Éva Kisdi

Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree

We present a general framework for modelling adaptive trait dynamics in which we integrate various concepts and techniques from modern ESS-theory. The concept of evolutionarily singular strategies is introduced as a generalization of the ESS-concept. We give a full classification of the singular strategies in terms of ESS-stability, convergence stability, the ability of the singular strategy to invade other populations if initially rare itself, and the possibility of protected dimorphisms occurring within the singular strategys neighbourhood. Of particular interest is a type of singular strategy that is an evolutionary attractor from a great distance, but once in its neighbourhood a population becomes dimorphic and undergoes disruptive selection leading to evolutionary branching. Modelling the adaptive growth and branching of the evolutionary tree can thus be considered as a major application of the framework. A haploid version of Levenes ‘soft selection’ model is developed as a specific example to demonstrate evolutionary dynamics and branching in monomorphic and polymorphic populations.

Density Dependent Life History Evolution in Fluctuating Environments

Environmental fluctuation may not only alter the life history optimization problem but also query optimization itself. Under density regulation annual growth rate is influenced by the direct effect of fluctuation as well as by an indirect effect due to fluctuating population density. For a weak fluctuation there is an optimal strategy which is slightly different from the stable environment optimum, since (a) it should adapt to an average density altered by fluctuation, (b) it should diminish the fluctuation in annual growth rate caused by direct and indirect effect of environmental fluctuation, and (c) it should exploit an increase, but avoid a decrease in average annual growth rate caused by fluctuation. The “optimal” strategy becomes meaningless if the fluctuation is strong, because long run growth rates are not independent of the established population. Coexistence (or exclusion of the rare strategy) may be mediated by a sufficiently strong fluctuation, which is illustrated by a simple model elucidating the connection with resource-competition models. Moreover, some other consequences of strong fluctuation are demonstrated by the example of a lottery model, such as multiple ESS, ESS which cannot invade an established population, and historical events which determine the outcome of the evolution.

Adaptive Dynamics of Speciation: Ecological Underpinnings

Speciation occurs when a population splits into ecologically differentiated and reproductively isolated lineages. In this chapter, we focus on the ecological side of nonallopatric speciation: Under what ecological conditions is speciation promoted by natural selection? What are the appropriate tools to identify speciation-prone ecological systems? For speciation to occur, a population must have the potential to become polymorphic (i.e., it must harbor heritable variation). Moreover, this variation must be under disruptive selection that favors extreme phenotypes at the cost of intermediate ones. With disruptive selection, a genetic polymorphism can be stable only if selection is frequency dependent (Pimm 1979; see Chapter 3). Some appropriate form of frequency dependence is thus an ecological prerequisite for nonallopatric speciation. Frequency-dependent selection is ubiquitous in nature. It occurs, among many other examples, in the context of resource competition (Christiansen and Loeschcke 1980; see Box 4.1), predator–prey systems (Marrow et al. 1992), multiple habitats (Levene 1953), stochastic environments (Kisdi and Meszena 1993; Chesson 1994), asymmetric competition (Maynard Smith and Brown 1986), mutualistic interactions (Law and Dieckmann 1998), and behavioral conflicts (Maynard Smith and Price 1973; Hofbauer and Sigmund 1990). The theory of adaptive dynamics is a framework devised to model the evolution of continuous traits driven by frequency-dependent selection. It can be applied to various ecological settings and is particularly suitable for incorporating ecological complexity. The adaptive dynamic analysis reveals the course of long-term evolution expected in a given ecological scenario and, in particular, shows whether, and under which conditions, a population is expected to evolve toward a state in which disruptive selection arises and promotes speciation. To achieve analytical tractability in ecologically complex models, many adaptive dynamic models (and much of this chapter) suppress genetic complexity with the assumption of clonally reproducing phenotypes (also referred to as strategies or traits). This enables the efficient identification of interesting features of the engendered selective pressures that deserve further analysis from a genetic perspective.

Individual optimization: Mechanisms shaping the optimal reaction norm

In general, optimal reaction norms in heterogeneous populations can be obtained only by iterative numerical procedures (McNamara, 1991; Kawecki and Stearns, 1993). We consider two particular, but biologically plausible and analytically tractable cases of individual optimization to gain insight into the mechanisms which shape the optimal reaction norm of fecundity in relation to an environmental variable or an individual trait. In the first case, we assume that the quality of the environment (e.g. food abundance) or the quality of the individual (e.g. body size) is fixed during its entire life; it may also be a heritable individual trait. In the second case, individual quality is assumed to change randomly such that the probability distribution of quality in the next year is the same for the parent and for her offspring. For these two cases, we obtain analytical expressions for the shape of the optimal reaction norm, which are heuristically interpretable in terms of underlying selective mechanisms. It is shown that better quality may reduce the optimal fecundity. This outcome is particularly likely if better quality increases a fecundity-independent factor of parental survival in a long-lived species with fixed quality.