additional information regarding the survey or questionnaire used in the study and ensure that you have provided sufficient details that others could replicate the analyses. For instance, if you developed a questionnaire as part of this study and it is not under a copyright more restrictive than CC-BY, please include a copy, in both the original language and English, as Supporting Information.

Added in S3 appendix

3. We note that you have stated that you will provide repository information for your data at acceptance. Should your manuscript be accepted for publication, we will hold it until you provide the relevant accession numbers or DOIs necessary to access your data. If you wish to make changes to your Data Availability statement, please describe these changes in your cover letter and we will update your Data Availability statement to reflect the information you provide.

All data necessary for replication has been updated under the Figshare repository 10.6084/m9.figshare.12563549. The anonymized data includes all the decisions taken in the experimental game (rawdata, N=4096), and a reduced data from our surve (mini_survey, N=256) that includes all questions used in our linear regressions. We did not include the full survey because we did not use all questions in the analysis, and some questions reveal delicate information about e.g. being victims of displacement or violence by illegal armed groups.

4. In your Data Availability statement, you have not specified where the minimal data set underlying the results described in your manuscript can be found. PLOS defines a study's minimal data set as the underlying data used to reach the conclusions drawn in the manuscript and any additional data required to replicate the reported study findings in their entirety. All PLOS journals require that the minimal data set be made fully available. For more information about our data policy, please see http://journals.plos.org/plosone/s/data-availability.

Upon re-submitting your revised manuscript, please upload your study’s minimal underlying data set as either Supporting Information files or to a stable, public repository and include the relevant URLs, DOIs, or accession numbers within your revised cover letter. For a list of acceptable repositories, please see http://journals.plos.org/plosone/s/data-availability#loc-recommended-repositories. Any potentially identifying patient information must be fully anonymized.

Important: If there are ethical or legal restrictions to sharing your data publicly, please explain these restrictions in detail. Please see our guidelines for more information on what we consider unacceptable restrictions to publicly sharing data: http://journals.plos.org/plosone/s/data-availability#loc-unacceptable-data-access-restrictions. Note that it is not acceptable for the authors to be the sole named individuals responsible for ensuring data access.

We will update your Data Availability statement to reflect the information you provide in your cover letter.

5. Please amend your list of authors on the manuscript to ensure that each author is linked to an affiliation. Authors’ affiliations should reflect the institution where the work was done (if authors moved subsequently, you can also list the new affiliation stating “current affiliation:….” as necessary).

All affiliations listed are current.

6. We noted in your submission details that a portion of your manuscript may have been presented or published elsewhere. [We are also submitting another manuscript based on the same data entitled “Uncertainty can help protect the local commons in the face of climate change” also available as a preprint at https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3468677. ] Please clarify whether this [conference proceeding or publication] was peer-reviewed and formally published. If this work was previously peer-reviewed and published, in the cover letter please provide the reason that this work does not constitute dual publication and should be included in the current manuscript.

The manuscript “Uncertainty can help protect the local commons in the face of climate change” is part of Caroline Schill’s PhD thesis defended at Stockholm University in 2016. The manuscript, from its initial draft, has benefited from the feedback from her PhD review committee, and was presented at the 6th World Congress of Environmental and Resource Economists in Gothenburg in 2018, and the International Conference for the Study of the Commons in Peru in 2019.

While relying on the same experiments, both papers differ in terms of the subset of data and methods (statistical analyses) used, level of analysis, metrics used, and scope of the conclusions. The paper led by Schill deals with how groups exploited shared resources in situations where climate change can introduce tipping points. It is a group level analysis, thus it focuses on overall sustained stock sizes as well as whether or not groups risk crossing the threshold as main variables of interests. Moreover, it uses inequality in catch rates (Gini coefficient) as a proxy for group cooperation. Schill’s paper has the advantage that group behaviour is independent among groups, lending itself for a different statistical approach (logit regressions with group level statistics). The disadvantage is that we cannot include individual level statistics such as the survey data, or individual risk and ambiguity preferences that we use on our PlosONE contribution.

Our paper submitted to PlosONE complements this group-level analysis used in the other manuscript by using individual-level information from post-experimental surveys, and risk / ambiguity elicitation tasks to better understand individual human behaviour in our experimental setting. Due to our main interest in the effects of thresholds on cooperation, we developed and introduced here a sophisticated metric of cooperation (different from Schill’s paper), which allowed us to disentangle cooperation from coordination effects at the individual level. For example, the PlosONE paper enables the distinction between cooperators and defectors that is fundamental in the cooperation literature, but inaccessible to the group level analysis. The PlosONE paper also develops a different methodological contribution to deal with dependencies in time, groups and individuals (3 potential sources of bias) on dynamic games. The manuscript led by Schill has not been peer-reviewed and published yet. We are currently in the process of getting it ready for re-submission. We will inform you if this status changes in the course of the revision process for this paper.

## Detailed response to reviewers:

### Reviewer 1:

The authors present and discuss empirical results of an experiment with fisherman in Columbia, conducted to study individuals’ decision in a common-pool resource dilemma. Particularly, the authors design treatments to better understand how cooperation depends on shocks in the resource growth, thresholds that determine that resource growth, uncertainty and risk. The authors show that, in all the conditions tested, fisherman cooperate more after the resource growth regime shifts. Notwithstanding, the risk condition is the one presenting a higher increase in cooperation. The authors conclude that uncertain thresholds increase the level of cooperation.

This work has several positive aspects: 1) first of all, it is noteworthy that the common-pool resource game is actually played by individuals that deal with such dilemmas in their daily lives; this makes, in my opinion, the collected data extremely valuable. 2) second, it is also remarkable that the experiments were conducted with “non-weird” subjects. 3) last but not least, the results are interesting in that they point out that uncertain thresholds increase cooperation. The analysis performed appears to be sound and the results are, as far as I know, original.

Despite several worthy features, I also found some unclear points in the manuscript:

1) to start with, the authors use a very specific growth structure, characterized by (not one, but) four thresholds defining different fish stock growth rates. What was the reason behind such specific thresholds and growth rates?

We should point out that our game builds on a dynamic common-pool resource game originally designed for the lab (i.e. with students as participants) by Lindahl et al. (2016), and further developed by Schill et al. (2015). The point of reference for the underlying growth function of that design is a logistic growth function with a sigmoid term (in particular a “Holling-type” III predation term to capture resource dynamics with a threshold. Such a non-concave growth function has been shown to approximate the dynamics of ecosystems with the potential for regime shifts, such as forests or coral reefs. Like Lindahl and Schill et al. we use for our study also a discrete version of this growth function in order to reduce complexity of experiment instructions.

According to our definition of thresholds, our study has only one threshold. Below a stock size of 28 fish, the fish resource recovery rate drops from 10 to 1 fish. Here the use of “threshold” is understood as a critical point below which the dynamics of the system change to a qualitatively different behaviour (a bifurcation or critical transition). The other discrete steps in the recovery rate correspond to natural dynamics of ecological populations, including fish. Low recovery rate at higher densities ensures that the population has a carrying capacity, that is, it cannot grow to infinity. It reflects the situation when too many fish are already in the system and available resources become scarce for them. Low recovery rate at lower densities reflects depensation, or the fact that it is difficult for individuals to find partners for mating, and crowding benefits such as schooling in fishes are lost when the population has low numbers. As a result, fishes spend more time hiding or avoiding predators than feeding and reproducing, known in the literature as the Allee effect (Allee 1932). These two assumptions are necessary to keep the realism of our experiment: the population does not grow to infinity, and at lower densities it is harder to reproduce. These two assumptions are also necessary conditions to recreate the maximum sustainable yield in our experimental design, that is, an intermediate population size at which the recovery rate is maximised (in our case from 20-28 stock size).

In our experimental design the possibility of a threshold is induced and framed as a climate event in three out of 4 treatments. Crossing the threshold however is a response to fishing effort by the group of players, not to the climate event alone. We explained the threshold and the different growth rates to our fisher participants through the game instructions. We further checked that fishers were familiar with regime shifts like dynamics (bifurcations) in the survey when asking whether they have experienced abrupt collapses in their resources. Most of them confirmed experience of regime shift dynamics. The theory of critical transitions requires that multiple equilibria can co-exist under similar conditions (parameters). These equilibria in our game are the high and low reproduction rates, and the similar conditions are the climate event.

Allee WC, Bowen E (1932). "Studies in animal aggregations: mass protection against colloidal silver among goldfishes". Journal of Experimental Zoology. 61 (2): 185–207. doi:10.1002/jez.1400610202.

2) related with the previous point: what are the general characteristics of the interaction that results from such thresholds, growth rates and number of players per group? (e.g., what would be a pareto optimal set of strategies? or fair? or Nash equilibria?). The authors provide metrics of cooperation and coordination to characterize their results, but would be relevant to, beforehand, state what is the expected/efficient behaviour of individuals in this interaction

The Pareto optima in our game are all sets of decisions that maintain the stock size at 28 (just before crossing the threshold) for treatments, and at 20 in the baseline. Given that players can only extract a discrete number of resources, the strategy often evolves towards a rotation scheme where the 10 fish reproduced per round are splitted equally among the 4 players over the long term. The Pareto optima then assumes a fair distribution of resources, an assumption that permeates to our metrics of cooperation. The Nash equilibria, on the other hand, depends on a number of assumptions that are violated in our experimental design. A Nash equilibrium exists in non-cooperative games when people cannot form coalitions. Our game allows communication and coalition forming. The dynamic feature of our game (that current decisions can affect the pay-off table of future decisions) make our game very sensitive to the last round effect. That is, an optimal (Nash) strategy is to collapse the resource if one believes the game is about to end. But since the end of the game is unknown to players, the Nash equilibria become taking all the fish stock on the first round to avoid others doing it before yourself. We intentionally designed the game to avoid the last round effect. We have discussed the relevance of these equilibria in previous theoretical work that introduces our game design. For the intuition underlying these expectations please consult Lindahl et al. (2016) and Schill et al. (2015) on which the design of our game is built. We have not included analytical clarifications on these equilibria because 1) they are described elsewhere, and 2) they do not clarify the key findings of our paper.

3) it is hard to grasp the meaning of several expressions used in the text, namely “Uncertain thresholds” or “risk of thresholds”. The threshold seems to be defined on the stock size, below which fish stock growth rate is reduced. Events can occur and reduce fish stock growth rate below the threshold. It seems that there can be risk and uncertainty on the future growth rate, but the threshold is always defined at 28 or 20. How come the threshold is said to be uncertainty or risky?

The threshold is indeed the point at which the dynamics tips and if it exists (depending on the treatment) it is always at the same stock size, known by participants. Below a stock size of 28, the growth rate drops drastically (from 10 to 1 fish only). According to our definition (see our answer above in 1), there is no threshold at a stock size of 20.“Uncertainty” and “Risk” refers to the probability of a climate event occurring which would induce a threshold in the resource dynamics. In other words, uncertainty and risk of a threshold do not refer to where the threshold is located but whether or not a threshold exists. In the risk treatment, the probability that the conditions enabling the threshold (the arrival of a climate event) were 50-50 (p = 0.5), and that probability was constant and known to all. In the uncertainty treatment, the probability range is known (p = 0.1-0.9) but the exact p is unknown to all. In the risk and uncertainty treatment, at any time after round 6, the players do not know if the climate event has happened and, hence, whether the threshold is activated or not — unless they cross it and realise that the recovery rate is not as high as it used to be.That’s why we refer to “uncertain thresholds” or the “risk of thresholds”. The third treatment was “Threshold” or when the threshold situation arrived for sure, with p = 1.

We realised that some formulations in the text (e.g. where we explain our cooperation index) could indeed let the reader assume that also baseline had a threshold (at stock size 20). We corrected for this, see line 206

4) one key conclusion of the paper is that “Fishers do reduce fishing in presence of thresholds”. But no scenario without thresholds was tested, as far as I understood. With or without event, the fish reproduction rate is always defined by thresholds defined on the stock size; lower growth rates when the stock approaches depletion is a feature present in all control and treatment scenarios. How can then be argued that “thresholds” increase cooperation? Compared with what?

We did test a scenario without a threshold. It is called baseline. Only the threshold, risk and uncertainty treatments have thresholds below which the growth rate reduces drastically. To highlight this clearly and early on in the paper, we revised the description of the treatments in the “Fishing game” section accordingly. See line 100-107. It is compared to the baseline treatment, where there is no threshold modifying the maximum sustainable yield (MSY) area of the recovery rate. As clarified in the previous question, the other levels in the recovery rate as function of stock size are simply the necessary assumptions to make the game biologically realistic. In fisheries, the MSY is defined as a concave continuous function between the recovery rate and the population size. Here to reduce the level of details when explaining the game, we simplified the concave function to a step function with 3 levels: 0 in the extremes, 5 in intermediate levels, and 10 in the MSY area. The simplification was made to make the game easier to understand and follow for the fishers.

5) seems rather strange that cooperation increases even in the baseline condition, where the second-stage is exactly the same as the first one. Actually, from the first to the second stage, the stock is replaced, which would imply that users are free to extract more without consequences. Any hypothesis for cooperation increasing also in the baseline condition?

Indeed, as time passes in the game, the stock size is reduced and even in the baseline scenario, it is not optimal to bring the stock size below 20 fishes. So people adjust their strategies to maintain the stock in the MYS area and thus maximise their own utility. That is why we observe fishing reduction in the baseline treatment. That is also why we used a difference-in-difference regression approach to detect treatment effects. Given that there is a decline in fishing effort in the baseline treatment, the real effect is whether the decline in the treatment is larger and significantly different from one expects to occur in the baseline. That’s indeed what we found.

6) if all treatments have threshold, why is a specific one called “threshold”? It seems that the distinctive feature of that treatment is for the event to occur deterministically.

We hope we could clarify well enough with our answers above that according to our threshold definition a discrete step in the underlying growth function is a necessary but not a sufficient condition for a threshold. As explained in our answer to comment 1) above, we use a discrete version of a logistic growth function with a sigmoid term to simplify the explanation of the game. A threshold, as we understand it, would be a discontinuous jump in a continuous function. That is, under certain parameter values in the dynamics of the system, two or more regimes can co-exist. Once the system hits that tipping point, the dynamics will jump from two (or more in certain cases) qualitative modes of behaviour, or equilibria. In our design, that qualitative change (or bifurcation) is reflected by changing the recovery rate from 10 to 1 below a stock size of 28. While the critical point is deterministic, its occurrence is stochastic depending on the treatment, because it can only be crossed if the climate event conditions are activated. That activation depends on a lottery that was played in every round in the second part of the game. We have added a figure with the recovery rates (as suggested by reviewer 2) to clarify the differences in recovery rates between treatments.

Overall, I believe that this work can become a good contribution to PLOS ONE. In my opinion, it should be revised to clarify, at least, the points mentioned above.

Minor details:

Line 80, page 2: Fishers facing thresholds tend to fish less -> compared with what?

Added text: “compared to the baseline”

Page 3, line 114: cooperation is maximized when C = 1 -> seems that efficiency is maximized when C=1. As the authors mention, C<1 means cooperation as well.

Indeed, it is the most efficient cooperative outcome. However since we are describing C (cooperation) in this sentence, we refer to 1 as being the maximum value possible that C can get while still being cooperation. Values > 1 means less cooperation under our formulation.

Fig. 1 caption: When the difference were -> was?

Change made to “was”

Fig. 1 caption: contorl

Corrected

Line 130, page 3: e regressed variables that summarizes -> summarize?

corrected

Line 180, page 5: Our findings supports -> support?

Corrected

Page 5: wihtout crossing

corrected

Fig. 3 caption: starndard

Corrected

SI: Page 1 line 26 -> sing up

Corrected

### Reviewer 2:

Review: Cooperation in the face of thresholds, risk, and uncertainty

This manuscript presents experimental evidence on the cooperative behaviours of individuals when faced to the risk of environmental crisis. Its main contribution is to provide insights on the behaviours of individuals used to manage resources, in contrast to previous work mostly focusing on WEIRD societies.

On the positive side, the manuscript provides a valuable contribution because (i) experimental evidence is always relevant (and this is particularly true in the field of evolution of cooperation dominated by theoretical work), and (ii) because the results of this study challenge previous conclusions mostly based on WEIRD societies. The introduction and the discussion are well written and referenced. The goal of the manuscript is well motivated. Previous work on the topic are cited and the authors do a good work at contextualising their study, either to motivate the study as in the introduction, or to connect their results in the discussion. The experimental design is solid. The authors show an expertise in statistics and data analysis, even if the complexity of the statistical analysis can sometimes limit the understanding of a reader.

The negative point is mainly the results section and the analysis (besides the statistical analysis) presented. First, some choices in the experimental design and the analysis lack justification (or alternatively, discussion of the consequences of these choices). For instance, the index created to measure cooperation appears arbitrary (arbitrary value in some cases, replenishment rate not taken in account, ...). The rationale behind the effects of the climate event is not clear. Authors sometimes use median and sometimes use the mean. Altogether, this can lead readers to doubt the robustness of the conclusion of the study. Second, the results section strongly needs rewriting. On the one hand, a large part of the results section is not result but the description of the method. On the other hand, the space dedicated to the actual results and analysis is limited with for instance, the main result on cooperation appears to be missing. Moreover, the plots are too complex and often not clear. Ultimately, this results in readers having to trust the conclusions and interpretations of the authors rather than reaching the same conclusions than the authors throughout the analysis.

To conclude, I favour publication, but at the condition of rewriting the results section. You can find below the detailed list of comments:

Title

Change the title to make it clear that the paper presents experimental evidence. For instance, add “Experimental evidence on [...]” or “[...] in fishers communities from Colombia”.

Title changed to: “Cooperation in the face of thresholds, risk, and uncertainty: experimental evidence in fisher communities from Colombia.”

Introduction

Some details at the end of the introduction should be moved to the next section. Authors should reconsider having a method section between introduction and results rather than at the end.

Thanks for the suggestion. We have rewritten the manuscript with a methods section after introduction and an extended results section.

The authors might be interested by theoretical work by Francisco C. Santos on the topic of cooperation with risk (for instance, https://www.pnas.org/content/pnas/108/26/10421.full.pdf) .

Thanks for the suggestion, we have added reference to the fascinating work of Santos and Pacheco. Thanks for the lead, we were not aware of their theoretical model that predicted some of our results in the public goods context, very relevant indeed!

Method

A figure that explains the replenishment rate would be helpful. For instance, the figure could be a line representing the population size of the fish stock, divided in sections for the different replenishment rate.

We have introduced the replenishment rate in text and a new Figure 1 as suggested

What are the effects of the diminishing returns? It could be argued that individuals taking a lot of fishes are actually cooperating because they reduce the population size down to the maximal productivity. If it does not matter e.g. it rarely happens, add a sentence stating it.

That case is included in our measure of cooperation under the assumption of equal sharing (because we divide by number of players in the group). So taking a lot of fish at the beginning, as long as it is not by taking advantage of others and aggregated extraction does not lead to crossing the threshold is considered cooperation. Cooperation (C) will have a value of 1 or less.

The climate event (i) reduces replenishment rate of low population size and (ii) reduces the interval of population size where the replenishment rate is optimal but does not affect the replenishment rate of this interval. What is the rationale behind this choice? For instance, why did not the authors consider that climate event simply reduces replenishment rate for any population size? As far as I know, this differs from most of theoretical work so how does this choice affects the results presented, and the comparison with theoretical work?

The main purpose of our study was to test how individual resource users behave in situations pervaded by thresholds when facing collective action dilemmas. In particular, we were interested to what extent fishers reduce their fishing effort in order to not contribute to cross the (potential) threshold. No matter whether the fishers face the baseline (no threshold) or one of the treatment conditions (potential threshold), it is best for the group to maintain stock sizes where the replenishment rate is the highest. Changing the recovery rate for larger population sizes would have created a confounding factor and reduced our ability to answer our research question. If we introduce both, a threshold and a lower recovery rate for high population sizes, we would have not been able to distinguish whether a change in response/behaviour was because of the threshold in population size (x-axis) or the change in recovery rate (y-axis).

The reviewer’s suggestion is excellent, and probably a good way forward to advance our understanding of the role of recovery rates in fishing behaviour. In the scope of our study, however, it would have created the necessity of including 3 treatments (with and without change on the y axis), and increase our sample size; making the test unfeasible with our limited budget.

An additional argument not to change homogeneously the climate effect to all population sizes, is that the effect of climate change as reported in the literature is not homogeneous. Changes in temperature affect species differently, and the effects can differ even within the same species depending on their lifestage. While there is general agreement that climate change and fishing pressure together have negative effects on marine food webs (Kirby et al 2009), it is still an open question whether climate alone is necessarily negative for food webs productivity (Buchholz 2019). For example, in Arctic food webs some authors predict an increase of primary productivity under climate change scenarios (Lewis 2020, Buchholz 2019), while others predict the opposite (Whitt et al 2020). For tropical ecosystems it is likely to be negative, but the response on the reproductive rate is species specific: some species will benefit from warming conditions while others will see their niche reduced. That differential response is what seems to happen in the sardine / anchovy shifts along the Peruvian and Californian coasts, where the shift in species abundances is driven by climate (ENSO oscillations) (Sugihara et al 2012).

Kirby, Richard R, Gregory Beaugrand, and John A Lindley. 2009. “Synergistic Effects of Climate and Fishing in a Marine Ecosystem.” Ecosystems 12 (4). SPRINGER: 548–61. doi:10.1007/s10021-009-9241-9.

Buchholz, Andrea Bryndum, Derek P Tittensor, Julia L Blanchard, William W L Cheung, Marta Coll, Eric D Galbraith, Simon Jennings, Olivier Maury, and Heike K Lotze. 2019. “Twenty‐First‐Century Climate Change Impacts on Marine Animal Biomass and Ecosystem Structure Across Ocean Basins.” Global Change Biology 25 (2). John Wiley & Sons, Ltd (10.1111): 459–72. doi:10.1111/gcb.14512.

Lewis, K M, G L van Dijken, and K R Arrigo. 2020. “Changes in Phytoplankton Concentration Now Drive Increased Arctic Ocean Primary Production.” Science 369 (6500): 198–202. doi:10.1126/science.aay8380.

Whitt, Daniel B, and Malte F Jansen. 2020. “Slower Nutrient Stream Suppresses Subarctic Atlantic Ocean Biological Productivity in Global Warming.” Proceedings of the National Academy of Sciences of the United States of America 117 (27): 15504–10. doi:10.1073/pnas.2000851117.

Lotze, Heike K, Derek P Tittensor, Andrea Bryndum-Buchholz, Tyler D Eddy, William W L Cheung, Eric D Galbraith, Manuel Barange, et al. 2019. “Global Ensemble Projections Reveal Trophic Amplification of Ocean Biomass Declines with Climate Change.” Proceedings of the National Academy of Sciences of the United States of America 116 (26): 12907–12. doi:10.1073/pnas.1900194116.

Sugihara, G, R May, H Ye, C h Hsieh, E Deyle, M Fogarty, and S Munch. 2012. “Detecting Causality in Complex Ecosystems.” Science 338 (6106). American Association for the Advancement of Science: 496–500. doi:10.1126/science.1227079.

Why does the fish stock is restored at turn 7? Did fishers know about this? Can it affect the results?

At the beginning of the game, we informed all participants that the game lasts several rounds and that it has two stages. We also told them that we will tell them when the first stage finishes and explain then what will happen in the second stage. In other words, they did not know beforehand that we would reset the stock size, i.e. results were not affected. After 6 rounds, we informed the fishers that they are now going to play the second stage of the game. Apart from the new information they received depending on which treatment their group was randomly allocated to, they were all told that we will reset the stock to 50 fish. The reason for restoring the stock is twofold. On the one hand it allows to make within-group comparisons (i.e. compare behaviour of the same individuals and groups before and after the treatments were introduced). Additionally, due to the dynamic nature of our game individual groups are likely to maintain different stock sizes over time and so we would have been faced with introducing treatments while some groups maintain very high stock sizes, others very low ones (e.g. below the not yet introduced thresholds). Hence, we could not disentangle to what extent a change in behaviour would be due to the introduction of a treatment or due to where exactly the group was at after 6 rounds.

L266 “There was no reproduction ...” -> Move this sentence up, where you explain the different replenishment rates.

Sentence moved

L259: “The event was meant to reduce ...” -> “The event reduces ...”

Changed

L297: remove the “than expected” and “initially planned”.

deleted

Did the fishers know the details about the different replenishment rates?

The fishers had complete knowledge about the different replenishment rates as well as every other aspect of the game design. See the instructions protocol in the SM. We also did 2-3 practice rounds before the game to make sure they understood how the replenishment rate worked.

L299: Add a reference for similar surveys in the literature to motivate the choice of the

survey (if it exists).

It is very common to complement behavioural economic experiments with post-experimental questionnaires or surveys see e.g. Anderies et al. 2011. The survey we used in this project is partly based on and inspired by post-experimental surveys used by the author team in previous studies. In particular: Maldonado and Moreno-Sanchez (2016) and Schill et al. (2015). We added this motivation and references to the text in the survey section.

In revising the paper, we also realised that it would be more useful for the reader to highlight in the survey section only the questions we actually use for this study rather than providing a detailed overview of all the sections of our large survey. We hope you agree with this revision.

References:

Anderies, J. M., M. A. Janssen, F. Bousquet, J.-C. Cardenas, D. Castillo, M.-C. Lopez, R. Tobias, B. Vollan, and A. Wutich. 2011. The challenge of understanding decisions in experimental studies of common pool resource governance. Ecological Economics 70(9):1571–1579.

Maldonado, J. H., and R. Del Pilar Moreno-Sanchez. 2016. Exacerbating the tragedy of the commons: Private inefficient outcomes and peer effect in experimental games with fishing communities. PLoS ONE 11(2):1–17.

Schill, C., T. Lindahl, and A.-S. Crépin. 2015. Collective action and the risk of ecosystem regime shifts: insights from a laboratory experiment. Ecology and Society 20(1):48.

Analysis

Why does the authors use median cooperation but mean extraction?

Because cooperation is not normally distributed and the center of its distribution has a special meaning in the context of our study . For example, the median of cooperation for the threshold treatment aligns almost perfectly with C = 1, an important reference point in our study (where cooperation is at its maximum). Hence for the purpose of our research question, magnitude of the effects are best described by the median rather than the mean. The mean extraction is not normally distributed either. But its distribution does not have an additional meaning in the context of our research question.

Check if this notation is “p = 0.1:0.9” is commonly used. Change to 0.1 < p < 0.9 instead?

We changed to the second choice as suggested.

L88 – L95. This should be in the method section.

We don’t understand this suggestion. L88-95 presents our first sets of results — that fishing effort is reduced under threshold, risk and uncertainty treatments — It shows that the result is consistent with different choices of correcting for robust standard error estimations. It also interprets the result in the light of the literature introduced earlier and cautious the reader about the confounding factors that the diff-in-diff regression does not address, then motivating the next set of results.

L99 -L128: This should be in the method section

We have moved the text to the methods section as suggested.

L99-105: There is no need to discuss the different definitions of cooperation in the literature. One sentence explaining cooperation and how it is defined in this study is enough.

See comment below:

The measure of cooperation used lacks justification. This can lead readers to doubt of the results on cooperation, which is problematic because this is the main result. I understand the difficulty to create an index that take in account both the number of fish taken and the situation of the fish stock (above or below the threshold). I would advise to either split the index in two, with one index describing if individuals take fish when the stock is below the threshold, and one index describing the amount of fishes taken when above the threshold. Alternatively, the author needs to better justify the index built.

In the broader literature, cooperation is often confounded as i) maintaining the resource, versus ii) following agreements. For example, in the classical one-shot prisoner's dilemma cooperation is taken as following an implicit agreement of non-defection. But in our game that definition is limiting because, as you point out, there are multiple dimensions to what cooperation means in a dynamic setting: when the choices of the present changes dynamically the payoff functions of the future. In economics, there is a handful of papers using dynamic games in common pool resource contexts; and most of them operationalise cooperation at the group level (not crossing the threshold) not at the individual one.

Calling for a more evolutionary perspective in our definition of cooperation allows us to include the aspect of fitness (or fitness loss) in the long term, and control for the scenario when people agree to collapse the resource. Would that be cooperation? For some economists it is because agents are maximising their returns. But within our framework it is not because by reducing the ability of the stock to recover, a person is reducing her own profits in the future (reducing fitness) — regardless of what the group do. So our way of measuring it allows us to speak of cooperators at the individual level, distinguish from defectors, and contrast cooperation versus mere coordination.

The option suggested is not feasible at the individual level because the fish taken below the threshold is an attribute of the group, not the individual. For example if the fish stock is 30 and all 4 players take 2 fishes (2*4 = 8) who should be made responsible for taking the extra fish? Crossing the threshold is a group level feature, not an individual one. It also changes the statistical analysis where the group is the unit of analysis and the number of rounds above or below threshold is a response variable. That is what we did on a separate paper for the group level analysis by means of a logistic regression [pre-print available here: https://www.ssrn.com/abstract=3468677]. That analysis, however, cannot make use of the individual level information we present in our manuscript e.g. the surveys.

Your questions, however, raises the issue that our measure and what motivates it does not come sufficiently clear in the current text. We have added some clarifications following your suggestions below as well as made some additional changes that should improve our justifications.

o Provide the rationale behind the choice made to build the index:

▪ For instance, “We consider that cooperation is represented by individuals

maintaining the fish stock in its most productive/sustainable state. Thus, cooperation happens when (i) individuals take a number of fishes that maintain the fish stock above the threshold, or (ii) take no fishes when the fish stock is below the threshold”

We adapted the text following your suggestion (see line XXX):

“Here we operationalise these definitions by measuring cooperation as the ratio of the individual extraction $x_{i,t}$ with respect to the optimal level for the group. Thus, cooperation happens when (i) individuals take a number of fishes that maintain the fish stock at the optimal level (i.e. above the threshold in the treatments), or when (ii) take no fishes when the fish stock is below the optimal level (i.e. below the threshold in the treatments)..”

▪ Using biological terms rather than mathematical terms helps readers understand the choice made to built the index. For instance: “To avoid division by zero or negative values, if the denominator is < 1 and x_i,t = 0 cooperation is set to C = 1 (212/4096 observations), [...]” can be replaced by “When the fish stock is below the threshold (denominator < 1) and fishers do not take any fish (x_i,t = 0), we consider that they cooperate C = 1”.

Change made

o The authors consider that fishers taking fish while the stock is below the threshold results in a cooperation value of 1.5. This value is arbitrary so what does happen when a different value is used?

This was an error in the text, the text should read “if the denominator is zero and x_i,t = 1, C = 1.5”. We introduced this rule to avoid division by zero. This seemingly arbitrary choice of value does not affect results in any way because it concerns only 17 / 4096 observations, i.e. 0.004% of the data. The important decision to follow here was to choose a value between 1 (maximum cooperation) and 2 (non-cooperative behaviour that could lead to the group crossing the threshold in one of the threshold treatments). An obvious choice for a value between 1 and 2 is 1.5. The error is corrected.

o It is confusing that a higher value of the cooperation index means lower cooperation. Change the index to (1 – C_i,t) or change the name of the index.

I don’t think a change of name or scale would do the trick because the underlying function has a concave shape with a maximum in 1. Transforming 1-C centres the distribution to zero, but the magnitude of the scores loses interpretability. C = 2 means people took twice of what was fair, C = 1 means they took 100% of what was fair, and C = 0.5 means they took 50% of what was fair favouring the common good over maximising individual earnings. That numeric interpretation is lost with negative and positive values (-1 is not a negative equivalent of +1).

We have also emphasised that singular points in time were not good indicators of cooperation, but rather the distribution across time. This is because rotation schemes could emerge when an individual in a round is allowed to take more than what is fair, if she allows others to do the same in the future. So it is the shape of the distribution (and its median because the observations are not normally distributed) rather than C_i, which is interpreted as cooperation in our study.

o Why does the replenishment rate is not taken in account in the cooperation index?

It is taken into account indirectly in the sign of the denominator for stock size values around the threshold. If the denominator is positive the replenishment rate is high. When the threshold has been crossed and the replenishment rate jumps to a lower value, the denominator is negative. Low values of the replenishment rate at high stock sizes are not taken into consideration in the cooperation index because these are not situations of scarcity or risk.

L120-123. It is not clear why the authors justify the choice of describing coordination this way. If the authors use the average cooperation across different rounds, deviation from cooperation for a single round should not be a problem. I would remove this part. Simply introduce coordination in a way to measure coordination.

We did not fully understand the comment. Our measure of coordination is simply to measure coordination, it is a distance measure on the fish extraction decisions (x_i,t). It does not take into account cooperation. There is a weak negative correlation between the two (shown in SFig 1), and as we argue above they measure different things. People can coordinate to collapse the resource or to maintain it above the threshold. Both strategies will score high on coordination, but cooperation will be low in the first case while high on the second. We introduced both measures to be able to distinguish between cases.

L120-123 introduces the reader to the case when coordination is high but not 1 (a rotation scheme emerged making choices among players similar), and cooperation is high on average (close to 1) but sometimes higher than 1 because of the rotation agreement (one or two players take more than what is fair while keeping the stock as a group above the threshold). The game does not allow people to fish non-discrete numbers of fish forcing sometimes such rotation agreements.

L128: Present the results of the effects of treatments on cooperation and coordination before starting to explain these effects. So far, the results section seems to lack the main result (no effect of treatments on cooperation)

We adapted the results section according to your suggestion regarding cooperation. The second sentence in the results section now reads as follows: “We also find that contrary to theoretical expectations, cooperation does not break down.” The result regarding coordination we have to report later (with the second set of regressions) as we cannot perform the DID random effects panel model with the variable coordination (because the similarity score is calculated over the rounds 1-6 for the first phase and 7-16 for the second).

L141: Not clear and this choice looks arbitrary. Add justification or reference.

The justification is that our experimental design focuses on the impacts of tipping points in natural resource dynamics, so for us it is more important how it affects the livelihood of fishers rather than their income per se. Our survey provides info on income as well as the frequency of bad days (or days without income); and of course they are correlated. We’ve chosen the second because it is closely related to the exposure of fishers to regime shift dynamics. Income per se might be compensated by other economic activities or alternative sources of income such as pension or remittances. The justification is in L288-92.

L149. Split the sentence for clarity. First part is about all treatments having an effect and second part is about a single treatment having an effect.

Modification added.

L157: But do individuals that reach agreement are explained by socio-economic effects?

Thanks for the suggestion, really good idea that we have not checked before. We tested it now and the only socio-economic factor that explains the proportion of agreements is unsurprisingly education. The p-value is 0.002, but the size of the effect is rather minimal 0.01. It means that for every additional year of education, the subject is likely to reach agreements in 0.01 rounds. The proportion of agreements is measured between 0-1 and corresponds to the number of rounds in which the group made agreements in the treatment stage (10 rounds max). Because the effect is so little, we don’t think it is worth including in the main text. If the editor and reviewer deem it necessary, we are however happy to include the respective regression table in the SM. Below a raw summary:

Call:

lm_robust(formula = prop_ag ~ Treatment + Place + education_yr +

BD_how_often + fishing_children + Risk + Amb, data = ind_coop %>%

filter(part == T) %>% ungroup(), clusters = group, se_type = "stata")

Standard error type: stata

Coefficients:

Estimate Std. Error t value Pr(>|t|) CI Lower CI Upper DF

(Intercept) 0.509674 0.127783 3.98859 0.0001781 0.254239 0.76511 62

TreatmentThreshold 0.109000 0.099416 1.09640 0.2771433 -0.089730 0.30773 62

TreatmentRisk 0.011077 0.123237 0.08988 0.9286704 -0.235271 0.25742 62

TreatmentUncertainty 0.104112 0.108432 0.96016 0.3407063 -0.112641 0.32086 62

PlaceB -0.180979 0.118071 -1.53280 0.1304129 -0.417000 0.05504 62

PlaceC 0.095775 0.087121 1.09934 0.2758723 -0.078377 0.26993 62

PlaceD -0.003950 0.120360 -0.03282 0.9739244 -0.244546 0.23665 62

education_yr 0.016855 0.007177 2.34840 0.0220580 0.002508 0.03120 62

BD_how_often -0.001341 0.012102 -0.11084 0.9120992 -0.025533 0.02285 62

fishing_children 0.025059 0.044248 0.56635 0.5732031 -0.063390 0.11351 62

Risk 0.004053 0.012261 0.33058 0.7420790 -0.020457 0.02856 62

Amb -0.010571 0.014910 -0.70897 0.4809979 -0.040377 0.01923 62

Multiple R-squared: 0.2235 , Adjusted R-squared: 0.1871

F-statistic: 2.083 on 11 and 62 DF, p-value: 0.03487

The results section ends without having the main result (no effect of treatment on cooperation) being clearly presented. It appears that the result section starts by describing the effect of treatments on the number/proportion of fishes taken and then jumps directly to how these effects can be explained (socio-economic factors, coordination and agreement).

As explained above, to another of your comments, the second sentence in the results section now reads as follows: “We also find that contrary to theoretical expectations, cooperation does not break down..” Furthermore, we clearly repeat this result now at the beginning of the third paragraph of the results section: “Besides the effects of treatments on the reduction of fishing effort, we find that cooperation does not break down .” This aligns with the caption used in Fig 2 to describe the main results of our paper.

Figures

• Figure 1:

What is before and after? I do not find explanations in the text. Does that mean that the cooperation presented is averaged on the rounds before and after the round 7?

Indeed, before and after corresponds to the introduction of the treatment in round 7. We included that information in the caption of the figure. The technical explanation and formulas to calculate the diff-in-diff regression are introduced in the Regressions section under the Methods. We added the number of observations to the caption.

I would advise to start the caption by a sentence presenting the plots, and then have a sentence describing more formally the analysis. For instance, “Effect of treatment (risk, threshold, uncertainty) on the individual extraction (top), proportion of stock (middle) and cooperation (bottom). The effects of the treatment are tested using ...”

We appreciate the suggestion but given that our main message seemed lost in your previous comments, we prefer to keep the start of the caption as is. It encapsulates our main result: fishers fish less but cooperation does not change. However, we do see the benefit of clearly referring to the three treatments versus baseline in the caption. We adapted the caption accordingly.

Replace “counterfactual” by “baseline” in the line type (or explain in the caption).

The counterfactual is not the baseline per se, it is what people in the treatment would have done if they would have played the baseline instead of the treatment. It relies on the parallel assumption of the diff-in-diff identification strategy. The counterfactual is not actually observed, it is inferred (see table with formulas in the methods). For more details we recommend:

Angrist and Pischke. 2009. Mostly harmless econometrics. Princeton Press

We have amended the caption with the clarification as suggested.

• Figure 2 is not clear at all.

First, it can be improved in term of appearance, e.g. the quality is low, the number of different plots is too high, the size of the plots change.

Second, a plot needs to support one or two conclusions rather than providing an exhaustive presentation of the results (this goes into supplementary materials). Split this figure in different figures.

Thanks for your comments and suggestions. We improved and simplified the figure accordingly.

• Figure 3

o If possible, colour the points as a function of their p-values, in the same way than Figure 1.

Suggestion implemented.

Discussion

• L175: First sentence is not clear.

L175: “Fishers under uncertain thresholds maintained higher levels of cooperation than when the risk of thresholds was known, but risk had a stronger effect at reducing individual fishing effort than uncertainty.” L207: “However, cooperation as measured in our study was not affected by our treatments.”. These two statements seem to contradict each other.

Indeed, there was a mistake. We have rephrased the first sentence as follows: “Fishers under uncertain thresholds showed lower levels of extraction than when the threshold was known. Risk had a stronger effect at reducing individual fishing effort than uncertainty.”

The second part of the statement was left unchanged.

L180: The authors state that uncertainty increase cooperation, but I thought that uncertainty did not affect the level of cooperation.

L180 reads: “Our findings supports the hypothesis that uncertainty can increase cooperative behaviour in public good settings when the value of the public good is sufficiently high”.

What we report is that cooperation does not decrease — does not break down. And it can increase, as suggested previously under certain circumstances, when it matters a lot to people e.g. their livelihood depends on it. We observe signals of increasing cooperation in the form of reduction of fishing effort as uncertainty increases. We observe both displacement of the distribution to C values 0-1 in Figure 2, and effects on reduction of variance in extraction (Figs 2 and 3). Cooperation increased but the differences to the counterfactual were not significant (Fig 1). Our main point is that cooperation does not break down. The studies on public goods measure cooperation differently (the size of contribution to the public good). Here they are compared with the size of reduction in use to the CPR.

L211: The author could cite Elinor Ostrom, e.g. Governing the commons (1990).

Reference added

Typo

A comma is often missing “,”: L316: “For risk the chances [...]”, L360: “As response variables we used […]”.

Commas added

Fig 1 caption: “contorl”. Corrected

L184 “effots”. Corrected

Fig2 caption: Add “Figure” before “A) and B)”. Added

Attachment

Submitted filename: Response_to_reviewers.pdf

Decision Letter 1

The Anh Han

2 Nov 2020

Cooperation in the face of thresholds, risk, and uncertainty: experimental evidence in fisher communities from Colombia

PONE-D-20-19709R1

Dear Dr. Rocha,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

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Academic Editor

PLOS ONE

Additional Editor Comments (optional):

Both reviewers are happy with the responses provided and changes made, by the authors. There are only some very minor aspects suggested by the reviewers but I bellieve they can be dealt with when preparing the final version of the manuscript.

Reviewers' comments:

Reviewer's Responses to Questions

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Reviewer #1: All comments have been addressed

Reviewer #3: All comments have been addressed

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Reviewer #1: (No Response)

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Reviewer #1: Thanks to the authors for the clarifying answers and the changes made in the manuscript. I am satisfied with the answers provided.

I found useful the explicit connection between the game studied and the previous works Schill (2015) [17] and Lindahl (2016) [21].

The answers provided clarify the distinction between the abrupt changes in reproduction rates that are due to 1) natural dynamics or that are due to 2) climate events. The authors only use “threshold” to refer to the latter. By reading the manuscript, however, I still found hard to apprehend the precise meaning of "threshold" in this work. Perhaps the new Figure 1 can be used to clarify this. The authors could mention in the caption that the discontinuities observed in the left panel only reflect natural reproduction dynamics. The caption of Fig. 1 in Schill (2015) [Ref 17] does a good job defining the meaning of threshold and some description along those lines could be added also here.

Reviewer #3: I would like to deeply thank the authors for their detailed answer. The authors have made the modifications suggested, and when they did not, they have well justified their choices or pointed out my mistakes or misunderstanding. I am in favour of publication.

For the comment on the role of socio-economic factors on the proportion of agreements, I let the authors take the decision on whether to include it in the manuscript. I thank the authors for taking the time to do this extra analysis. A last comment is that at line 87, there is a paragraph on the ethical review process. Ignore me if it is required to have this paragraph in the main text, but if not, I think the authors could move it to one of the supplementary materials.

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Reviewer #3: Yes: Cedric Perret

Acceptance letter

The Anh Han

17 Nov 2020

PONE-D-20-19709R1

Cooperation in the face of thresholds, risk, and uncertainty: experimental evidence in fisher communities from Colombia

Dear Dr. Rocha:

I'm pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now with our production department.

If your institution or institutions have a press office, please let them know about your upcoming paper now to help maximize its impact. If they'll be preparing press materials, please inform our press team within the next 48 hours. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information please contact onepress@plos.org.

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Associated Data

    This section collects any data citations, data availability statements, or supplementary materials included in this article.

    Supplementary Materials

    S1 File

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    Attachment

    Submitted filename: Review - PONE-D-20-19709.pdf

    Attachment

    Submitted filename: Response_to_reviewers.pdf

    Data Availability Statement

    The experimental data necessary for replication is available in a public repository (10.6084/m9.figshare.12563549). Game data and survey data used in this study has been anonymised. The code used for the analysis is publicly available at: https://github.com/juanrocha/BEST.


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