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We propose a model to investigate the dynamics of fashion traits purely driven by social interactions. We assume that people adapt their style to maximize social success, and we describe the interaction as a repeated group game in which the payoffs reflect the social norms dictated by fashion. On one hand, the tendency to imitate the trendy stereotypes opposed to the tendency to diverge from them to proclaim identity; on the other hand, the exploitation of sex appeal for dating success opposed to the moral principles of the society. These opposing forces promote diversity in fashion traits, as predicted by the modeling framework of adaptive dynamics. Our results link the so-called horizontal dynamics-- the primary driver of fashion evolution, compared with the vertical dynamics accounting for interclass and economic drivers--to style variety. [ABSTRACT FROM AUTHOR]

We unfold the bifurcation involving the loss of evolutionary stability of an equilibrium of the canonical equation of Adaptive Dynamics (AD). The equation deterministically describes the expected long-term evolution of inheritable traits - phenotypes or strategies - of coevolving populations, in the limit of rare and small mutations. In the vicinity of a stable equilibrium of the AD canonical equation, a mutant type can invade and coexist with the present - resident - types, whereas the fittest always win far from equilibrium. After coexistence, residents and mutants effectively diversify, according to the enlarged canonical equation, only if natural selection favors outer rather than intermediate traits - the equilibrium being evolutionarily unstable, rather than stable. Though the conditions for evolutionary branching - the joint effect of resident-mutant coexistence and evolutionary instability - have been known for long, the unfolding of the bifurcation has remained a missing tile of AD, the reason being related to the nonsmoothness of the mutant invasion fitness after branching. In this paper, we develop a methodology that allows the approximation of the invasion fitness after branching in terms of the expansion of the (smooth) fitness before branching. We then derive a canonical model for the branching bifurcation and perform its unfolding around the loss of evolutionary stability. We cast our analysis in the simplest (but classical) setting of asexual, unstructured populations living in an isolated, homogeneous, and constant abiotic environment; individual traits are one-dimensional; intra- as well as inter-specific ecological interactions are described in the vicinity of a stationary regime. [ABSTRACT FROM AUTHOR]

We show in this paper how simulations of ODEs and continuations of systems of algebraic equations can be combined to study the evolution of biodiversity in multispecies systems where phenotypic traits are genetically transmitted. We follow the adaptive dynamics (AD) approach, which provides a deterministic approximation of the evolutionary dynamics of stationary coexisting populations in terms of an ODE system, the so-called AD canonical equation. AD also provides explicit conditions to test whether a stable evolutionary equilibrium of the canonical equation is a branching point--resident and mutant morphs coexist and further differentiate, thus increasing biodiversity--or not. We analyze a standard parameterized family of prey-predator communities, described by the most standard ecological model, and propose an iterative procedure to obtain the branching portrait, explaining the dependence of branching scenarios on two (demographic, environmental, or control) parameters. Among a number of interesting results, in line with field studies and known ecological principles, we find that prey branching is induced by the predation pressure, and is favored when prey intraspecific competition is highly sensitive to the resident-mutant phenotypic mismatch, while predator branching is not possible when prey and predators are present in an equal number of morphs. This results in alternate prey-predator branching sequences with possible phases of prey unilateral branching. The guidelines for deriving a general method for analyzing the evolution of biodiversity are also discussed. The indications that can be obtained typically have a qualitative nature, but can be of help for the long-term conservation and management of biodiversity. [ABSTRACT FROM AUTHOR]

We present in this paper the first example of chaotic evolutionary dynamics in biology. We consider a Lotka-Volterra tritrophic food chain composed of a resource, its consumer, and a predator species, each characterized by a single adaptive phenotypic trait, and we show that for suitable modeling and parameter choices the evolutionary trajectories approach a strange attractor in the three-dimensional trait space. The study is performed through the bifurcation analysis of the so-called canonical equation of Adaptive Dynamics, the most appropriate modeling approach to long-term evolutionary dynamics. [ABSTRACT FROM AUTHOR]

The analysis of a simple model shows that exploitation of fish stocks can entrain in the long run the substantial decline or even the collapse of the stock, as well as difficulties in stock recovery, loss of fishery resilience, and reduction of the mean fish size. The results are in agreement with numerous observations, even though they are obtained with a simple model in which the harvesting fleet and the fish stock are considered as unstructured predator and prey. The study is carried out for the typical case of fleet dimension not too sensitive to the year-to-year fluctuations of the stock and assuming that the sole cause of evolution is technological innovation. The analysis is performed by means of Adaptive Dynamics, an approach born in theoretical biology which is used here in the context of technological change. Although the results are qualitatively consistent with those obtained long ago through the principles of bioeconomics, it is fair to stress that the underlying assumptions are different. In fact, in the bioeconomic approach fleet technology does not evolve and fishing effort varies to produce economic optimization, while in the Adaptive Dynamics approach technological innovation is the key driver. The paper is purely theoretical and the proposed model can hardly be tuned on any real fishery. No practical guidelines for managers can therefore be drawn, if not the general conclusion that long-term sustainability of exploited fish stocks can only be achieved if strategic parameters influencing technological change are kept under strict control. [Copyright &y& Elsevier]

The paper describes the slow evolution of two adaptive traits that regulate the interactions between two mutualistic populations (e.g. a flowering plant and its insect pollinator). For frozen values of the traits, the two populations can either coexist or go extinct. The values of the traits for which populations extinction is guaranteed are therefore of no interest from an evolutionary point of view. In other words, the evolutionary dynamics must be studied only in a viable subset of trait space, which is bounded due to the physiological cost of extreme trait values. Thus, evolutionary dynamics experience so-called border collision bifurcations, when a system invariant in trait space hits the border of the viable subset. The unfolding of standard and border collision bifurcations with respect to two parameters of biological interest is presented. The algebraic and boundary-value problems characterizing the border collision bifurcations are described together with some details concerning their computation. [ABSTRACT FROM AUTHOR]

The evolution of cannibalistic traits in consumer populations is studied in this paper with the approach of adaptive dynamics theory. The model is kept at its minimum complexity by eliminating some environmental characteristics, like heterogeneity and seasonalities, and by hiding the size-structure of the population. Evolutionary dynamics are identified through numerical bifurcation analysis, applied both to the ecological (resident–mutant) model and to the canonical equation of adaptive dynamics. The result is a rich catalog of evolutionary scenarios involving evolutionary stable strategies and branching points both in the monomorphic and dimorphic dynamics. The possibility of evolutionary extinction of highly cannibalistic populations is also ascertained. This allows one to explain why cannibalism can be a transient stage of evolution. [Copyright &y& Elsevier]