Evolution of honest reward signal in flowers

Abstract

Some flowering plants signal the abundance of their rewards by changing their flower colour, scent or other floral traits as rewards are depleted. These floral trait changes can be regarded as honest signals of reward states for pollinators. Previous studies have hypothesized that these signals are used to maintain plant-level attractiveness to pollinators, but the evolutionary conditions leading to the development of honest signals have not been well investigated from a theoretical basis. We examined conditions leading to the evolution of honest reward signals in flowers by applying a theoretical model that included pollinator response and signal accuracy. We assumed that pollinators learn floral traits and plant locations in association with reward states and use this information to decide which flowers to visit. While manipulating the level of associative learning, we investigated optimal flower longevity, the proportion of reward and rewardless flowers, and honest- and dishonest-signalling strategies. We found that honest signals are evolutionarily stable only when flowers are visited by pollinators with both high and low learning abilities. These findings imply that behavioural variation in learning within a pollinator community can lead to the evolution of an honest signal even when there is no contribution of rewardless flowers to pollinator attractiveness.

1. Introduction

(a). Pollinator rewards and honest signals in flowers

Through evolution, animal-pollinated plants acquired various floral traits that enhance attractiveness to pollinators, including rewards such as nectar and excess pollen, a showy appearance and the production of scent [1]. The effect of a reward on pollinator attraction is strengthened when pollinators learn the relationship between a given floral trait and its associated reward [2]. Here, we refer to floral traits that can be associatively learned by pollinators as ‘floral signs’. When pollinators associate floral signs with rewards, the floral signs are expected to develop reputations as indicators of reward quality or quantity. These general reputations may also facilitate the emergence of free riders [3] that produce rewardless flowers mimicking the rewarding flowers and ‘freeride’ the benefit of floral sign reputations without rewarding [4].

Despite the obvious advantage of mimicking rewarding flowers, plants often alter floral signs depending on rewarding state. One example is floral colour change; the retention of old, rewardless, but fully turgid flowers with an altered colour [5]. Plants may change their flower colour when nectar production decreases (with or without pollination) and pollinators can distinguish the reward state based on these colour differences [6–8]. Likewise, some plants may change their chemical scent bouquet in relation to nectar volume [9,10]. More obviously, some plants bear coloured or scented nectar [11,12], which also leads to a change in floral sign as the reward decreases.

In these cases, change in floral signs allow pollinators to distinguish between rewarding and rewardless flowers. Therefore, these changes can be regarded as honest signals of the reward state. Hereafter, we refer to these phenomena as ‘honest reward signals’, wherein floral signs change in accordance with the abundance of the reward. Honest signals allow pollinators to avoid visiting rewardless flowers; however, retaining rewardless flowers with honest signals does not appear to offer a benefit to the plant.

One major hypothesis explaining this perplexing scenario is that the retention of sign-changed flowers increases attractiveness to pollinators [6]. Retaining old flowers enlarges the overall display (i.e. the number of open flowers on a plant), and may thereby increase pollinator visitation. But this may come at a cost if repeated pollinator visits to old flowers reduce reproductive success via geitonogamy [6,7]. An optimal explanation may be that honest signals maximize plant visual attractiveness while simultaneously guiding pollinators to younger flowers with high rewards [7]. However, there is evidence that older flowers may provide little to no contribution to pollinator attraction [13–15]. Therefore, our understanding of the benefits of honest flower signals remains unclear.

Additionally, according to signalling theory, honest signals are realized only when dishonest-signalling (i.e. free-riding) is costly; otherwise, the emergence of free riders makes the signal unreliable for receivers [16–18]. This means that for revealing the condition for the evolution of honest flower signal, the cost of dishonest-signalling should be also considered.

(b). Pollinator learning abilities and the evolution of honest signals

To understand the benefits and costs of honest and dishonest signals in flowers, a key factor to consider is the behavioural response of pollinators to both the floral sign and reward state [19]. Pollinator responses may vary based on their learned association with the reward state. Therefore, a pollinator's learning ability is likely to influence the evolution of honest reward signals.

Pollinator learning ability consists of two components [20]. The first is learning to associate rewarding flowers with their floral sign [2,6]. This component allows pollinators to visit rewarding flowers efficiently and may enhance the benefits of signalling for plants. The second is spatial learning, which allows pollinators to avoid plants with rewardless flowers [21,22]. This component will reduce the frequency of pollinator visits to rewardless flowers and may also prevent the development or invasion of free riders. The combination of these two components dictates pollinator responses to floral signs.

Despite the clear importance of pollinator learning on the evolution of honest signals, almost no theoretical trials have been conducted (but it has been discussed in some empirical works, e.g. [20]). Sun et al. [23] found that costly signals are only maintained by rewarding plants when communities contain both rewarding and rewardless species. However, they assumed that the reward state of a given plant is constant and, thus, their results cannot address changes in floral signs and related changes in reward abundance. Belsare et al. [24] demonstrated that floral display size can accurately represent reward state, as a result of coevolution of the investment in display size and reward production. However, this study also did not include change in floral sign over time. Consequently, the influence of pollinator behavioural dynamics on the evolutionary development of honest signals remains unclear.

We aimed to determine the conditions under which honest reward signals are likely to evolve while focusing on pollinator responses to floral signs and associative learning. We considered three traits that could be subject to evolution: (i) the period during which a single flower is maintained; (ii) the proportion of the rewarding and non-reward periods; and (iii) the floral signs during rewarding and rewardless periods. We assumed that pollinators estimate the reward state of a given flower and determine which flowers to visit based on this estimation. The accuracy of this estimation depends on the degree of associative learning with floral sign and location. Based on these assumptions, we constructed a theoretical model and calculated the evolutionary trajectory of floral traits with changing parameter values.

2. Model

(a). Floral traits

First, we explain the floral traits used in this model. Consider a pollinator-dependent plant that produces a constant number of flowers during a floral season. Each flower produces a reward for a period of time (rewarding period) and, after that time, the flower may be maintained without a reward (rewardless period). Let x and y denote the proportion of the rewarding period and the flower longevity, i.e. the lengths of the rewarding and rewardless periods are xy and (1 − x)y, respectively. We considered four signalling strategies of floral signs during rewarding and rewardless periods. Given that we were focused on the evolutionary process of honest signal development, we used an initial state wherein all resident plants used a consistent floral sign, hereafter known as ‘sign A’, in both rewarding and rewardless periods (figure 1a); we refer to this as a ‘sign-consistent’ strategy. Under a sign-consistent scenario, pollinators cannot distinguish between rewarding and rewardless flowers prior to visiting flowers.

Figure 1.

Four signalling strategies. (a) Sign-consistent strategy, which uses the same floral sign (sign A, white) in both the rewarding and rewardless period. This is the strategy of residents at the initial state. (b) Rewarding-signal strategy, which uses sign B (black) during the rewarding period to indicate the existence of a reward. (c) Rewardless-signal strategy, which uses sign B during the rewardless period to indicate the absence of a reward. (d) The use of sign B during both the rewarding and rewardless period is also a sign-consistent strategy.

Plants can help pollinators detect rewards by using an alternative floral sign (sign B) in either the rewarding or rewardless period (figure 1bc). In the former, sign B indicates the presence of a reward, and in the latter, sign B indicates the absence of reward. We refer these strategies as ‘rewarding-signal’ strategy and ‘rewardless-signal’ strategy, respectively. Note that these two strategies are defined based on the comparison with the sign-consistent residents (i.e. consistently using sign A). If a population is filled by either rewarding-signal or rewardless-signal strategies, we cannot distinguish differences without knowing the original floral sign of the residents. Last, we considered a strategy wherein plants use sign B in both the rewarding and rewardless periods (figure 1d). This is a form of a sign-consistent strategy, but we distinguished these two types to investigate their evolutionary stability; then we refer them as ‘consistent strategy with sign A’ or ‘sign B’.

In the following analyses, we represent the plant individual with the proportion of the rewarding period x, flower longevity y and the signalling strategy Z as (x, y, Z), where $Z\in \{C,L,R,C{\hspace{0.17em}}^{\mathrm{\prime }}\}$ and the characters C, L, R and C′ denote the consistent strategy with sign A (i.e. residents at the initial state), a rewardless-signal strategy (change from sign A to sign B), a rewarding-signal strategy (change from sign B to sign A) and a consistent strategy with sign B. We also represent a population with proportions of C, L and R in a population are f_C, f_L, f_R as ($\overline{x}$, $\overline{y}$, f_C, f_L, f_R), where $\overline{x}$ and $\overline{y}$ are the mean proportion of rewarding period and the mean flower longevity in the population.

(b). Pollinator visitation rates

In this subsection, we consider how pollinators change their visitation rate in response to floral traits. We assumed that pollinators cannot distinguish spatial differences between flowers on the same plant individual. After multiple visits, a pollinator should be able to estimate the probability that a focal flower contains a reward based on its floral sign and spatial location. Pollinators with greater learning abilities would more frequently use floral sign and/or spatial location information in their estimations. We assumed that the probabilities that a pollinator can use the information of floral sign (we represent this as α) is independent from that of location (β). The probability of a pollinator using both pieces of information is thus αβ. Hereafter, we call α and β as the ‘usability of floral sign’ and ‘usability of location’. These two usabilities reflect a pollinator's learning ability, but we note that high learning ability may not always realize high usability values. For example, if pollinators frequently forage in novel areas, they will have little opportunity to use learned spatial information and their use for location information will be low regardless of their learning ability.

Pollinators estimate the probability that a flower has a reward (estimated reward probability) based on information gained from a focal flower. To keep our analyses manageable, we assumed that the estimated reward probability is equal to the conditional probability of a reward existing under the provided information, i.e. the probability that a randomly chosen flower has a reward. Therefore, there are four combinations of useable information for estimation: (i) floral sign and location information; (ii) floral sign information only; (iii) location information only; and (iv) no information. We represent the estimated reward probabilities of these four cases as P_αβ,Z,i, P_α,Z,i, P_β,Z,i and P_0,Z,i, respectively, where s is the signalling strategy of the focal flower and i is the rewarding (i = 1) or rewardless (i = 2) period. The estimated reward probabilities of flowers on an individual plant (x, y, Z) within a population ($\overline{x}$,$\overline{y}$, f_C, f_L, f_R) under these four cases becomes

$$\begin{array}{c}{P}_{\alpha \beta ,Z,i}=\{\begin{array}{cc}1& \text{if\hspace{0.17em}}i=1\hspace{0.17em}\text{and}\hspace{0.17em}Z=L\hspace{0.17em}\text{or}\hspace{0.17em}R\\ 0& \text{if\hspace{0.17em}}i=2\hspace{0.17em}\text{and}\hspace{0.17em}Z=L\hspace{0.17em}\text{or}\hspace{0.17em}R\\ x& \text{if}\hspace{0.17em}Z=C\hspace{0.17em}\text{or}\hspace{0.17em}{C}^{\mathrm{\prime }}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\end{array}\end{array},$$ 2.1a

$$\begin{array}{c}{P}_{\alpha ,Z,i}=\{\begin{array}{cc}\frac{(\hspace{0.17em}{f}_C+f_L)\overline{x}}{\hspace{0.17em}{f}_C+f_R(1-\overline{x})+f_L\overline{x}}& \text{if\hspace{0.17em}}Z=C\hspace{0.17em}\text{or}\hspace{0.17em}(Z=L\wedge i=1)\hspace{0.17em}\mathrm{or}\hspace{0.17em}(Z=R\wedge i=2)\\ \frac{(\hspace{0.17em}{f}_{C^{\mathrm{\prime }}}+f_R)\overline{x}}{\hspace{0.17em}{f}_{C^{\mathrm{\prime }}}+f_R\overline{x}+f_L(1-\overline{x})}& \text{if}Z=C^{\mathrm{\prime }}\hspace{0.17em}\text{or}\hspace{0.17em}(Z=L\wedge i=2)\hspace{0.17em}\mathrm{or}\hspace{0.17em}(Z=R\wedge i=1)\end{array}\end{array},$$ 2.1b

$$\begin{array}{c}{P}_{\beta ,Z,i}=x\end{array},$$ 2.1c

$$\begin{array}{c}\text{and}{P}_{0,Z,i}=\overline{x}\end{array}$$ 2.1d

(see electronic supplementary material, appendix S1.1 for derivation details).

Because whether pollinators can use floral sign and/or location information depends on α and β, the mean estimated reward probability is derived from the average of P_αβ,Z,i, P_α,Z,i, P_β,Z,i and P_0,Z,I and weighted by α and β:

$$E_i(x,Z|\overline{x},f_C,f_R,f_L)=\alpha [\beta P_{\alpha \beta ,Z,i}+(1-\beta )P_{\alpha ,Z,i}]\begin{array}{c}+\hfill \end{array}(1-\alpha )[\beta P_{\beta ,Z,i}+(1-\beta )P_{0,Z,i}],$$ 2.2

where i indicates the rewarding (i = 1) or rewardless period (i = 2). Note that the estimated reward probability is independent of the flower longevity of mutants and residents, y and $\overline{y}$, respectively. We assumed that pollinators randomly choose a flower on each visit based on the mean estimated reward probabilities of flowers within the population. The visitation rate to a focal flower is

$$\begin{array}{c}{V}_i(x,y,Z|\overline{x},\overline{y},f_C,f_R,f_L)=\hfill \\ \lambda \frac{E_i{(x,Z|\overline{x},f_C,f_R,f_L)}^{\gamma }}{{\sum }_{Z^{\mathrm{\prime }}=\{C,R,L,C^{\mathrm{\prime }}\}}\{\overline{x}\overline{y}{E}_1{(\overline{x},Z^{\mathrm{\prime }}|\overline{x},f_C,f_R,f_L)}^{\gamma }+(1-\overline{x})\overline{y}{E}_2{(\overline{x},Z^{\mathrm{\prime }}|\overline{x},f_C,f_R,f_L)}^{\gamma }\}}\hfill \end{array}$$ 2.3

where λ determines the visitation rate. The coefficient γ determines the influence of the estimated reward probability on flower choice; at γ = 0, estimated reward probabilities have no influence on flower choice, and at γ = 1, the visitation rate to a focal flower increases linearly with its estimated reward probability.

(c). Plant fitness

In this subsection, we define the plant fitness depending on the pollinator visits and floral traits. Consider that focal plant populations are pollinated by M types of pollinators, each of which can have different usability (α, β) or visitation rate (V) values. The total number of pollinator visits to a focal flower is therefore

$$\begin{array}{c}N(x,y,Z|\overline{x},\overline{y},f_C,f_R,f_L)=\hfill \\ \sum _{m=1}^M\{xy{V}_{m,1}(x,y,Z|\overline{x},\overline{y},f_C,f_R,f_L)+(1-x)y{V}_{m,2}(x,y,Z|\overline{x},\overline{y},f_C,f_R,f_L)\}\hspace{0.17em}\hfill \end{array},$$ 2.4

where V_m,1 and V_m,2 are the visitation rates (i.e. equation (2.3)) of the m-th pollinator species during rewarding and rewardless periods, respectively. We assumed that reproductive success increases with the total number of pollinator visits (N), following a saturating function. Plants should pay the cost of reward production and flower maintenance, which are assumed to increase linearly with the length of the rewarding period (xy) and flower longevity (y), respectively. The contribution on the fitness of a focal flower (x, y, Z) within a monomorphic population ($\overline{x}$,$\overline{y}$, f_C, f_L, f_R) is therefore

$$\begin{array}{c}W(x,y,Z|\overline{x},\overline{y},f_C,f_R,f_L)=\frac{N(x,y,Z|\overline{x},\overline{y},f_C,f_R,f_L)}{N(x,y,Z|\overline{x},\overline{y},f_C,f_R,f_L)+\kappa }-\rho xy-\sigma y\hfill \end{array},$$ 2.5

where κ determines the slope of saturation curve between reproductive success and pollinator visitation, and ρ and σ are coefficients of the cost of reward production and flower maintenance, respectively. We assumed that the plant produces constant numbers of flowers regardless of its strategy; then the plant fitness is proportional to equation (2.5).

We assumed that quantitative genes for flower longevity and the proportion of the rewarding period are well mixed within the population by outcrossing. Given this, we can assume that residents have the same flower longevity $(\overline{y})$ and rewarding period proportion $(\overline{x})$ regardless of their signalling strategies. We also assumed that a mutation in signalling strategy is rare enough that the appearance of a mutant with an alternative signalling strategy would occur after the evolution of flower longevity and rewarding period proportion reach a stable state. Following these assumptions and the adaptive dynamics theory [25,26], we investigated (i) the evolutionary outcome of a single invasion of a mutant with an honest signal (i.e. a rewarding-signal or rewardless-signal strategy) into a sign-consistent resident population, and (ii) the evolutionarily stable state under multiple invasions of mutants with the four possible signalling strategies (see the electronic supplementary material, appendices S1.2 and S1.3 for further details).

3. Results

We investigated the evolution of honest reward signals by examining the possibility of invasion of a mutant with an honest signal into a sign-consistent population and its subsequent evolutionary stability (electronic supplementary material, appendix S1.3). Because the invasion of different signalling strategies can also change the optimal rewarding period proportion (x) and flower longevity (y), we note that these analyses also included the evolutionary dynamics of x and y.

(a). Evolution of reward signals when pollinator usability is homogeneous

First, we focused on the scenario where pollinators are homogeneous, i.e. all pollinators have the same usability (M = 1). Figure 2a,b shows the outcomes of an invasion of a rare mutant with a rewarding- and rewardless-signal strategy, respectively, into a sign-consistent population by changing the degree of usabilities, α and β (figure 2a,b). Rewarding-signal mutants can invade a population when pollinators have low location usability (grey area in figure 2a), while rewardless-signal mutants cannot invade, regardless of usability (figure 2b).

Figure 2.

Evolutionary outcomes following a single invasion of rewarding-signal strategy (a) and rewardless-signal strategy (b), and the evolutionarily stable state under multiple invasions (c) when the pollinator community is homogeneous. The x- and y-axes show the usability of floral signs (α) and locations (β), respectively. In (a,b), colours represent the result of an invasion of a mutant with an honest signal into a resident sign-consistent population, i.e. failure to invade (white) or replacement of sign-consistent residents (dark grey). Contour curves show the proportion of the rewarding period (x) for each outcome. Hatched regions indicate that plants do not maintain rewardless flowers (i.e. x = 1). In (c), colours indicate the evolutionarily stable state, i.e. plants do not maintain rewardless flowers (hatched), or there is no evolutionarily stable state and the sign-consistent strategy and rewarding-signal strategy alternately emerge (black, see the electronic supplementary material, appendix S2 in detail). Parameter values are γ = 2, λ = 64, κ = 1, ρ = 0.1, σ = 0.02.

This qualitative difference between the rewardless- and rewarding-signal strategies is caused by the difference of the difficulties among pollinators in detecting rewarding flowers. Rewarding-signal mutants display rewarding flowers using a new floral sign (sign B), allowing pollinators to distinguish rewarding flowers easily. Unless pollinators cannot use the information of floral sign at all (α = 0), mutants would receive more pollinator visits than residents. By contrast, when mutants have a rewardless-signal strategy, pollinators cannot distinguish rewarding flowers using floral signs (sign A) because sign-consistent residents use the same floral sign. Rewardless-signal mutants may encourage revisits if pollinators can learn the locations of honest plants (i.e. high α and high β). However, under this scenario, the maintenance of rewardless flowers becomes maladaptive because pollinators can avoid plants producing rewardless flowers. This logic further explains why the rewarding-signal cannot invade when pollinators have high location usability (see white-hatched areas in figure 2a). Consequently, rewardless-signal strategy cannot invade into a sign-consistent population, regardless of the pollinators' usability.

When pollinators have low location usability, rewarding-signal mutants can successfully invade and replace the resident population (grey areas in figure 2a). However, in most cases, as a result of the evolution of flower longevity and rewarding period proportion, plants should eventually cease to maintain their rewardless flowers (grey-hatched areas in figure 2a), excluding when pollinators lack floral sign and location information (see lower-left region in figure 2a). Moreover, even if the rewarding-signal strategy became established, it eventually became evolutionally unstable under multiple invasions of mutants (figure 2c). Populations with rewarding-signal residents could be invaded and replaced by sign-consistent mutants with sign B (figure 1d), because mutants can attract more pollinators by free-riding on the reputation of rewarding sign B. However, once free riders form the population, the population effectively returns to a sign-consistent strategy. The established sign-consistent population is then invaded and replaced by a rewarding-signal strategy with another floral sign (sign C). Consequently, the population is alternately filled by a rewarding-signal strategy and a sign-consistent strategy and, thus, there is no evolutionarily stable state under multiple invasions of mutants (black areas in figure 2c; electronic supplementary material, appendix S2 for further details).

According to numerical analyses with varied parameter values, the coexistence of an honest signal and the sign-consistent strategy can be evolutionary stable under extremely limited conditions (electronic supplementary material, appendix S3.3). Furthermore, we could not find a parameter set wherein the honest signal strategy filled the population, which indicates that the evolution of honest signals rarely occurs when pollinator's usability is homogeneous.

(b). Evolution of reward signals when pollinator usability is heterogeneous

Next, we considered a scenario where the pollinator community contains two pollinator types (M = 2). In this analysis, we assumed that one type of pollinator was less informed, which we defined as pollinators that do not use floral sign or location information (α = β = 0). Following the approach illustrated in figure 2, we investigated the evolutionary outcomes after a single invasion of rewarding-signal strategy (figure 3a), rewardless-signal strategy (figure 3b) and the evolutionarily stable state under multiple invasions (figure 3c). Rewarding-signal mutants can invade and replace sign-consistent residents under a wider range of parameters than in a homogeneous pollinator community (figure 3a). In most cases, plants maintained both rewarding and rewardless flowers (figure 3a). Moreover, in contrast with the homogeneous pollinator scenario, the rewardless-signal strategy can invade and replace the resident population when one pollinator has high usability of both floral sign and location (i.e. is well informed) (dark grey area in figure 3b). Plants with a sign-consistent strategy and a rewardless-signal strategy can coexist when location usability is relatively small (light grey area in figure 3b).

Figure 3.

Evolutionary outcomes following a single invasion of rewarding-signal strategy (a) and rewardless-signal strategy (b), and the evolutionarily stable state under multiple invasions (c) when a pollinator community is heterogeneous. The x- and y-axes show the usability of the first pollinator type (i.e. α₁ and β₁), and those of second pollinator types are fixed at α₂ = β₂ = 0, respectively. In (a,b), the light grey colour indicates that mutants invade and coexist with residents. The meaning of other colours, contour curves and hatched areas follow the descriptions provided in figure 2. In (c), colours indicate the evolutionarily stable state, i.e. plants do not maintain rewardless flowers (hatched), the honest signal is evolutionarily stable (dark grey), the coexistence of sign-consistent and rewardless-signal strategies is evolutionarily stable (light grey) or there is no evolutionarily stable state and sign-consistent and rewarding-signal strategies alternately emerge (black). Parameter values were γ₁ = γ₂ = 2, λ₁ = λ₂ = 32, κ = 1, ρ = 0.1, σ = 0.02.

Considering the scenario of multiple mutant invasions with all possible signalling strategies, both the rewardless- and rewarding-signal strategies become evolutionarily stable when one pollinator is well informed (dark grey area in figure 3c). The consistent strategy with sign A and the rewardless-signal strategy, or the consistent strategy with sign B and the rewarding-signal strategy, can coexist when location usability is relatively low (light grey area in figure 3c). We investigated all possible combinations of the usability of the two pollinators and found that the honest signal could only evolve when one pollinator is less informed and the other is well informed (electronic supplementary material, appendix S3.4). This tendency is robust even if we choose different parameter values (electronic supplementary material, appendix S3.4).

The evolution of an honest signal only occurs when pollinators are sensitive to differences in estimated reward probability when determining their visitation rate (i.e. a large γ, figure 4). The honest signal could be evolutionary stable as long as the proportion of the contribution of less-informed pollinators is higher than a threshold level (horizontal axis of figure 4). This implies that an honest signal can evolve even when pollinators with low usability make only a small contribution to plant reproductive success.

Figure 4.

Influence of the fraction of well-informed pollinators (horizontal axis) and the importance of reward probability for the visitation rate (vertical axis) on the evolutionarily stable state when a pollinator community contains well- and less-informed pollinators (i.e. α₁ = β₁ = 1, α₂ = β₂ = 0). Coloured areas follow the description provided for figure 3c. Parameter values were γ₁ = γ₂ = γ (vertical axis). The horizontal axis shows the fraction of sp1 (i.e. λ₁/(λ₁ + λ₂) with keeping λ₁ + λ₂ = 64). Other parameter values follow that of figure 3.

These results indicate that heterogeneity in usability within the pollinator community is important for the evolution of an honest signal. For an honest signal to be evolutionarily stable, invasion by free-riding mutants must be prevented. This can only be achieved when pollinators can distinguish between the flowers of honest plants and free riders. Thus, for plants to be honest, they must be visited by well-informed pollinators. However, visitation by well-informed pollinators is insufficient to maintain rewardless flowers, because rewardless flowers with honest signals are avoided and thus offer no benefit if the community comprises entirely well-informed pollinators. The condition wherein the retention of rewardless flowers is advantageous is when less-informed pollinators contribute to pollination through visiting rewardless flowers. Given that less-informed pollinators do not recognize honest signals, rewardless flowers (regardless of their signalling strategy) increase the total number of pollinator visits without inflicting costs associating reward production. Therefore, heterogeneity in pollinator usability can lead to the evolution of an honest signal in plants.

We also considered models based on alternative assumptions about (i) the difference in reproductive success from male and female functions, and (ii) the cost of geitonogamous pollination, but the general tendency was not changed by these factors (see the electronic supplementary material, appendix S4 for the details).

4. Discussion

(a). Variation in usability within the pollinator community promotes the evolution of an honest signal

Plant species sometimes exhibit dynamic changes in floral colour or smell, which occur in correlation with a reduction of pollinator rewards [5,9,10]. These floral sign changes appear in various angiosperm groups and are thought to assist pollinators in selecting rewarding flowers [5,27,28], although no research has clearly elucidated the evolutionary conditions leading to sign-changing flowers. Our results indicate that an honest reward signal is a strategy to increase visitation by less-informed pollinators but keep the good reputation of rewarding flowers for well-informed pollinators (figure 3c). Although this may appear paradoxical, the benefit of an honest signal lies in deceiving less-informed pollinators into carrying pollen without a reward. This is a new perspective on honest reward signals in plants and provides a novel hypothesis to explain the evolution of sign change in flowers.

In our model, one important condition for the evolution of honest signal is the existence of both well- and less-informed pollinators (figure 3). Under natural conditions, a pollinator community would be likely to include both types of pollinator. The usability of floral signs obviously varies among pollinator taxonomic groups, given the differences in visual and olfactory systems [29–31] and flexibilities in colour or odour preferences owing to associative learning with rewards [32–34]. Likewise, the usability of plant locations varies among pollinator groups. There is ample evidence that eusocial bees and birds frequently use individual plant-level spatial memory to locate rewarding plants [35,36]. Individual bees are known to vary in their ability to use floral signs and locations. For example, more experienced foragers can often efficiently choose rewarding flowers based on their memory of floral signs and locations, whereas inexperienced foragers choose conspicuous plants irrespective of reward value [20,22]. Therefore, bee foraging sites often include both experienced and inexperienced foragers [35,37] and we suggest that this could facilitate the evolution of honest floral signals.

Plant species with sign-changing flowers are often visited by pollinator groups known for their high abilities in both sign-reward associative learning and spatial learning (e.g. eusocial bees or birds) and by other animal orders or families (electronic supplementary material, appendix S5). Ohashi et al. [28] show that plant species with colour-changing flowers tend to bloom when bees appear in visitor fauna. These tendencies suggest the association between honest-signalling plants and behavioural variation of pollinators. Furthermore, behavioural experiments using bumblebees showed that plants with a rewardless-signal strategy, as described in our model (figure 1c), tend to receive more visits than those with a sign-consistent signal strategy or those that only maintain rewarding flowers. This is because the rewardless-signal strategy receives revisits by experienced bees and occasional visits by inexperienced ones [20]. These experiments support our conclusions that the honest signal strategy increases total visits by attracting both well- and less-informed pollinators.

(b). Benefits of retaining rewardless and sign-changed flowers

Previously, the honest reward signal in flowers has been mainly explained with relevance to the floral display size. Retaining rewardless flowers increases the number of open flowers on the plant, and such a larger display can often increase pollinator visits per plant (e.g. [6,7,38]). Reducing reward with sign change may help to suppress the costs associated with large display [15], such as geitonogamous pollination [39,40]. However, it is reported that the increase in visitation rate decelerates with floral display size [41] and seems to disappear in large plants (e.g. floral colour-changing trees: [15]). The display effect is often not observed even in colour-changing flowers [13–15]. These imply the limitation to explain the honest signal only by the display effect.

On the other hand, our model shows another benefit of retaining rewardless and sign-changed flowers, i.e. deceiving less-informed pollinators into carrying pollen without a reward. This means that the coexistence of the occasional visitors and well-informed pollinators might explain the evolution of honest signal without assuming a display size effect. Importantly, the explanations found in previous studies and our hypothesis are not mutually exclusive. Both an increase in display size and the benefit of occasional visitation could contribute to the evolution of an honest signal.

To evaluate the relative influence of these two factors, we need a theoretical model with further details of the pollination processes. For example, because the display size effect and its cost (e.g. geitonogamous pollination) depends on how the pollinators move between flowers on the same plant and between plants, the model should explicitly consider the pollinator visitation patterns among flowers for determining the effect of display size. Too biased visitation patterns often lead the non-random mating, which might cause different predictions from our results, like evolutionary branching or speciation [42,43] (but see the electronic supplementary material, appendix S3.2). Further analyses of the model including the pollen dynamics like the removal rate from stamens or the origin of the pollen on the stigma is important for deeper understanding of the evolutionary backgrounds of honest rewarding signal.

(c). Evolutionary dynamics caused by free-rider invasion

We showed that the evolution of signalling strategy often causes a situation where the plant population can be alternately invaded by reward-signalling plants and associated free riders (black areas in figures 2c and 3c), which leads to change in floral signs at the population level. This means that each invasion of a rewarding-signal strategy with a new floral sign will change the floral sign of the population, generating diversity in floral signs (e.g. sign C, D, E, etc.) without a shift in pollinators. This novel finding may help to explain diversity in flower evolution that cannot be explained by pollinator shifts. Closely related species are often pollinated by similar animal groups but display different floral traits, such as petal colour [44]. In some plant lineages, including floral colour-changing species, non-colour-changing congeners display different floral colours and appear to receive visits by similar insect groups [28]. Our model suggests that these examples may be the result of invasions of honest signals and replacement by free riders without a pollinator shift, although we need to consider other possible factors and their cumulative effects on the evolution of floral colours or scents [44].

The free-riding strategy might not be possible for some floral traits. For example, when plants use coloured or scented nectar as the signal, it is difficult to convey a reward sign during the rewardless period [11,12,45]. In such cases, free riders of coloured or scented nectar will not emerge and, therefore, these honest reward signals would be evolutionarily stable only when the honest signals invade a sign-consistent resident population (i.e. grey areas in figures 2a and 3a). In other words, when plants cannot ‘lie’ about the existence of reward, the condition that an honest signal is evolutionarily stable is relaxed; variation in pollinator learning abilities or the existence of well-informed pollinators are not necessary. This prediction might be supported by the well-known coloured nectar examples of the Mauritian Nesocodon mauritianus and two Trochetia species, which are solely pollinated by a single gecko species [46,47].

5. Conclusion

Our study explains that honest reward signal can evolve to adapt to efficient pollinators while retaining the benefit of attracting occasional visitors. We showed that the existence of occasional visits by less-informed pollinators can dramatically change the evolution of floral traits, even when their contribution is smaller than that of well-informed pollinators (figure 4). Although many studies in pollination ecology have only focused on so-called primary pollinators (but see [48]), our study suggests a crucial role for others, seemingly less important pollinators. Our results suggest that it is important not to oversimplify the evolutionary dynamics between flowers and floral visitors by studying what appears to be only the important subsets of them. Our study also revealed the importance of the pollinators’ usabilities, i.e. how sensitively pollinators respond to the location and floral signs learned associated with rewards. Because we evaluated the usabilities from the realized pollinator visits instead of the degree of learning, the pollinators’ usabilities could be also affected by various ecological factors (e.g. plant density: [49], landmarks for pollinators: [50], competitors: [51], predators: [52]). This suggests that even when pollinator fauna are similar, environmental conditions can lead to variation in usability, which then leads to different selective pressures on floral traits. Although many pollination ecology studies have focused only on taxonomic groups of pollinators, our study suggests that behavioural diversity in pollinators can change the evolutionary dynamics of floral traits, especially of signalling strategies.

Data accessibility

The source code of the simulation program used in this study has been uploaded at Zenodo doi: 10.5281/zenodo.4387285.

Authors' contributions

K.I. conceived and designed the study, carried out the model analyses and numerical calculations, and drafted the manuscript. M.F.S. participated in the design of the study, M.F.S. and K.M. aided in interpreting the results and co-wrote the manuscript. All authors gave final approval for publication and agree to be held accountable for the work performed therein.

Competing interests

The authors declare no competing interests.

Funding

This study was supported by JSPS Oversea Research Fellowship (201960610) to K.I., Grant-in-Aid for Research Activity start-up (19K21198) to K.M. and Grant-in-Aid for JSPS fellows (no. 13J00371) to M.F.S.