Positive correlations in species functional contributions drive the response of multifunctionality to biodiversity loss

Abstract

Changes in biodiversity can severely affect ecosystem functioning, but the impacts of species loss on an ecosystem's ability to sustain multiple functions remain unclear. When considering individual functions, the impacts of biodiversity loss depend on correlations between species functional contributions and their extinction probabilities. When considering multiple functions, the impacts of biodiversity loss depend on correlations between species contributions to individual functions. However, how correlations between extinction probabilities and functional contributions determine the impact of biodiversity loss on multifunctionality (MF) is not well understood. Here, we use biodiversity loss simulations to examine the influence of correlations among multiple functions and extinction probabilities on the diversity–MF relationship. In contrast with random extinction, we find that the response of MF to biodiversity loss is influenced by the absence of positive correlations between species functional contributions, rather than by negative correlations. Communities with a high number of pairwise positive correlations in functional contributions achieve higher levels of MF, but are also less resilient to extinction. This work implies that understanding how species extinction probabilities correlate with their contribution to MF can help identify the degree to which MF will change with ongoing biodiversity loss and target conservation efforts to maximize MF resiliency.

1. Introduction

A defining characteristic of the Anthropocene is that the rates of biodiversity change are dramatically higher than what has been observed over thousands and millions of years, except in times of mass extinction [1]. Although an asymptotic relationship between biodiversity and ecosystem function is among the most common patterns observed, predicting how ecosystems respond to these rapid rates of biodiversity change remains challenging [2–4]. The impact of biodiversity change on ecosystem functioning occurs through a variety of trait-based mechanisms, such as how species respond to novel environmental drivers, how they contribute to ecosystem functioning, and selection and complementarity effects [5–7]. Critically, extinction probabilities impact the order in which species are lost and the effect of biodiversity change on any single ecosystem function [8]. Single ecosystem functions, however, might be poor indicators of the impacts of biodiversity change since multiple ecosystem functions respond to biodiversity change in complex ways. Because society values many functions simultaneously, understanding how ecosystem multifunctionality (MF) responds to non-random species loss is critical for predicting the state of ecosystems in the Anthropocene.

Central to most mechanisms by which biodiversity change impacts single and multiple ecosystem functions are the life history, physiological, biomechanical, resource use, and other organismal trade-offs that are ubiquitous among microorganisms, plants, and animals [9,10]. Organismal trade-offs, measured through correlations between traits, can underpin the resiliency of single functions to biodiversity change because they link species extinction probabilities to how they contribute to ecosystem function (often predicted by response and effect traits, respectively; [6,7,11]). When these two species properties are positively correlated, ecosystems are unlikely to sustain function with ongoing biodiversity loss because important contributors to function have a higher extinction probability and are functionally irreplaceable by other species in a community [8]. For example, the patterns of low ecosystem resilience have been commonly observed in aquatic ecosystems, where large-bodied fish species, which are targeted by fishermen, play important roles in nitrogen and phosphorous recycling [12,13]. By contrast, when traits that determine extinction probabilities and functional contributions are negatively or uncorrelated, individual ecosystem functions might remain unchanged or even increase if the loss of one species releases a high-performing species from interspecific competition [14]. However, how correlations between species extinction probabilities and their functional contributions to many functions mediate the response of MF to biodiversity loss has not been assessed.

Beyond linking species extinction probabilities with their contribution to functions, correlations among species functional contributions can influence the relationship between biodiversity and MF [15,16]. Biodiversity–MF experiments are typically randomly assembled, and in these communities, negative correlations between species functional contributions decrease the probability that multiple functions can be maintained at high levels [17]. This is because when species functional contributions are negatively correlated, no particular species can maintain all functions, and higher biodiversity is needed to support more functions [16,17]. By contrast, when species are added randomly, positive correlations among species functional contributions increase variation in the relationship between biodiversity and MF [15,16]. This pattern likely arises because in randomly assembled experiments, the increase in MF for each additional species depends on how strongly that additional species contributes to function, although the mechanisms are not clear. Since most MF experiments are randomly assembled while extinction in nature is generally directional, understanding how correlations between traits that determine species' extinction probabilities and contributions to multiple functions scale to shape the response of MF to biodiversity change is critical.

Recently, the recognition that biodiversity provides multiple functions has reignited the debate on how much species identities or biodiversity per se influence MF and by extension the response of MF to biodiversity change [16,18,19]. Particularly, how biodiversity effects, driven by complementarity between species [20], on individual functions scale to MF could influence their response to biodiversity change. Complementarity, measured as the excess of a mixture's performance in relation to the performance of component species' monoculture [21], typically arises from interspecific interactions (e.g. niche partitioning, facilitation), can vary in strength depending on individual functions [22,23], and can occur irrespective of species identities [2,24]. Beyond the trivial case where complementarity between species is null, its effect on any single function can be weak, such that the maximum performance still occurs in mixtures with the dominant species (non-transgressive overyielding), or strong, such that the highest performance exceeds that of any monoculture (transgressive overyielding; [5]). Most commonly, increasing biodiversity effects in individual functions additively increases the strength of the biodiversity–MF relationship [15,16,19,25]. However, how biodiversity effects determine the impact of changing community composition on MF is not well understood [2,24].

Here, we disentangle how correlations between species contributions to different functions, between species extinction probabilities and their overall contribution to MF, and complementarity interactively and independently affect the response of MF to species loss. Using simulated biodiversity–ecosystem function experiments, we factorially manipulate the correlation between extinction probabilities and functional contributions along a gradient of increasing complementarity between species to explore: (i) how correlations between species functional contributions influence the biodiversity–MF relationship, (ii) how correlations between species functional contributions and extinction probabilities affect the number of species needed to maintain MF, and (iii) how complementarity influences the number of species needed to maintain MF. Although correlations in species functional contributions are often invoked as underlying the mechanisms between biodiversity and MF [15,26], few studies have evaluated how different extinction scenarios affect the relationship between biodiversity and MF. Empirically, this can be challenging because it is experimentally intractable; however, through our simulations, we were able to explore a variety of trade-off scenarios, particularly by manipulating the number and types of pairwise correlations between species contributions to different functions, and between species extinction probabilities and their overall contribution to MF. Through this study, we are able to provide clear expectations for how MF responds to different biodiversity change scenarios.

2. Material and methods

Simulation experiments consisted of varying numbers of species in replicate ecosystems in which each species contributed to six different ecosystem functions. Individual ecosystem functions were modelled based on the diversity interaction model proposed by Kirwan et al. [5]:

$$F_k=\sum _{i=1}^S{\beta }_{ik}{P}_i+\sum _{i=1}^S{\delta }_{ijk}{P}_i{P}_j+{\epsilon }_k,$$ 2.1

where F_k is function k; P_i is the relative abundance of the ith (jth) species with i, j = 1, … , S; β_ik is the expected contribution to function k by species i in monoculture; δ_ijk is how the interaction between species i and j affect function k and ε_k is the error. The first term represents the species identity effect and the second term represents the diversity effect arising from complementarity. In our model, we assumed that each β_ik was determined by an effect trait. While the diversity interaction model is a statistical model usually used to analyse the relationship between biodiversity and ecosystem functions in experiments, because of its robust ability to predict these relationships, our approach was to use the model as a basis for the simulations. Further interpretations of the model are in Kirwan et al. [5].

We defined four initial scenarios with 30 species each that represent the possible spectrum of pairwise correlation structures between species contributions to functions (listed in table 1). In order to manipulate correlations in functional contributions, species β_ik were drawn from lognormal distribution (mean = 1, s.d. = 1) and sorted positively or negatively, depending on the trade-off scenario. For example, for a scenario in which two β_ik were uncorrelated, and two β_ik were positively correlated with each other but negatively correlated with the other two, we first assigned species a β_ik randomly from the lognormal distribution, and subsequently sorted two β_ik values in ascending order and the other two in descending order. Species abundances were randomly drawn from a lognormal distribution (mean = 1, s.d. = 1) and used to calculate P_i.

Table 1.

Summary of trade-off scenarios used in the study and their corresponding count of pairwise correlations between species functional contributions. Each β_k corresponds to a species contribution to function k. In the different scenarios, ‘R’ refers to whether the β_k vector was randomized, ‘+’ to whether the vector was sorted in ascending order, and ‘−’ whether it was assorted in descending order.

	6R	2R, 4+	3+, 3−	6+
β1	R	R	+	+
β2	R	R	+	+
β3	R	+	+	+
β4	R	+	−	+
β5	R	+	−	+
β6	R	+	−	+
random	15	9	0	0
synergies	0	6	6	15
trade-offs	0	0	9	0

For each of the above starting points, four extinction scenarios were simulated: (i) species-specific extinction probabilities were random (i.e. extinction probabilities were uncorrelated with species-specific contributions to individual functions), (ii) species-specific extinction probabilities were positively correlated with their contribution to function (i.e. the highest contributor to function is the most likely to go extinct; from here on ‘high to low’), (iii) extinction probabilities were negatively correlated with their contribution to function (i.e. the lowest contributor to function is the most likely to go extinct; from here on ‘low to high’), and (iv) extinction probabilities were negatively correlated with their abundance (i.e. the species with the lowest abundance had the highest extinction probabilities; from here on ‘abundance’). For random extinction scenarios, species were sampled without replacement using the ‘sample’ function in R (version 3.4.2). For non-random extinction scenarios, we first estimated a species contribution to MF by averaging the β_ik of each species. This value was defined as a species extinction probability and used as a vector of probability weights to remove species using the ‘sample’ function in R. Finally, for abundance-based scenarios, species abundances were scaled between 0.001 and 0.999 and this vector was used as a vector of probability weights for sampling.

Finally, for each correlation and extinction scenario, the strength of complementarity was manipulated to represent three additional scenarios: no complementarity (δ_ijk = 0), non-transgressive overyielding (δ_ijk = 5), and transgressive overyielding (δ_ijk = 15). These specific values were selected based on the range of β_ik values, with the non-transgressive overyielding scenario less than the mean β_i of all functions, and the transgressive overyielding more than the max β_i of all functions. In this experiment, we assume that all species interact in the same way (i.e. complementarity effects occur irrespective of species identities), but further implications of different values of δ_ijk are discussed in Kirwan et al. [5] and Dooley et al. [25]. Each scenario was simulated 100 times for a total of 7200 simulations (four different correlation structures, three extinction scenarios, and three complementarity scenarios).

To estimate an MF index, we used the threshold-based method, which is the most widely used and comprehensive approach [16,27]. Briefly, each function was scaled between 0 and 1 by subtracting the raw value from the maximum and dividing the obtained value by the range of raw values (maximum subtracted by the minimum). MF was then defined as the number of functions with a value above a threshold set as an integer percentage of maximum function value ranging from 1% to 99%.

We systematically analysed the relationship between biodiversity and MF at all thresholds between 1% and 99%. First, to understand how each scenario affected the relationship between biodiversity and MF, we obtained the slope and residuals between species richness and MF at all thresholds for each simulation. This slope, which provides an estimate for the change in MF per additional species, is commonly used to determine how MF responds to biodiversity change. A positive slope indicates that MF increases per species added, while a negative slope indicates that MF decreases per each additional species. Additionally, we analysed how extinction order and correlation among species functional contributions affected the overall change in MF per species added across all thresholds in each scenario through a linear mixed effect model with change in MF per species added as the response variable, the interaction between extinction order and correlation as the fixed effects, and threshold as a random factor [28]. Significant pairwise differences were further analysed by calculating differences of least squares means and confidence intervals with the difflsmeans function from the lmerTest package in R [29]. While our focus is on species loss rather than addition, we decided to keep the y-axis as the latter, as is common in biodiversity–MF studies. However, results are discussed in terms of species loss, which is the reflection about the y-axis.

In addition to analysing the slope and residuals of the relationship between MF and biodiversity, for each simulated scenario, we obtained the minimum number of species needed to maintain all six functions above each threshold. We then estimated the mean and standard error for each threshold. Third, we computed the probability of maintaining MF by obtaining the number of simulations per each scenario maintaining all functions above the set threshold and dividing that by the total number of simulations (n = 100). All simulations and analyses were conducted using R (version 3.4.2 [30]).

3. Results

Extinction order had a discernible impact on the response of MF to biodiversity loss (figure 1; for full statistical results see electronic supplementary material, table S1). When extinction was random, the correlation structure between species contributions to individual functions (i.e. β_ik) did not affect the slope of the relationship between species richness and MF (figure 2). In other words, when extinction was random, the strength of the biodiversity–MF relationship was similar across all thresholds regardless of correlations between species functional contributions. However, in these random extinction scenarios, increasing the number of pairwise positive correlations in functional contributions increased the variation of the biodiversity–MF relationship across all thresholds, as expected (electronic supplementary material, figure S1). Positive correlations between functional contributions increased the range of thresholds over which all functions could be maintained from approximately 20% in scenarios where all functional contributions were randomly correlated to almost 99% in scenarios where all functional contributions were positively correlated (figure 3), as well as the probability that those thresholds would be reached (figure 4). Scenarios in which extinction probabilities were negatively correlated with abundance, such that rarer species were more likely to go extinct, tended to be similar to random extinction scenarios and were included in the electronic supplementary material, figures S2–S6.

Figure 1.

Box plot depicting the change in MF per species added across the three different simulated extinction scenarios (random, or independent of extinction probabilities; low to high: the lowest contributor to function is the most likely to go extinct; high to low: the highest contributor to function is the most likely to go extinct; for abundance-based extinction scenarios see the electronic supplementary material). Rows represent different levels of complementarity (no complementarity, non-transgressive overyielding, and transgressive overyielding). Colours depict the different correlation structures between species functional contributions, as described in table 1. Box plots with different letters are significantly different from each other at p > 0.05. For full statistical results see electronic supplementary material, table S1. (Online version in colour.)

Figure 2.

The change in MF per species added across all threshold levels. Columns represent the three different extinction scenarios (random, or independent of extinction probabilities; low to high: the lowest contributor to function is the most likely to go extinct; high to low: the highest contributor to function is the most likely to go extinct; for abundance-based extinction scenarios see the electronic supplementary material S2). Rows represent different levels of complementarity (no complementarity, non-transgressive overyielding, and transgressive overyielding). Colours depict the different correlation structures between species functional contributions described in table 1. (Online version in colour.)

Figure 3.

The minimum number of species needed to maintain all six functions above the different thresholds. Rows, columns, and colours refer to the same attributes described in figure 2. The dotted vertical lines represent the maximum thresholds at which MF is maintained. (Online version in colour.)

Figure 4.

The probability that all functions could be maintained above each threshold, estimated as the number of simulations per each scenario maintaining MF divided by the total number of simulations. Rows, columns, and colours refer to the same attributes described in figure 2. (Online version in colour.)

Extinction scenarios where extinction probabilities and functional contributions were correlated differed strongly from random-based extinction scenarios (figure 1; electronic supplementary material, table S1). In high-to-low scenarios (i.e. when species extinction probabilities were positively related to their multifunctional contribution), the change in MF per species was higher across thresholds than random extinction scenarios (figure 2). By contrast, in low-to-high scenarios (i.e. when species extinction probabilities were negatively related to their multifunctional contribution), the change in MF per each additional species was largely negative across thresholds (figure 2). In other words, in high-to-low scenarios, biodiversity loss decreased MF, whereas loss in low-to-high scenarios MF increased with biodiversity loss. Additionally, although the range of thresholds at which MF was maintained were similar for all scenarios, the number of species needed to maintain those MF levels were strongly related to extinction mode (figure 3). Specifically, in high-to-low scenarios, the number of species needed to maintain MF across thresholds was consistently higher than for other extinction scenarios.

Correlations between species functional contributions interacted with extinction order to determine the response of MF to biodiversity change (figure 1; electronic supplementary material, table S1). While the number of positive pairwise correlations between functional contributions had no effect in random or abundance extinction scenarios, in trait-based extinction scenarios, the number of positive pairwise correlations affected the magnitude of the biodiversity–MF relationship (more positive in high-to-low scenarios; more negative in low-to-high scenarios; figure 1). Further, with more positive pairwise correlations between functional contributions, the number of species needed to maintain MF increased across intermediate thresholds for high-to-low scenarios, although not for low-to-high scenarios (figure 3). Finally, increasing the number of positive pairwise correlations between functional contributions increased the probability of maintaining MF across intermediate thresholds in all extinction scenarios (figure 4).

Complementarity increased the effect of biodiversity on MF across thresholds as well as the threshold ranges at which the relationship was positive, regardless of extinction scenario or the presence of pairwise positive or negative correlations between species functional contributions (figure 2). Additionally, increasing complementarity increased the range of thresholds where all functions were maintained (figure 3), together with the probability of maintaining higher thresholds of MF (figure 4). Despite this overall positive effect of complementarity, random-based extinction scenarios always had a more restricted range of thresholds at which all six functions were met.

4. Discussion

Here, we show how organismal trade-offs, by linking species extinction probabilities and contributions to MF, determine the ability of communities to maintain MF with ongoing biodiversity change through three related mechanisms. First, while most MF experiments manipulate biodiversity randomly [15,17,31], the effect of biodiversity on MF, and how correlations between species functional contributions shape this relationship, depends on the order in which species are lost. When species extinction probabilities and functional contributions are positively correlated, such that a strong contributor also has characteristics that make it more likely to go extinct, MF will exhibit low resiliency to biodiversity change. Second, while the literature has emphasized the importance of negative correlations between species functional contributions in affecting the biodiversity–MF relationship [17,18], we show that their effect is virtually indistinguishable from scenarios in which functional contributions are uncorrelated. Thus, the absence of positive correlations between species functional contributions, rather than the presence of negative correlations, determines the impact of biodiversity loss on MF. Third, complementarity both increases the change in MF per species lost together with the probability that high levels of MF can be maintained with ongoing biodiversity loss. These results show how information on the correlation between functional contributions and extinction probabilities can be scaled to the ecosystem level to predict how MF will respond to biodiversity change.

A central finding is that positive correlations between species functional contributions are fundamental in shaping how MF responds to biodiversity loss. Consistent with the previous studies based on randomly assembled communities [15,16], increasing the number of pairwise positive correlations in functional contributions increases the variance in the biodiversity–MF relationship (electronic supplementary material, figure S1) and the probability that high levels of MF can be achieved (figure 4). We find that the higher variability associated with positive correlations is largely an artefact of random extinction. Because MF is sensitive to the inclusion of a strong contributor, when species are lost randomly, the change in MF per species becomes more variable as the number of pairwise positive correlations increases. Additionally, achieving high levels of MF depends on including a species that strongly contributes to many functions, and only when all functional contributions are positively correlated is this probability non-zero (figure 4). On the other hand, the relationship between biodiversity and MF does not differ strongly in the presence of negative correlations or when functional contributions are uncorrelated. This is clearly illustrated when comparing the scenario in which three functional contributions were positively correlated and three negatively correlated (i.e. 3+, 3−) and the scenario in which two functional contributions were uncorrelated and four positively correlated (i.e. 2R4+; table 1). Both of these scenarios have six pairwise positive correlations, but the former has nine negative correlations and the latter nine uncorrelated functional contributions. Both scenarios are similar in terms of the change in MF per species lost (figure 1; electronic supplementary material, table S1), the range of thresholds where MF is maintained (figure 3), and the probability of achieving those thresholds (figure 4). In contrast with the prominent emphasis given to the role of negative correlations between species functional contributions [17,19], these results indicate that the absence of positive correlations drives how MF responds to biodiversity change.

The important role of positive correlations among functional contributions on the MF–biodiversity relationship becomes more evident when considering how their presence interacts with extinction order. First, beyond affecting the variance in the biodiversity–MF relationship, in non-random scenarios, positive correlations in functional contributions also affect the slope between biodiversity and MF across thresholds (figure 2). In low-to-high scenarios (i.e. when the lowest contributor to function has the highest extinction probability), MF increases per species lost because ongoing biodiversity change causes an increase in the proportional abundance of the highest contributor. By contrast, when the highest contributor to function has the highest extinction probability (high-to-low extinction scenario), the change in MF per species lost is negative, indicating that, as strong contributors are removed, remaining species are unable to compensate for their role. Abundance-based and random extinction scenarios were similar, possibly because species' abundance and functional contributions were unrelated, indicating a weaker role for simple ‘mass-ratio’ effects in MF [11]. Previous work has shown that at low MF thresholds, biodiversity has a positive effect and at high thresholds, the effect is negative [15]. However, these results suggest that this pattern is most prevalent when extinction is random or abundance-based, such that mass-ratio effects have a more prevalent role. Second, extinction order determines the minimum number of species needed to maintain MF across thresholds: more species are consistently needed when extinction probabilities and contributions to MF are positively correlated than when negatively correlated or uncorrelated (figure 3). This supports and extends previous work based on single functions indicating that positive correlations between extinction probabilities and functional contributions increase the probability of losing MF to biodiversity change (or ecosystem vulnerability; sensu [8]). Finally, although higher levels of MF can be achieved with more pairwise positive correlations among functional contributions, a concomitant positive relationship between extinction probabilities and functional contributions makes MF more sensitive to species loss. In sum, correlations linking species' contributions to MF and extinction probabilities cause a larger decrease in MF resiliency to biodiversity than would be expected from random or abundance-based biodiversity loss.

Complementarity had a strong influence on how MF responded to biodiversity change, primarily by minimizing the importance of positive correlations between extinction probabilities and contributions to MF. As expected and consistent with previous work [16,25], complementarity increased slope values between biodiversity and MF (figure 1) and the probability that high levels of MF could be achieved (figure 4), regardless of extinction mode or correlations among functional contributions. Because the effect of complementarity is directly related to the number of species, and not species identities, complementarity decreased the importance of positive correlations in functional contributions and of any strong contributor to MF. However, with complementarity, maintaining those higher levels of MF required more species (figure 3). This identity-independent effect of complementarity is partially a result of how it was modelled [25]. While in our study complementarity occurred irrespective of species identities and functions, complementarity arises from species interactions related to competition and facilitation, which can depend on a variety of community and ecosystem properties (e.g. functional guilds, type of function, ecosystem context; [2,5,19,32]). These interactions themselves could be correlated with particular traits and thus be dependent on organismal trade-offs. Nevertheless, quantifying complementarity is challenging and few studies have estimated how it varies in nature, although it is potentially critical in shaping the response of MF to biodiversity loss [20].

The correlation between species extinction probabilities and their functional contributions has received considerable attention for its ability to predict the response of ecosystems to realistic biodiversity change scenarios (sometimes predicted by response and effect traits [6,7,33]). Because organismal trade-offs are ubiquitous, this correlation framework has been used to understand how a variety of ecosystems, including freshwaters [12], coral reefs [13], and forests [4], respond to anthropogenic factors, typically in two-dimensional space (i.e. between one environmental driver and one ecosystem function). However, extending this approach to predict the effect of biodiversity change on MF is challenging because MF is influenced by how a species contributes to many functions simultaneously (potentially predicted by multiple effect traits). Defining a species that is a strong contributor to multiple functions can be especially difficult when functional contributions are negatively or uncorrelated. In our simulations, we estimated a species’ multifunctional importance as the average contribution to each individual function. However, other approaches are possible, such as by weighing functions or also using dimension reduction techniques [18,34]. Further, while our models were spatially static, ecosystem context can also affect species functional roles [32,35], and extending our modelling approach to include spatial variation can aid in gaining a landscape-scale perspective on MF. Despite these caveats, our results, in combination with previous work on single functions [7,33], suggest that disentangling how species extinction probabilities and functional contributions correlate in nature can predict the resilience of MF to biodiversity change.

5. Conclusion

In the last decade, biodiversity–ecosystem functioning research has increasingly focused on multiple functions and services finding that, in addition to the role of dominant species (i.e. the selection effect) and complementarity, organismal trade-offs are fundamental to the biodiversity–MF relationship. Current research, however, has been predominately based on experiments in which biodiversity has varied independent of species' traits, an approach that treats extinction as essentially a random process. Random, or trait-independent, extinction, however, does not reflect the majority of mechanisms driving biodiversity change in the Anthropocene [36]. Non-random extinction scenarios based on species’ traits, such as body size in vertebrates [12,13] and wood density in trees [37], have shown that when there are positive correlations between traits that affect extinction probabilities and traits that determine how species contribute to individual functions, the likelihood of systems functioning within long-term norms declines. Here, we extended these principles of trait-based extinction and concomitant impacts on single functions to MF and show that positive correlations between contributions to single functions as well as how these are correlated with extinction probabilities determine how MF responds to biodiversity change. These results indicate that rather than being driven by the presence of negative correlations between functional contributions [15,17,31], the resiliency of MF depends on the absence of positive correlations. Complementarity, if independent of the identities of the interacting species, can minimize the role of positive correlations in determining how biodiversity change affects MF. In sum, this work implies that conserving both specific species as well as biodiversity is critical to minimize the impact of biodiversity loss on MF, especially when species contribute to multiple functions simultaneously.

Data accessibility

While no new data was used in the study, the code to perform the modelling and analysis is included as a supplement.

Authors' contributions

S.A.H., K.A., and A.O. conceived the initial study. S.N. then helped refine the scope. S.A.H. ran the analysis and led the writing of the manuscript. All authors contributed substantially to revisions.

Competing interests

We declare we have no competing interests.

Funding

S.A.H. was supported by a Columbia University's Dean Fellowship and New York Community Trust Edward Prince Goldman Scholarship in Science; A.O. was supported by an Earth Institute Fellowship and NatureNet Science Fellowship.