Search Results

You are looking at 1 - 4 of 4 items for

  • Author or Editor: S. A. H. Geritz x
  • Refine by Access: All Content x
Clear All Modify Search

We review mechanisms that lead to cyclic evolution with alternating levels of diversity. Such cycles involve directional evolution towards a so-called evolutionary branching point, where selection becomes disruptive and splits the population into two strategies. Coevolution of these strategies eventually leads to the extinction of one of them. The remaining strategy evolves back to the evolutionary branching point, and a new cycle begins. There are a number of different evolutionary mechanisms that can produce this kind of cycles including chance extinction, switching between population dynamical attractors, and coevolution with an ecologically distinct species. We also present an example for branching-extinction cycles where the direction of evolution changes between monomorphic and dimorphic populations solely due to the different levels of diversity. The latter cycles exhibit a novel feature: Even though extinction is deterministic in the sense that it is unavoidable and always occurs at the same trait values, it is random which of the two coexisting strategies goes extinct. As a result, long and short cycles alternate in a random sequence.

Restricted access

We present a model for the gradual evolution towards dioecy in cosexual plants with geitonogamous selfing. We show how geitonogamous selfing (i.e. transfer of pollen between flowers on the same plant) can facilitate the evolution of dioecy (i.e. separate male and female individuals) in cosexual plants (i.e. both sexual functions on the same plant). We study the effect of parameters such as inbreeding depression, the attraction costs per flower, and the total amount of resources available per plant. We also consider different flower architectures (limited versus unlimited potential number of seeds per flower) and pollination biologies (biotic versus abiotic). We find that (1) if there is no maximum to the number of seeds per flower, then cosexuality is evolutionarily stable whenever the inbreeding depression is less than one-half. With abiotic pollination and an inbreeding depression greater than one-half, dioecy evolves via evolutionary branching, that is, through the gradual differentiation towards male and female plants, but only after the population has first evolved to a cosexual strategy with an intermediate sex ratio. The evolution of dioecy requires higher levels of inbreeding depression if pollination is by insects, but is facilitated by increasing the total amount of resources available per plant. (2) If the potential number of seeds per flower is limited, we get basically the same results as with an unlimited seed number per flower, but the outcome now also depends on the attraction costs per flower. With high attraction costs, the population can evolve to gynodioecy (females and cosexuals in the same population). Further increasing inbreeding depression leads to dioecy. Our results give a possible explanation of Darwin's observation that dioecy is more common in plant species with abiotic pollination and in large species with many flowers such as trees.

Restricted access
T. J. de Jong
S. A. H. Geritz

Erratum [corrected printing of Fig. 1, misprinted in De Jong, T. J. and Geritz, S. A. H. (2001):  The role of geitonogamy in the gradual evolution towards dioecy in cosexual plants. Selection 2:133-146, on p. 136.]

Restricted access

Matrix game theory and optimisation models offer two radically different perspectives on the outcome of evolution. Optimisation models consider frequency-independent selection and envisage evolution as a hill-climbing process on a constant fitness landscape, with the optimal strategy corresponding to the fitness maximum. By contrast, in evolutionary matrix games selection is frequency-dependent and leads to fitness equality among alternative strategies once an evolutionarily stable strategy has been established. In this review we demonstrate that both optimisation models and matrix games represent limiting cases of the general framework of nonlinear frequency-dependent selection. Adaptive dynamics theory considers arbitrary nonlinear frequency and density dependence and envisages evolution as proceeding on an adaptive landscape that changes its shape according to which strategies are present in the population. In adaptive dynamics, evolutionarily stable strategies correspond to conditional fitness maxima: the ESS is characterised by the fact that it has the highest fitness if it is the established strategy. In this framework it can also be shown that dynamical attainability, evolutionary stability, and invading potential of strategies are pairwise independent properties. In optimisation models, on the other hand, these properties become linked such that the optimal strategy is always attracting, evolutionarily stable and can invade any other strategy. In matrix games fitness is a linear function of the potentially invading strategy and can thus never exhibit an interior maximum: Instead, the fitness landscape is a plane that becomes horizontal once the ESS is established. Due to this degeneracy, invading potential is part of the ESS definition for matrix games and dynamical attainability is a dependent property. We conclude that nonlinear frequency-dependent theory provides a unifying framework for overcoming the traditional divide between evolutionary optimisation models and matrix games.

Restricted access