PubMed Health⌕ Search

Biomedical subjects

Michael Doebeli

Publications and source records attributed to Michael Doebeli.

18 recordsLinked to original sources
PubMed2007

Multimodal pattern formation in phenotype distributions of sexual populations.

During bouts of evolutionary diversification, such as adaptive radiations, the emerging species cluster around different locations in phenotype space. How such multimodal patterns in phenotype space can emerge from a single ancestral species is a fundamental question in biology. Frequency-dependent competition is one potential mechanism for such pattern formation, as has previously been shown in models based on the theory of adaptive dynamics. Here, we demonstrate that also in models similar to those used in quantitative genetics, phenotype distributions can split into multiple modes under the force of frequency-dependent competition. In sexual populations, this requires assortative mating, and we show that the multimodal splitting of initially unimodal distributions occurs over a range of assortment parameters. In addition, assortative mating can be favoured evolutionarily even if it incurs costs, because it provides a means of alleviating the effects of frequency dependence. Our results reveal that models at both ends of the spectrum between essentially monomorphic (adaptive dynamics) and fully polymorphic (quantitative genetics) yield similar results. This underscores that frequency-dependent selection is a strong agent of pattern formation in phenotype distributions, potentially resulting in adaptive speciation.

Animals↗
PubMed2006

Evolutionary games and population dynamics: maintenance of cooperation in public goods games.

The emergence and abundance of cooperation in nature poses a tenacious and challenging puzzle to evolutionary biology. Cooperative behaviour seems to contradict Darwinian evolution because altruistic individuals increase the fitness of other members of the population at a cost to themselves. Thus, in the absence of supporting mechanisms, cooperation should decrease and vanish, as predicted by classical models for cooperation in evolutionary game theory, such as the Prisoner's Dilemma and public goods games. Traditional approaches to studying the problem of cooperation assume constant population sizes and thus neglect the ecology of the interacting individuals. Here, we incorporate ecological dynamics into evolutionary games and reveal a new mechanism for maintaining cooperation. In public goods games, cooperation can gain a foothold if the population density depends on the average population payoff. Decreasing population densities, due to defection leading to small payoffs, results in smaller interaction group sizes in which cooperation can be favoured. This feedback between ecological dynamics and game dynamics can generate stable coexistence of cooperators and defectors in public goods games. However, this mechanism fails for pairwise Prisoner's Dilemma interactions and the population is driven to extinction. Our model represents natural extension of replicator dynamics to populations of varying densities.

Animals↗
PubMed2006

Scale-free extinction dynamics in spatially structured host-parasitoid systems.

Much of the work on extinction events has focused on external perturbations of ecosystems, such as climatic change, or anthropogenic factors. Extinction, however, can also be driven by endogenous factors, such as the ecological interactions between species in an ecosystem. Here we show that endogenously driven extinction events can have a scale-free distribution in simple spatially structured host-parasitoid systems. Due to the properties of this distribution there may be many such simple ecosystems that, although not strictly permanent, persist for arbitrarily long periods of time. We identify a critical phase transition in the parameter space of the host-parasitoid systems, and explain how this is related to the scale-free nature of the extinction process. Based on these results, we conjecture that scale-free extinction processes and critical phase transitions of the type we have found may be a characteristic feature of many spatially structured, multi-species ecosystems in nature. The necessary ingredient appears to be competition between species where the locally inferior type disperses faster in space. If this condition is satisfied then the eventual outcome depends subtly on the strength of local superiority of one species versus the dispersal rate of the other.

Animals↗
PubMed2005

Synergy and discounting of cooperation in social dilemmas.

The emergence and maintenance of cooperation by natural selection is an enduring conundrum in evolutionary biology, which has been studied using a variety of game theoretical models inspired by different biological situations. The most widely studied games are the Prisoner's Dilemma, the Snowdrift game and by-product mutualism for pairwise interactions, as well as Public Goods games in larger groups of interacting individuals. Here, we present a general framework for cooperation in social dilemmas in which all the traditional scenarios can be recovered as special cases. In social dilemmas, cooperators provide a benefit to the group at some cost, while defectors exploit the group by reaping the benefits without bearing the costs of cooperation. Using the concepts of discounting and synergy for describing how benefits accumulate when more than one cooperator is present in a group of interacting individuals, we recover the four basic scenarios of evolutionary dynamics given by (i) dominating defection, (ii) coexistence of defectors and cooperators, (iii) dominating cooperation and (iv) bi-stability, in which cooperators and defectors cannot invade each other. Generically, for groups of three or more interacting individuals further, more complex, dynamics can occur. Our framework provides the first unifying approach to model cooperation in different kinds of social dilemmas.

Animals↗
PubMed2005

Unparallel diversification in bacterial microcosms.

Adaptive speciation has gained popularity as a fundamental process underlying the generation of diversity. We tested whether populations respond to similar forms of disruptive selection by diversifying in similar or parallel ways by investigating diversified populations of Escherichia coli B evolved in glucose and glucose-acetate environments. In both environments, the populations have differentiated into two phenotypes, named for their characteristic colony morphologies: large (L) and small (S). Each type is heritable and this polymorphism (or 'diversified pair') appears to be maintained by negative frequency dependence. The L and S phenotypes from different environments are convergent in their colony morphology and growth characteristics. We tested whether diversification was parallel by conducting competition experiments between L and S types from different environments. Our results indicate that replicate diversified pairs from different environments have not diversified in parallel ways and suggest that subtle differences in evolutionary environment can crucially affect the outcome of adaptive diversification.

Acetates↗
PubMed2005

What we have also learned: adaptive speciation is theoretically plausible.

A recent Perspectives article by Gavrilets (2003) on the theory of speciation ignored advances in understanding processes of adaptive speciation, in which the splitting of lineages is an adaptation caused by frequency-dependent selection. Adaptive, or sympatric, speciation has been modeled since the 1960s, but the large amount of attention from both empirical and theoretical biologists that adaptive speciation has received in recent years goes far beyond what was described in Gavrilets' paper. Due to conceptual advances based on the theory of adaptive dynamics, adaptive speciation has emerged as a theoretically plausible evolutionary process that can occur in many different ecological settings.

Adaptation, Biological↗
PubMed2005

The coevolutionary dynamics of antagonistic interactions mediated by quantitative traits with evolving variances.

Quantitative traits frequently mediate coevolutionary interactions between predator and prey or parasite and host. Previous efforts to understand and predict the coevolutionary dynamics of these interactions have generally assumed that standing genetic variation is fixed or absent altogether. We develop a genetically explicit model of coevolution that bridges the gap between these approaches by allowing genetic variation itself to evolve. Analysis of this model shows that the evolution of genetic variance has important consequences for the dynamics and outcome of coevolution. Of particular importance is our demonstration that coevolutionary cycles can emerge in the absence of stabilizing selection, an outcome not possible in previous models of coevolution mediated by quantitative traits. Whether coevolutionary cycles evolve depends upon the strength of selection, the number of loci, and the rate of mutation in each of the interacting species. Our results also generate novel predictions for the expected sign and magnitude of linkage disequilibria in each species.

Biological Evolution↗
PubMed2004

Effects of neighbourhood size and connectivity on the spatial Continuous Prisoner's Dilemma.

The Prisoner's Dilemma, a two-person game in which the players can either cooperate or defect, is a common paradigm for studying the evolution of cooperation. In real situations cooperation is almost never all or nothing. This observation is the motivation for the Continuous Prisoner's Dilemma, in which individuals exhibit variable degrees of cooperation. It is known that in the presence of spatial structure, when individuals "play against" (i.e. interact with) their neighbours, and "compare to" ("learn from") them, cooperative investments can evolve to considerable levels. Here, we examine the effect of increasing the neighbourhood size: we find that the mean-field limit of no cooperation is reached for a critical neighbourhood size of about five neighbours on each side in a Moore neighbourhood, which does not depend on the size of the spatial lattice. We also find the related result that in a network of players, the critical average degree (number of neighbours) of nodes for which defection is the final state does not depend on network size, but only on the network topology. This critical average degree is considerably (about 10 times) higher for clustered (social) networks, than for distributed random networks. This result strengthens the argument that clustering is the mechanism which makes the development and maintenance of the cooperation possible. In the lattice topology, it is observed that when the neighbourhood sizes for "interacting" and "learning" differ by more than 0.5, cooperation is not sustainable, even for neighbourhood sizes that are below the mean-field limit of defection. We also study the evolution of neighbourhood sizes, as well as investment level. Here, we observe that the series of the interaction and learning neighbourhoods converge, and a final cooperative state with considerable levels of average investment is achieved.

Animals↗
PubMed2004

The evolutionary origin of cooperators and defectors.

Coexistence of cooperators and defectors is common in nature, yet the evolutionary origin of such social diversification is unclear. Many models have been studied on the basis of the assumption that benefits of cooperative acts only accrue to others. Here, we analyze the continuous snowdrift game, in which cooperative investments are costly but yield benefits to others as well as to the cooperator. Adaptive dynamics of investment levels often result in evolutionary diversification from initially uniform populations to a stable state in which cooperators making large investments coexist with defectors who invest very little. Thus, when individuals benefit from their own actions, large asymmetries in cooperative investments can evolve.

Altruism↗
PubMed2004

Spatial structure often inhibits the evolution of cooperation in the snowdrift game.

Understanding the emergence of cooperation is a fundamental problem in evolutionary biology. Evolutionary game theory has become a powerful framework with which to investigate this problem. Two simple games have attracted most attention in theoretical and experimental studies: the Prisoner's Dilemma and the snowdrift game (also known as the hawk-dove or chicken game). In the Prisoner's Dilemma, the non-cooperative state is evolutionarily stable, which has inspired numerous investigations of suitable extensions that enable cooperative behaviour to persist. In particular, on the basis of spatial extensions of the Prisoner's Dilemma, it is widely accepted that spatial structure promotes the evolution of cooperation. Here we show that no such general predictions can be made for the effects of spatial structure in the snowdrift game. In unstructured snowdrift games, intermediate levels of cooperation persist. Unexpectedly, spatial structure reduces the proportion of cooperators for a wide range of parameters. In particular, spatial structure eliminates cooperation if the cost-to-benefit ratio of cooperation is high. Our results caution against the common belief that spatial structure is necessarily beneficial for cooperative behaviour.

Animals↗
PubMed2004

Evolution of niche width and adaptive diversification.

Theoretical models suggest that resource competition can lead to the adaptive splitting of consumer populations into diverging lineages, that is, to adaptive diversification. In general, diversification is likely if consumers use only a narrow range of resources and thus have a small niche width. Here we use analytical and numerical methods to study the consequences for diversification if the niche width itself evolves. We found that the evolutionary outcome depends on the inherent costs or benefits of widening the niche. If widening the niche did not have costs in terms of overall resource uptake, then the consumer evolved a niche that was wide enough for disruptive selection on the niche position to vanish; adaptive diversification was no longer observed. However, if widening the niche was costly, then the niche widths remained relatively narrow, allowing for adaptive diversification in niche position. Adaptive diversification and speciation resulting from competition for a broadly distributed resource is thus likely if the niche width is fixed and relatively narrow or free to evolve but subject to costs. These results refine the conditions for adaptive diversification due to competition and formulate them in a way that might be more amenable for experimental investigations.

Adaptation, Physiological↗
PubMed2004

Genetic correlations and the coevolutionary dynamics of three-species systems.

The majority of species interact with at least several others. We develop simple genetic models of coevolution between three species where interactions are mediated by quantitative traits. We assume that one of the species has two quantitative traits, each of which governs its interaction with one of the other two species. We use this model to explore how genetic correlations between the two traits in the multivariate species shape the evolutionary dynamics and outcomes of three species interactions. Our results suggest that genetic correlations are most important when at least one of the interactions is between a predator and prey or parasite and host. In these cases, genetic correlations between traits lead to a wide variety of novel coevolutionary outcomes and dynamics. In particular, genetic correlations can affect the existence and stability of coevolutionary equilibrium points, and they can lead to recurrent or permanent maladaptation. When the three species interact only as competitors or mutualists, however, genetic correlations have no effect on the outcome of coevolution. In all cases, our results reveal the surprising conclusion that both positive and negative genetic correlations between traits have qualitatively identical effects on coevolutionary dynamics.

Alleles↗
PubMed2004

Experimental evidence for sympatric ecological diversification due to frequency-dependent competition in Escherichia coli.

We investigate adaptive diversification in experimental Escherichia coli populations grown in serial batch cultures on a mixture of glucose and acetate. All 12 experimental lines were started from the same genetically uniform ancestral strain but became highly polymorphic for colony size after 1000 generations. Five populations were clearly dimorphic and thus serve as a model for an adaptive lineage split. We analyzed the ecological basis for this dimorphism by studying bacterial growth curves. All strains exhibit diauxie, that is, sequential growth on the two resources. Thus, they exhibit phenotypic plasticity, using mostly glucose when glucose is abundant, then switching to acetate when glucose concentration is low. However, the coexisting strains differ in their diauxie pattern, with one cluster in the dimorphic populations growing better in the glucose phase, and the other cluster having a much shorter lag when switching to the acetate phase. Using invasion experiments, we show that the dimorphism of these two ecological types is maintained by frequency-dependent selection. Using a mathematical model for the adaptive dynamics of diauxie behavior, we show that evolutionary branching in diauxie behavior is a plausible theoretical scenario. Our results support the hypothesis that, in our experiments, adaptive diversification from a genetically uniform ancestor occurred due to frequency-dependent ecological interactions. Our results have implications for understanding the evolution of cross-feeding polymorphism in microorganisms, as well as adaptive speciation due to frequency-dependent selection on phenotypic plasticity.

Adaptation, Physiological↗
PubMed2003

Speciation along environmental gradients.

Traditional discussions of speciation are based on geographical patterns of species ranges. In allopatric speciation, long-term geographical isolation generates reproductively isolated and spatially segregated descendant species. In the absence of geographical barriers, diversification is hindered by gene flow. Yet a growing body of phylogenetic and experimental data suggests that closely related species often occur in sympatry or have adjacent ranges in regions over which environmental changes are gradual and do not prevent gene flow. Theory has identified a variety of evolutionary processes that can result in speciation under sympatric conditions, with some recent advances concentrating on the phenomenon of evolutionary branching. Here we establish a link between geographical patterns and ecological processes of speciation by studying evolutionary branching in spatially structured populations. We show that along an environmental gradient, evolutionary branching can occur much more easily than in non-spatial models. This facilitation is most pronounced for gradients of intermediate slope. Moreover, spatial evolutionary branching readily generates patterns of spatial segregation and abutment between the emerging species. Our results highlight the importance of local processes of adaptive divergence for geographical patterns of speciation, and caution against pitfalls of inferring past speciation processes from present biogeographical patterns.

Animals↗
PubMed2003

Metapopulation dynamics with quasi-local competition.

Stepping-stone models for the ecological dynamics of metapopulations are often used to address general questions about the effects of spatial structure on the nature and complexity of population fluctuations. Such models describe an ensemble of local and spatially isolated habitat patches that are connected through dispersal. Reproduction and hence the dynamics in a given local population depend on the density of that local population, and a fraction of every local population disperses to neighboring patches. In such models, interesting dynamic phenomena, e.g. the persistence of locally unstable predator-prey interactions, are only observed if the local dynamics in an isolated patch exhibit non-equilibrium behavior. Therefore, the scope of these models is limited. Here we extend these models by making the biologically plausible assumption that reproductive success in a given local habitat not only depends on the density of the local population living in that habitat, but also on the densities of neighboring local populations. This would occur if competition for resources occurs between neighboring populations, e.g. due to foraging in neighboring habitats. With this assumption of quasi-local competition the dynamics of the model change completely. The main difference is that even if the dynamics of the local populations have a stable equilibrium in isolation, the spatially uniform equilibrium in which all local populations are at their carrying capacity becomes unstable if the strength of quasi-local competition reaches a critical level, which can be calculated analytically. In this case the metapopulation reaches a new stable state, which is, however, not spatially uniform anymore and instead results in an irregular spatial pattern of local population abundance. For large metapopulations, a huge number of different, spatially non-uniform equilibrium states coexist as attractors of the metapopulation dynamics, so that the final state of the system depends critically on the initial conditions. The existence of a large number of attractors has important consequences when environmental noise is introduced into the model. Then the metapopulation performs a random walk in the space of all attractors. This leads to large and complicated population fluctuations whose power spectrum obeys a red-shifted power law. Our theory reiterates the potential importance of spatial structure for ecological processes and proposes new mechanisms for the emergence of non-uniform spatial patterns of abundance and for the persistence of complicated temporal population fluctuations.

Competitive Behavior↗
PubMed2003

Sexual dimorphism and adaptive speciation: two sides of the same ecological coin.

Models of adaptive speciation are typically concerned with demonstrating that it is possible for ecologically driven disruptive selection to lead to the evolution of assortative mating and hence speciation. However, disruptive selection could also lead to other forms of evolutionary diversification, including ecological sexual dimorphisms. Using a model of frequency-dependent intraspecific competition, we show analytically that adaptive speciation and dimorphism require identical ecological conditions. Numerical simulations of individual-based models show that a single ecological model can produce either evolutionary outcome, depending on the genetic independence of male and female traits and the potential strength of assortative mating. Speciation is inhibited when the genetic basis of male and female ecological traits allows the sexes to diverge substantially. This is because sexual dimorphism, which can evolve quickly, can eliminate the frequency-dependent disruptive selection that would have provided the impetus for speciation. Conversely, populations with strong assortative mating based on ecological traits are less likely to evolve a sexual dimorphism because females cannot simultaneously prefer males more similar to themselves while still allowing the males to diverge. This conflict between speciation and dimorphism can be circumvented in two ways. First, we find a novel form of speciation via negative assortative mating, leading to two dimorphic daughter species. Second, if assortative mating is based on a neutral marker trait, trophic dimorphism and speciation by positive assortative mating can occur simultaneously. We conclude that while adaptive speciation and ecological sexual dimorphism may occur simultaneously, allowing for sexual dimorphism restricts the likelihood of adaptive speciation. Thus, it is important to recognize that disruptive selection due to frequency-dependent interactions can lead to more than one form of adaptive splitting.

Adaptation, Biological↗