What life cycle graphs can tell about the evolution of life histories

We analyze long-term evolutionary dynamics in a large class of life history models. The model family is characterized by discrete-time population dynamics and a finite number of individual states such that the life cycle can be described in terms of a population projection matrix. We allow an arbitrary number of demographic parameters to be subject to density-dependent population regulation and two or more demographic parameters to be subject to evolutionary change. Our aim is to identify structural features of life cycles and modes of population regulation that correspond to specific evolutionary dynamics. Our derivations are based on a fitness proxy that is an algebraically simple function of loops within the life cycle. This allows us to phrase the results in terms of properties of such loops which are readily interpreted biologically. The following results could be obtained. First, we give sufficient conditions for the existence of optimisation principles in models with an arbitrary number of evolving traits. These models are then classified with respect to their appropriate optimisation principle. Second, under the assumption of just two evolving traits we identify structural features of the life cycle that determine whether equilibria of the monomorphic adaptive dynamics (evolutionarily singular points) correspond to fitness minima or maxima. Third, for one class of frequency-dependent models, where optimisation is not possible, we present sufficient conditions that allow classifying singular points in terms of the curvature of the trade-off curve. Throughout the article we illustrate the utility of our framework with a variety of examples

Adaptive Walks on Changing Landscapes: Levins' Approach Extended

The assumption that trade-offs exist is fundamental in evolutionary theory. Levins (Am. Nat. 96 (1962) 361-372) introduced a widely adopted graphical method for analyzing evolution towards an optimal combination of two quantitative traits, which are traded off. His approach explicitly excluded the possibility of density- and frequency-dependent selection. Here we extend Levins method towards models, which include these selection regimes and where therefore fitness landscapes change with population state. We employ the same kind of curves Levins used: trade-off curves and fitness contours. However, fitness contours are not fixed but a function of the resident traits and we only consider those that divide the trait space into potentially successful mutants and mutants which are not able to invade ('invasion boundaries'). The developed approach allows to make a priori predictions about evolutionary endpoints and about their bifurcations. This is illustrated by applying the approach to several examples from the recent literature

The Evolution of Simple Life-Histories: Step Towards Classification

We present a classification of the evolutionary dynamics for a class of simple life-history models. The model class considered is characterised by discrete time population dynamics, density-dependent population growth, by the assumption that individuals can occur in two states, and that two evolving traits are coupled by a trade-off. Individual models differ in the choice of traits that are presumed to evolve and in the way population regulation is incorporated. The classification is based on a fitness measure that is sign equivalent to invasion fitness but algebraically simpler. We classify models according to curvature properties of the fitness landscape and whether the evolutionary dynamics can be analysed by means of an optimisation criterion. The first classification allows us to infer whether trait combinations that are characterised by a zero fitness gradient are susceptible to invasion by similar trait combinations. The second classification distinguishes models where evolutionary change is frequency-independent from models that give rise to frequency dependence. Given certain symmetry assumptions we can extend the classification in the latter case by splitting selection into a density-dependent and a frequency-dependent component. We apply our approach to several simple life-history models and demonstrate how our classification facilitates an analytical analysis. We conclude by discussing some general patterns that emerge from our analysis and by hinting at several possible extensions

The Evolution of Resource Specialization through Frequency-Dependent and Frequency-Independent Mechanisms

Levin's fitness set approach has shaped the intuition of many evolutionary ecologists about resource specialization: if the set of possible phenotypes is convex, a generalist is favored, while either of the two specialists is predicted for concave phenotype sets. An important aspect of Levins approach is that it explicitly excludes frequency-dependent selection. Frequency-dependence emerged in a series of models that studied the degree of character displacement of two consumers coexisting on two resources. Surprisingly, the evolutionary dynamics of a single consumer type under frequency-dependence has not been studied in detail yet. We analyze a model of one evolving consumer feeding on two resources and show that, depending on the trait considered to be subject to evolutionary change, selection is either frequency-independent or frequency-dependent. This difference is explained by the effects different foraging traits have on the consumer-resource interactions. If selection is frequency-dependent, then the population can become dimorphic through evolutionary branching at the trait value of the generalist. Those traits with frequency-independent selection, however, do indeed follow the predictions based on Levin's fitness set approach. This dichotomy in the evolutionary dynamics of traits involved in the same foraging process was not previously recognized

Conservation of the Segmented Germband Stage: Robustness or Pleiotropy?

Gene expression patterns of the segment polarity genes in the extended and segmented germband stage are remarkably conserved among insects. To explain the conservation of these stages, two hypotheses have been proposed. One hypothesis states that the conservation reflects a high interactivity between modules, so that mutations would have several pleiotropic effects in other parts of the body, resulting in stabilizing selection against mutational variation. The other hypothesis states that the conservation is caused by robustness of the segment polarity network against mutational changes. When evaluating the empirical evidence for these hypotheses, we found strong support for pleiotropy and little evidence supporting robustness of the segment polarity network. This points to a key role for stabilizing selection in the conservation of these stages. Finally, we discuss the implications for robustness of organizers and long-term conservation in general

The Evolutionary Ecology of Dominance-Recessivity.

An "adaptive dynamics" modeling approach to the evolution of dominance-recessivity is presented. In this approach fitness derives from an explicit ecological scenario. The ecology consists of a within-individual part presenting a locus with regulated activity, and a between-individual part that is a two-patch soft selection model. Evolutionary freedom is allowed at a single locus. The evolutionary analysis considers directed random walks on trait space, generated by invasions of mutants. The phenotype of an individual is determined by allelic parameters. Mutations can have two effects: they either affect the affinity of the promoter sequence for transcription factors, or they affect the gene product. The dominance interaction between alleles derives from their promoter affinities. I show by means of an example that additive genetics is evolutionarily unstable when selection and evolution maintain two alleles in the population. In such a situation, dominance interactions can become stationary close to additive genetics or they continue to evolve at a very slow pace towards dominance-recessivity. The probability that a specific dominance interaction will evolve depends on the relative mutation rate of promoter compared to gene product and the distribution of mutational effect sizes. Either of both alleles in the dimorphism can become dominant and dominance-recessivity is always most likely to evolve. Evolution then approaches a population state where every phenotype in the population has a maximum viability in one of the two patches. When the within-individual part is replaced by a housekeeping locus that codes for a metabolic enzyme, evolution favors a population of two alleles on the same conditions as for a regulated locus. In the case of housekeeping gene however, the evolutionary dynamics is attracted towards a population state where the heterozygote phenotype equal the optimum phenotypes in the two patches.

Delayed maturation in temporally structured populations with non-equilibrium dynamics

In this paper we study the evolutionary dynamics of delayed maturation in semelparous individuals. We model this in a two-stage clonally reproducing population subject to density-dependent fertility. The population dynamical model allows multiple, cyclic and/or chaotic attractors, thus allowing it to illustrate how (i) evolutionary stability is primary a property of a population dynamical system as a whole, and (ii) that the evolutionary stability of a demographic strategy by necessity derives from the evolutionary stability of the stationary population dynamical systems it can engender, i.e., its associated population dynamical attractors. Our approach is based on numerically estimating invasion exponents, defined as the theoretical long-term average relative growth rates of different mutant population densities in the stationary environment defined by a resident population system. For some combinations of resident and mutant trait values we have to consider multivalued invasion exponents, which makes the evolutionary argument more complicated (and more interesting) than is usually envisaged. Multivaluedness occurs (i) when more than one attractor is associated with the values of the residents' demographic parameters, or (ii) when the setting of the mutant parameters makes the descendants of a single mutant reproduce exclusively either in even or odd years, so that a mutant population is affected by either subsequence of the fluctuating resident densities only. Non-equilibrium population dynamics or random environmental noise select for strategists with a non-zero probability to delay maturation. When there is an evolutionary attracting pair of such a strategy and a population dynamical attractor engendered by it, this delaying probability is a Continuously Stable Strategy, this is an Evolutionarily Unbeatable Strategy which also is Stable in a long term evolutionary sense. Population dynamical, i.e., temporary, coexistence of delaying and non-delaying strategists is possible with non-equilibrium dynamics, but adding random environmental noise to the model destroys this coexistence. Adding random noise also shifts the CSS towards a higher probability of delaying maturation

Delayed Maturation in Temporally Structured Populations with Non-Equilibrium Dynamics.

In this paper we study the evolutionary dynamics of delayed maturation in semelparous individuals. We model this in a two-stage clonally reproducing population subject to density-dependent fertility. The population dynamical model allows multiple, cyclic and/or chaotic attractors, thus allowing it to illustrate how (i) evolutionary stability is primary a property of a population dynamical system as a whole, and (ii) that the evolutionary stability of a demographic strategy by necessity derives from the evolutionary stability of the stationary population dynamical systems it can engender, i.e., its associated population dynamical attractors. Our approach is based on numerically estimating invasion exponents, defined as the theoretical long-term average relative growth rates of different mutant population densities in the stationary environment defined by a resident population system. For some combinations of resident and mutant trait values we have to consider multivalued invasion exponents, which makes the evolutionary argument more complicated (and more interesting) than is usually envisaged. Multivaluedness occurs (i) when more than one attractor is associated with the values of the residents' demographic parameters, or (ii) when the setting of the mutant parameters makes the descendants of a single mutant reproduce exclusively either in even or odd years, so that a mutant population is affected by either subsequence of the fluctuating resident densities only. Non-equilibrium population dynamics or random environmental noise select for strategists with a non-zero probability to delay maturation. When there is an evolutionary attracting pair of such a strategy and a population dynamical attractor engendered by it, this delaying probability is a Continuously Stable Strategy, this is an Evolutionarily Unbeatable Strategy which also is Stable in a long term evolutionary sense. Population dynamical, i.e., temporary, coexistence of delaying and non-delaying strategists is possible with non-equilibrium dynamics, but adding random environmental noise to the model destroys this coexistence. Adding random noise also shifts the CSS towards a higher probability of delaying maturation.

What life cycle graphs can tell about the evolution of life histories

We analyze long-term evolutionary dynamics in a large class of life history models. The model family is characterized by discrete-time population dynamics and a finite number of individual states such that the life cycle can be described in terms of a population projection matrix. We allow an arbitrary number of demographic parameters to be subject to density-dependent population regulation and two or more demographic parameters to be subject to evolutionary change. Our aim is to identify structural features of life cycles and modes of population regulation that correspond to specific evolutionary dynamics. Our derivations are based on a fitness proxy that is an algebraically simple function of loops within the life cycle. This allows us to phrase the results in terms of properties of such loops which are readily interpreted biologically. The following results could be obtained. First, we give sufficient conditions for the existence of optimisation principles in models with an arbitrary number of evolving traits. These models are then classified with respect to their appropriate optimisation principle. Second, under the assumption of just two evolving traits we identify structural features of the life cycle that determine whether equilibria of the monomorphic adaptive dynamics (evolutionarily singular points) correspond to fitness minima or maxima. Third, for one class of frequency-dependent models, where optimisation is not possible, we present sufficient conditions that allow classifying singular points in terms of the curvature of the trade-off curve. Throughout the article we illustrate the utility of our framework with a variety of examples

Adaptive walks on changing landscapes: Levins' approach extended

The assumption that trade-offs exist is fundamental in evolutionary theory. Levins (Am. Nat. 96 (1962) 361-372) introduced a widely adopted graphical method for analyzing evolution towards an optimal combination of two quantitative traits, which are traded off. His approach explicitly excluded the possibility of density- and frequency-dependent selection. Here we extend Levins method towards models, which include these selection regimes and where therefore fitness landscapes change with population state. We employ the same kind of curves Levins used: trade-off curves and fitness contours. However, fitness contours are not fixed but a function of the resident traits and we only consider those that divide the trait space into potentially successful mutants and mutants which are not able to invade ('invasion boundaries'). The developed approach allows to make a priori predictions about evolutionary endpoints and about their bifurcations. This is illustrated by applying the approach to several examples from the recent literature