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Predation drives complex eco-evolutionary dynamics in sexually selected traits [1]

['Brian A. Lerch', 'Department Of Biology', 'University Of North Carolina At Chapel Hill', 'Chapel Hill', 'North Carolina', 'United States Of America', 'Maria R. Servedio']

Date: 2023-04

Predation plays a role in preventing the evolution of ever more complicated sexual displays, because such displays often increase an individual’s predation risk. Sexual selection theory, however, omits a key feature of predation in modeling costs to sexually selected traits: Predation is density dependent. As a result of this density dependence, predator–prey dynamics should feed back into the evolution of sexual displays, which, in turn, feeds back into predator–prey dynamics. Here, we develop both population and quantitative genetic models of sexual selection that explicitly link the evolution of sexual displays with predator–prey dynamics. Our primary result is that predation can drive eco-evolutionary cycles in sexually selected traits. We also show that mechanistically modeling the cost to sexual displays as predation leads to novel outcomes such as the maintenance of polymorphism in sexual displays and alters ecological dynamics by muting prey cycles. These results suggest predation as a potential mechanism to maintain variation in sexual displays and underscore that short-term studies of sexual display evolution may not accurately predict long-run dynamics. Further, they demonstrate that a common verbal model (that predation limits sexual displays) with widespread empirical support can result in unappreciated, complex dynamics due to the density-dependent nature of predation.

Here, we develop eco-evolutionary models of sexual selection that explicitly treat the cost to expressing a display as increasing predation risk. To best connect our results to both the evolutionary and ecological literature, we develop (1) a model that maximizes ecological realism and aligns with literature on eco-evolutionary feedbacks in predator–prey systems using a continuous-time, quantitative genetic framework and (2) a model that maximizes genetic realism and aligns with important contributions in the sexual selection literature using a discrete-time, population genetic framework. The essential features of both approaches are that they track prey density, predator density, and a sexual display that males may express to increase their attractiveness to females, but which puts them at higher risk of predation. We show that sexual selection qualitatively alters population dynamics and that predator–prey dynamics, in turn, generate novel evolutionary outcomes, demonstrating that rich eco-evolutionary dynamics can result from sexual selection.

Mechanistically modeling interactions between predation and sexual selection is of particular importance because evolution may occur on ecological timescales [ 43 – 47 ], with the resulting interplay between changes in population density and trait evolution driving eco-evolutionary feedbacks (wherein evolution alters population dynamics, which, in turn, alter evolution [ 48 – 52 ]). Sexually selected traits can evolve on ecological timescales [ 53 – 58 ], but few studies have considered the effects of eco-evolutionary dynamics on such traits [ 59 , 60 ]. In competitive systems, rapid evolution via sexual selection may facilitate coexistence [ 61 ]. In predator–prey systems, eco-evolutionary feedbacks have been demonstrated empirically [ 62 – 68 ], although there is no direct evidence for eco-evolutionary feedbacks affecting sexually selected traits in these systems. However, the strong influence of displays on predation risk (which, e.g., doubles in Trinidadian guppies [ 7 ]; Poecilia reticulata) suggests that sexual displays may also have a strong influence on predator populations. In general, prey evolution can either drive or dampen predator–prey cycles [ 69 – 73 ]. However, previous work tends to model predation risk trading off with growth [ 69 , 70 , 74 ] or competitive ability [ 71 ], with different trade-offs leading to qualitatively different outcomes [ 75 – 77 ]. The empirically justified mechanism of a sexually selected benefit to a display trait differs from previously explored trade-offs because there is not necessarily an ecological benefit to expressing a sexual display.

From an ecological perspective, important consequences of evolution in predator–prey systems are well known. For example, optimal foraging behavior may shape functional responses (how predation rate changes with prey density) [ 22 – 24 ] and coevolution helps structure predator–prey communities [ 25 – 28 ]. Sexual behavior can be important for ecological dynamics through interactions with predation [ 29 , 30 ] and by mediating population growth [ 31 – 35 ] and extinction risk [ 36 – 42 ].

Widespread evidence suggests that sexual displays used to attract mates often increase an individual’s risk of being predated [ 1 – 11 ]. Such costs inhibit the evolution of sexual displays across various sensory modalities in taxa ranging from fish to frogs to insects [ 12 – 17 ]. Despite empirical evidence that predation serves as a major constraint on the evolution of sexual displays, theoretical models of sexual selection that mechanistically model predation as the source of natural selection have not been developed. Rather, past models treat costs of expressing sexual displays phenomenologically, assuming fixed population densities and frequency-independent selection against the display [ 18 , 19 ]. These assumptions are incompatible with predation being the cost to expressing displays because predation is density dependent, and thus, viability selection against sexual displays should also be density dependent. Density-dependent selection against sexual displays could explain the maintenance of genetic variation in display traits despite persistent positive sexual selection through female choice (the “lek paradox”) [ 20 , 21 ], especially if natural selection fluctuates in strength due to coupling with predator–prey cycles.

Results

Our primary result (regardless of model details; see Methods) is that predation can drive complex evolutionary dynamics in sexual displays (Fig 1). We see endogenous cycles previously undescribed in comparable models of sexual selection. When predator density is low, viability selection is relaxed so both prey density and display frequency increase. Once this occurs, predator density also increases, thus driving a decline in prey density and strengthening selection against the display trait, decreasing its frequency. This general pattern occurs in both the discrete and continuous model (Fig 1).

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TIFF original image Download: Fig 1. Eco-evolutionary cycles of predator–prey systems coupled with sexual selection. (a-d, f) show population density and trait frequency/value through time (see legend). (a) Continuous model with high amplitude eco-evolutionary cycles: prey growth rate r c = 2, handling time t h = 1, display-dependent predation cost s c = 10, basal predation rate b c = 5, preference strength a c = 5, conversion efficiency c c = 0.1, predator mortality rate m = 0.05, prey genetic variation σ = 0.1. (b) Continuous model with eco-evolutionary cycles showing long lag in the display cycle: r c = 3, t h = 0.75, s c = 5, b c = 8, a c = 10, c c = 0.1, m = 0.1, σ = 0.1. (c) Discrete model with high period eco-evolutionary cycles: r d = 4, s d = 15, b d = 15, a d = 1.05, c d = 0.1. (d) Discrete model with low amplitude, low period, eco-evolutionary cycles: r d = 5, s d = 5, b d = 20, a d = 1.25, c d = 0.1. (e) Comparison between predator–prey cycles with (orange) and without (gray) evolution (see Methods for model details) in the discrete model. Parameters same as (d). (f) Eco-evolutionary cycles in the Fisher process model: r d = 4, s d = 4, b d = 10, a d = 2, c d = 0.1. This Figure can be generated using S1 Code. https://doi.org/10.1371/journal.pbio.3002059.g001

Feedbacks inherent to predator–prey dynamics are essential in the generation of evolutionary cycles in sexual displays. Without explicitly including population dynamics, evolutionary cycles are never observed (Fig 2, right column). Furthermore, stable polymorphism in the sexual display can occur in the discrete model; such polymorphism relies upon the density-dependent nature of predation and thus requires population dynamics (Fig 2D–2F). Clearly, ecology can have important influences on sexual selection, leading to qualitatively distinct outcomes. Evolving sexual displays also alter predator–prey dynamics. Overall, evolution tends to decrease the amplitude of prey cycles and the range over which they occur (Figs 1E and S1), since prey can evolve to decrease their predation risk in response to increased predation by muting their displays. It can be further shown that rather than eco-evolutionary feedbacks per se, the most important role of eco-evolutionary dynamics is to determine emergent long-run trait values/densities. That is, choosing fixed, arbitrary long-run values for predator and prey densities or for evolutionary traits, and considering only the evolutionary or ecological submodels, respectively, results in dramatically different qualitative dynamics than considering the full eco-evolutionary model (compare S1 Fig to Fig 2).

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TIFF original image Download: Fig 2. The role of eco-evolutionary dynamics as a function of preference strength and predation cost. Comparing to S1 Fig demonstrates the importance of eco-evolutionary dynamics in setting long-run density and trait values if one were to consider either model in isolation. (a–c) The continuous model with r c = 2, b c = 5, σ = 0.1, c c = 0.1, m = 0.1, t h = 0.5. (a) Equilibrium outcomes from the full, eco-evolutionary model. (b) Outcomes with only predator–prey dynamics. (c) Outcomes with only sexual selection. Green indicates that the sexual display is lost. Gray indicates that a stable equilibrium is reached. For (a, b), gray contours correspond to equilibrium male prey density N m * (see legend). For (c), gray contours correspond to the mean display trait value at equilibrium (compare to Fig 3). Yellow-orange indicates sustained cycles, with the shading giving the amplitude of the male prey’s cycle (see legend), which correlates with period and the amplitude cycles in all other variables (S2 Fig). Note that, although subtle, cycles in the purely ecological model are higher amplitude (lighter shading). (d–f) The discrete model with r d = 5, b d = 15, c d = 0.1. (d) Equilibrium outcomes from the full, eco-evolutionary model. Purple indicates the sexual display fixes and predators go extinct. Blue indicates the sexual display fixes and predators persist. Orange indicates variation is maintained in the sexual display. White indicates extinction. Solid regions correspond to reaching a stable equilibrium, striped regions indicate sustained cycles. (e) Outcomes with only predator–prey dynamics (blue means the predator persists). (f) Outcomes with only display evolution (blue means the display fixes). That (b) is much more similar to (a) (and e to d) than is true in S1 Fig indicates that ecological interactions are altered in the full eco-evolutionary model due to the way that densities and trait values are set, not just due to eco-evolutionary feedbacks per se. In contrast, that (c) is comparably different from (a) as in S1 Fig indicates that eco-evolutionary feedbacks per se are also responsible for altering evolutionary outcomes. This Figure can be generated using S1 Code. https://doi.org/10.1371/journal.pbio.3002059.g002

In the continuous model, fluctuations in the relative strengths of natural and sexual selection are enhanced by both display-based predation costs s c and preference strengths a c being large, thus making sustained eco-evolutionary cycles more likely (Fig 3). As expected with predator–prey cycles, faster saturation of predation with prey density (higher t h ) makes predators most efficient when prey are rare (and least efficient when they are common), leading to more frequent and exaggerated cycles (Fig 3). Low predator death rate m means that predator density responds slowly to decreasing predation rate, also making cycles more likely and exaggerated (Fig 3). The amplitude of cycles is greatest with high display costs s c but is relatively insensitive to preference strength (Fig 3). In ecological models, the lag from prey peak to predator peak is shorter than one-quarter of the period length [78]. With an evolving, sexually selected trait, however, we find the lag is longer (typically between one-quarter and one-half the period length; S2E Fig), but not as long as reversed cycles (predator-led) that occur in other evolving predator–prey systems [63,79,80]. When cycles do not occur in the continuous model, prey and predators often coexist at a stable equilibrium. In this case, increasing the cost of a display (s c ) and decreasing the preference strength (a c ) decrease the mean display trait value at equilibrium (gray, Fig 3). While increasing the basal predation rate b c results in more of parameter space with eco-evolutionary cycles, prey growth rate r c and genetic variation σ do not have a large effect on equilibrium outcomes (S3 Fig).

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TIFF original image Download: Fig 3. Eco-evolutionary outcomes from the continuous model. Horizontal axis is display-based predation cost s c , and vertical axis is preference strength a c . Each panel represents a different predator death rate m or handing time t h . Regions have the same meaning as Fig 2, except in grayscale regions, lighter colors correspond to higher display trait value at equilibrium and in dark green-yellow-orange regions dark green and yellow colors correspond to higher amplitude of cycles in the display trait (which correlates to period and the amplitude of cycles in other state variables; S2 Fig). Note that the trait is lost and cycles are purely ecological in the bottom right, rust-colored region of (b). r c = 2, b c = 5, σ = 0.1, c c = 0.1. This Figure can be generated using S1 Code. https://doi.org/10.1371/journal.pbio.3002059.g003

Eco-evolutionary models of predator–prey systems typically lack detail regarding genetic architecture and covariance even though their dynamics depend critically on genetic parameters [73,75,81–83]. Our discrete model assesses the importance of explicit genetic detail and allows genetic variation to change naturally with time. In the discrete model, eco-evolutionary cycles neighbor a region where polymorphism is maintained in the sexual display (Fig 4; solid orange) and are only observed when the display-dependent predation cost s d is much larger than the preference strength a d (Fig 4; striped orange). This occurs because a high display-based predation cost s d strongly couples high predator density to a decrease in display frequency. Again, we find that higher amplitude eco-evolutionary cycles occur when the cost of displays is stronger, though now low preference strength also leads to larger cycles (S4 Fig). Once preference strength becomes too strong or the predation cost too weak, the sexual display goes to fixation (purple and blue, Fig 4). As the display-based predation cost s d increases, predation rate increases, causing transitions from predator extinction with prey sexual display fixed (when the basal predation rate alone is too low for predator persistence) to either a stable equilibrium of both predators and prey with the sexual display fixed or maintained variation in the display trait with eco-evolutionary cycles, depending on the preference strength a d . If the predation cost is too large, both species go extinct. Prey extinction at high predation cost s d corresponds to evolutionary suicide: If not for the evolution of the sexual display, the prey would not suffer from the predation cost and thus could persist. Sexual selection has been discussed as a driver of evolutionary suicide [37], a result supported in the ostracod fossil record [41,42]; these results add predation as a mechanism by which female choice can drive populations extinct in models [84].

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TIFF original image Download: Fig 4. Eco-evolutionary outcomes from the discrete model. Horizontal axis is display-based predation cost s d , and vertical axis is preference strength a d . Each panel represents a different basal predation rate b d and prey growth rate r d . Colors and stripes have the same meaning as in Fig 2. Striped blue and green indicates only ecological cycles, whereas striped orange corresponds to eco-evolutionary cycles. White regions indicate that density becomes negative (which we interpret as extinction). If the model did remain well behaved, we believe that this region would mostly consist of eco-evolutionary cycles; however, the cycle amplitude is too large and negative densities result. The dashed black vertical line seen in some panels is the display-based predation cost below, which predator extinction is stable (thus, regions of blue or orange to the left of this line indicate bistability). Note that the scale of the horizontal axis changes across rows. c d = 0.1. This Figure can be generated using S1 Code. https://doi.org/10.1371/journal.pbio.3002059.g004

Typical explanations for the evolutionary elaboration of female preferences require that they become genetically correlated with the display trait (the Fisher process) [85]. This occurs naturally upon extending the discrete model to consider evolving preferences at an additional locus that controls whether females mate randomly or prefer to mate with displaying males (with preference strength a d ; see Methods). Under the Fisher process, numerical iteration of the recursion equations shows that variation in the sexual display is more likely to be maintained (orange) and eco-evolutionary cycles are more frequent (especially with low initial preference frequency; Fig 5A). Note that in this model, cycles may be long transients but not sustained indefinitely (see Methods for details). Preference itself may cycle due to density-dependent predation (Fig 1F), but these cycles have small amplitude since preferences only evolve due to indirect selection. Unsurprisingly, increasing the initial frequency of mating preference in the population expands the parameters for which the male display trait fixes (Fig 5), with results converging to the discrete model without coevolving preferences when the preference frequency is close to 1 (Fig 5C).

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[1] Url: https://journals.plos.org/plosbiology/article?id=10.1371/journal.pbio.3002059

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