The large body of theory on speciation with gene flow has brought to light fundamental difference... more The large body of theory on speciation with gene flow has brought to light fundamental differences in the effects of two types of mating rules on speciation: preference/trait rules, in which divergence in both (female) preferences and (male) mating traits is necessary for assortment, and matching rules, in which individuals mate with like individuals on the basis of the presence of traits or alleles that they have in common. These rules can emerge from a variety of behavioral or other mechanisms in ways that are not always obvious. We discuss the theoretical properties of both types of rules and explain why speciation is generally thought to be more likely under matching rather than preference/trait rules. We furthermore discuss whether specific assortative mating mechanisms fall under a preference/trait or matching rule, present empirical evidence for these mechanisms, and propose empirical tests that could distinguish between them. The synthesis of the theoretical literature on th...
Predation is a major factor driving evolution, and organisms have evolved adaptations increasing ... more Predation is a major factor driving evolution, and organisms have evolved adaptations increasing their survival chances. However, most defenses incur trade-offs between benefits and costs. Many organisms save costs by employing inducible defenses as responses to fluctuating predation risk. The level of defense often increases with predator densities. However, individual predation risk should not only depend on predator density but also on the density of conspecifics. If the predator has a saturating functional response one would predict a negative correlation between prey density and individual predation risk and hence defense expression. Here, we tested this hypothesis using six model systems, covering a taxonomic range from protozoa to rotifers and crustaceans. In all six systems, we found that the level of defense expression increased with predator density but decreased with prey density. In one of our systems, i.e. in Daphnia, we further show that the response to prey density is...
According to a recent survey, ecologists and evolutionary biologists feel that theoretical and em... more According to a recent survey, ecologists and evolutionary biologists feel that theoretical and empirical research should coexist in a tight feedback loop but believe that the two domains actually interact very little. We evaluate this perception using a citation network analysis for two data sets, representing the literature on sexual selection and speciation. Overall, 54%-60% of citations come from a paper's own category, whereas 17%-23% are citations across categories. These cross-citations tend to focus on highly cited papers, and we observe a positive correlation between the numbers of citations a study receives within and across categories. We find evidence that reviews can function as integrators between the two literatures, argue that theoretical models are analogous to specific empirical study systems, and complement our analyses by studying a cocitation network. We conclude that theoretical and empirical research are more tightly connected than generally thought but tha...
We propose a model to analyze a quantitative trait under frequency-dependent disruptive selection... more We propose a model to analyze a quantitative trait under frequency-dependent disruptive selection. Selection on the trait is a combination of stabilizing selection and intraspecific competition, where competition is maximal between individuals with equal phenotypes. In addition, there is a density-dependent component induced by population regulation. The trait is determined additively by a number of biallelic loci, which can have different effects on the trait value. In contrast to most previous models, we assume that the allelic effects at the loci can evolve due to epistatic interactions with the genetic background. Using a modifier approach, we derive analytical results under the assumption of weak selection and constant population size, and we investigate the full model by numerical simulations. We find that frequency-dependent disruptive selection favors the evolution of a highly asymmetric genetic architecture, where most of the genetic variation is concentrated on a small number of loci. We show that the evolution of genetic architecture can be understood in terms of the ecological niches created by competition. The phenotypic distribution of a population with an adapted genetic architecture closely matches this niche structure. Thus, evolution of the genetic architecture seems to be a plausible way for populations to adapt to regimes of frequency-dependent disruptive selection. As such, it should be seen as a potential evolutionary pathway to discrete polymorphisms and as a potential alternative to other evolutionary responses, such as the evolution of sexual dimorphism or assortative mating.
We study a two-locus model of a quantitative trait with a continuum-of alleles and multilinear ep... more We study a two-locus model of a quantitative trait with a continuum-of alleles and multilinear epistasis that evolves under mutation, selection, and genetic drift. We derive analytical results based on the so-called House of Gauss approximation for the genetic variance, the mean phenotype, and the mutational variance in the balance of the evolutionary forces. The analytical work is complemented by extensive individual-based computer simulations. We find that (1) analytical results are accurate in a large parameter space; (2) epistasis always reduces the equilibrium genetic variance, as predicted in earlier studies that exclude drift; (3) large-scale stochastic fluctuations and non-equilibrium phenomena like adaptive inertia can strongly influence the evolution of the genetic architecture of the trait.
The extent to which sexual selection is involved in speciation with gene flow remains an open que... more The extent to which sexual selection is involved in speciation with gene flow remains an open question and the subject of much research. Here, we propose that some insight can be gained from considering the concept of magic traits (i.e., traits involved in both reproductive isolation and ecological divergence). Both magic traits and other, “non-magic”, traits can contribute to speciation via a number of specific mechanisms. We argue that many of these mechanisms are likely to differ widely in the extent to which they involve sexual selection. Furthermore, in some cases where sexual selection is present, it may be prone to inhibit rather than drive speciation. Finally, there are a priori reasons to believe that certain categories of traits are much more effective than others in driving speciation. The combination of these points suggests a classification of traits that may shed light on the broader role of sexual selection in speciation with gene flow. In particular, we suggest that ...
We investigate the dynamic effects of an inducible prey defense in the Nicholson-Bailey predator-... more We investigate the dynamic effects of an inducible prey defense in the Nicholson-Bailey predator-prey model. We assume that the defense is of all-or-nothing type but that the probability for a prey individual to express the defended phenotype increases gradually with predator density. Compared to a defense that is independent of predation risk, an inducible defense facilitates persistence of the predator-prey system. In particular, inducibility reduces the minimal strength of the defense required for persistence. It also promotes stability by damping predator-prey cycles, but there are exceptions to this result: first, a strong inducible defense leads to the existence of multiple equilibria, and sometimes, to the destruction of stable equilibria. Second, a fast increase in the proportion of defended prey can create predator-prey cycles as the result of an over-compensating negative feedback. Non-equilibrium dynamics of the model are extremely complex.
We investigate the dynamic effects of an inducible prey defense in the Nicholson-Bailey predator-... more We investigate the dynamic effects of an inducible prey defense in the Nicholson-Bailey predator-prey model. We assume that the defense is of all-or-nothing type but that the probability for a prey individual to express the defended phenotype increases gradually with predator density. Compared to a defense that is independent of predation risk, an inducible defense facilitates persistence of the predator-prey system. In particular, inducibility reduces the minimal strength of the defense required for persistence. It also promotes stability by damping predator-prey cycles, but there are exceptions to this result: first, a strong inducible defense leads to the existence of multiple equilibria, and sometimes, to the destruction of stable equilibria. Second, a fast increase in the proportion of defended prey can create predator-prey cycles as the result of an over-compensating negative feedback. Non-equilibrium dynamics of the model are extremely complex.
We develop and analyze an explicit multilocus genetic model of coevolution. We assume that intera... more We develop and analyze an explicit multilocus genetic model of coevolution. We assume that interactions between two species (mutualists, competitors, or victim and exploiter) are mediated by a pair of additive quantitative traits that are also subject to direct stabilizing selection toward intermediate optima. Using a weak-selection approximation, we derive analytical results for a symmetric case with equal locus effects and no mutation, and we complement these results by numerical simulations of more general cases. We show that mutualistic and competitive interactions always result in coevolution toward a stable equilibrium with no more than one polymorphic locus per species. Victim-exploiter interactions can lead to different dynamic regimes including evolution toward stable equilibria, cycles, and chaos. At equilibrium, the victim is often characterized by a very large genetic variance, whereas the exploiter is polymorphic in no more than one locus. Compared to related one-locus or quantitative genetic models, the multilocus model exhibits two major new properties. First, the equilibrium structure is considerably more complex. We derive detailed conditions for the existence and stability of various classes of equilibria and demonstrate the possibility of multiple simultaneously stable states. Second, the genetic variances change dynamically, which in turn significantly affects the dynamics of the mean trait values. In particular, the dynamics tend to be destabilized by an increase in the number of loci.
The large body of theory on speciation with gene flow has brought to light fundamental difference... more The large body of theory on speciation with gene flow has brought to light fundamental differences in the effects of two types of mating rules on speciation: preference/trait rules, in which divergence in both (female) preferences and (male) mating traits is necessary for assortment, and matching rules, in which individuals mate with like individuals on the basis of the presence of traits or alleles that they have in common. These rules can emerge from a variety of behavioral or other mechanisms in ways that are not always obvious. We discuss the theoretical properties of both types of rules and explain why speciation is generally thought to be more likely under matching rather than preference/trait rules. We furthermore discuss whether specific assortative mating mechanisms fall under a preference/trait or matching rule, present empirical evidence for these mechanisms, and propose empirical tests that could distinguish between them. The synthesis of the theoretical literature on th...
Predation is a major factor driving evolution, and organisms have evolved adaptations increasing ... more Predation is a major factor driving evolution, and organisms have evolved adaptations increasing their survival chances. However, most defenses incur trade-offs between benefits and costs. Many organisms save costs by employing inducible defenses as responses to fluctuating predation risk. The level of defense often increases with predator densities. However, individual predation risk should not only depend on predator density but also on the density of conspecifics. If the predator has a saturating functional response one would predict a negative correlation between prey density and individual predation risk and hence defense expression. Here, we tested this hypothesis using six model systems, covering a taxonomic range from protozoa to rotifers and crustaceans. In all six systems, we found that the level of defense expression increased with predator density but decreased with prey density. In one of our systems, i.e. in Daphnia, we further show that the response to prey density is...
According to a recent survey, ecologists and evolutionary biologists feel that theoretical and em... more According to a recent survey, ecologists and evolutionary biologists feel that theoretical and empirical research should coexist in a tight feedback loop but believe that the two domains actually interact very little. We evaluate this perception using a citation network analysis for two data sets, representing the literature on sexual selection and speciation. Overall, 54%-60% of citations come from a paper's own category, whereas 17%-23% are citations across categories. These cross-citations tend to focus on highly cited papers, and we observe a positive correlation between the numbers of citations a study receives within and across categories. We find evidence that reviews can function as integrators between the two literatures, argue that theoretical models are analogous to specific empirical study systems, and complement our analyses by studying a cocitation network. We conclude that theoretical and empirical research are more tightly connected than generally thought but tha...
We propose a model to analyze a quantitative trait under frequency-dependent disruptive selection... more We propose a model to analyze a quantitative trait under frequency-dependent disruptive selection. Selection on the trait is a combination of stabilizing selection and intraspecific competition, where competition is maximal between individuals with equal phenotypes. In addition, there is a density-dependent component induced by population regulation. The trait is determined additively by a number of biallelic loci, which can have different effects on the trait value. In contrast to most previous models, we assume that the allelic effects at the loci can evolve due to epistatic interactions with the genetic background. Using a modifier approach, we derive analytical results under the assumption of weak selection and constant population size, and we investigate the full model by numerical simulations. We find that frequency-dependent disruptive selection favors the evolution of a highly asymmetric genetic architecture, where most of the genetic variation is concentrated on a small number of loci. We show that the evolution of genetic architecture can be understood in terms of the ecological niches created by competition. The phenotypic distribution of a population with an adapted genetic architecture closely matches this niche structure. Thus, evolution of the genetic architecture seems to be a plausible way for populations to adapt to regimes of frequency-dependent disruptive selection. As such, it should be seen as a potential evolutionary pathway to discrete polymorphisms and as a potential alternative to other evolutionary responses, such as the evolution of sexual dimorphism or assortative mating.
We study a two-locus model of a quantitative trait with a continuum-of alleles and multilinear ep... more We study a two-locus model of a quantitative trait with a continuum-of alleles and multilinear epistasis that evolves under mutation, selection, and genetic drift. We derive analytical results based on the so-called House of Gauss approximation for the genetic variance, the mean phenotype, and the mutational variance in the balance of the evolutionary forces. The analytical work is complemented by extensive individual-based computer simulations. We find that (1) analytical results are accurate in a large parameter space; (2) epistasis always reduces the equilibrium genetic variance, as predicted in earlier studies that exclude drift; (3) large-scale stochastic fluctuations and non-equilibrium phenomena like adaptive inertia can strongly influence the evolution of the genetic architecture of the trait.
The extent to which sexual selection is involved in speciation with gene flow remains an open que... more The extent to which sexual selection is involved in speciation with gene flow remains an open question and the subject of much research. Here, we propose that some insight can be gained from considering the concept of magic traits (i.e., traits involved in both reproductive isolation and ecological divergence). Both magic traits and other, “non-magic”, traits can contribute to speciation via a number of specific mechanisms. We argue that many of these mechanisms are likely to differ widely in the extent to which they involve sexual selection. Furthermore, in some cases where sexual selection is present, it may be prone to inhibit rather than drive speciation. Finally, there are a priori reasons to believe that certain categories of traits are much more effective than others in driving speciation. The combination of these points suggests a classification of traits that may shed light on the broader role of sexual selection in speciation with gene flow. In particular, we suggest that ...
We investigate the dynamic effects of an inducible prey defense in the Nicholson-Bailey predator-... more We investigate the dynamic effects of an inducible prey defense in the Nicholson-Bailey predator-prey model. We assume that the defense is of all-or-nothing type but that the probability for a prey individual to express the defended phenotype increases gradually with predator density. Compared to a defense that is independent of predation risk, an inducible defense facilitates persistence of the predator-prey system. In particular, inducibility reduces the minimal strength of the defense required for persistence. It also promotes stability by damping predator-prey cycles, but there are exceptions to this result: first, a strong inducible defense leads to the existence of multiple equilibria, and sometimes, to the destruction of stable equilibria. Second, a fast increase in the proportion of defended prey can create predator-prey cycles as the result of an over-compensating negative feedback. Non-equilibrium dynamics of the model are extremely complex.
We investigate the dynamic effects of an inducible prey defense in the Nicholson-Bailey predator-... more We investigate the dynamic effects of an inducible prey defense in the Nicholson-Bailey predator-prey model. We assume that the defense is of all-or-nothing type but that the probability for a prey individual to express the defended phenotype increases gradually with predator density. Compared to a defense that is independent of predation risk, an inducible defense facilitates persistence of the predator-prey system. In particular, inducibility reduces the minimal strength of the defense required for persistence. It also promotes stability by damping predator-prey cycles, but there are exceptions to this result: first, a strong inducible defense leads to the existence of multiple equilibria, and sometimes, to the destruction of stable equilibria. Second, a fast increase in the proportion of defended prey can create predator-prey cycles as the result of an over-compensating negative feedback. Non-equilibrium dynamics of the model are extremely complex.
We develop and analyze an explicit multilocus genetic model of coevolution. We assume that intera... more We develop and analyze an explicit multilocus genetic model of coevolution. We assume that interactions between two species (mutualists, competitors, or victim and exploiter) are mediated by a pair of additive quantitative traits that are also subject to direct stabilizing selection toward intermediate optima. Using a weak-selection approximation, we derive analytical results for a symmetric case with equal locus effects and no mutation, and we complement these results by numerical simulations of more general cases. We show that mutualistic and competitive interactions always result in coevolution toward a stable equilibrium with no more than one polymorphic locus per species. Victim-exploiter interactions can lead to different dynamic regimes including evolution toward stable equilibria, cycles, and chaos. At equilibrium, the victim is often characterized by a very large genetic variance, whereas the exploiter is polymorphic in no more than one locus. Compared to related one-locus or quantitative genetic models, the multilocus model exhibits two major new properties. First, the equilibrium structure is considerably more complex. We derive detailed conditions for the existence and stability of various classes of equilibria and demonstrate the possibility of multiple simultaneously stable states. Second, the genetic variances change dynamically, which in turn significantly affects the dynamics of the mean trait values. In particular, the dynamics tend to be destabilized by an increase in the number of loci.
Uploads