Fitness Gradient Research Articles

Modelling the adaptive dynamics of traits involved in inter‐ and intraspecific interactions: An assessment of three methods

In recent years, three related methods have been used to model the phenotypic dynamics of traits under the influence of natural selection. The first is based on an approximation to quantitative genetic recursion equations for sexual populations. The second is based on evolution in asexual lineages with mutation‐generated variation. The third method finds an evolutionarily stable set of phenotypes for species characterized by a given set of fitness functions, assuming that the mode of reproduction places no constraints on the number of distinct types that can be maintained in the population. The three methods share the property that the rate of change of a trait within a homogeneous population is approximately proportional to the individual fitness gradient. The methods differ in assumptions about the potential magnitude of phenotypic differences in mutant forms, and in their assumptions about the probability that invasion or speciation occurs when a species has a stable, yet invadable phenotype. Determining the range of applicability of the different methods is important for assessing the validity of optimization methods in predicting the evolutionary outcome of ecological interactions. Methods based on quantitative genetic models predict that fitness minimizing traits will often be evolutionarily stable over significant time periods, while other approaches suggest this is likely to be rare. A more detailed study of cases of disruptive selection might reveal whether fitness‐minimizing traits occur frequently in natural communities.

Dynamics of Adaptation and Evolutionary Branching

We present a formal framework for modeling evolutionary dynamics with special emphasis on the generation of diversity through branching of the evolutionary tree. Fitness is defined as the long term growth rate which is influenced by the biotic environment leading to an ever-changing adaptive landscape. Evolution can be described as a dynamics in a space with variable number of dimensions corresponding to the number of different types present. The dynamics within a subspace is governed by the local fitness gradient. Entering a higher dimensional subspace is possible only at a particular type of attractors where the population undergoes evolutionary branching.

Spatial evolutionary game theory: Hawks and Doves revisited

We consider a spatial generalization of evolutionary game theory in which strategies are distributed over a spatial array of sites. We assume that the strategy corresponding to a given site has local interactions with the strategies sitting on neighbouring sites, and that the strategies change if neighbouring strategies are doing better. After briefly setting the stage with a formal definition of spatial evolutionary game theory, we consider the spatial extension of the Hawk-Dove game, and we show that the results are qualitatively different from those obtained from classical evolutionary game theory. For example, the proportion of Hawks in the population is in general lower in the spatial game than in the classical one. We also consider spatial generalizations of the extensions of the Hawk-Dove game obtained by including strategies such as Retaliator and Bully. Here, too, the results from the spatial game are very different from the classical results. In particular, with space Retaliator is a much more successful strategy than one would expect from classical considerations. This suggests that, in general, spatial structure may facilitate the evolution of strategies such as Retaliator, which do not necessarily prosper classically, and which are reminiscent of the \`nice', \`provokable' and `forgiving' strategies which seem to play a central role in the evolution of cooperation. The results indicate that including spatial structure in evolutionary game theory is a fruitful extension.

The Selection Gradient of an Infinite-Dimensional Trait

The selection gradient is of central importance in evolutionary biology because it quantifies the forces of directional selection acting on a trait. Lande has shown that the selection gradient can be computed as the vector gradient of the log mean fitness when the trait is normally distributed. Using the framework of Gaussian processes and reproducing kernel Hilbert spaces, a rigorous definition is developed for the selection gradient of an infinite-dimensional trait. Lande’s result is then extended to this case.

Epidemiology of Physical Activity, Physical Fitness and Coronary Heart Disease

Observational population-based studies have consistently shown an inverse dose-response gradient between physical activity or fitness and coronary heart disease. This relationship is more firmly established in men. Existing studies suggest that the physical activity gradient, and perhaps the fitness gradient, is produced by a combination of varying levels of both the intensity and the amount of habitual physical activity. It is not at present possible to definitively describe the dose-response association between the intensity of physical activity and the risk of coronary heart disease. An answer to this important question awaits further research.

Evolutionarily unstable fitness maxima and stable fitness minima of continuous traits

We present models of adaptive change in continuous traits for the following situations: (1) adaptation of a single trait within a single population in which the fitness of a given individual depends on the population's mean trait value as well as its own trait value; (2) adaptation of two (or more) traits within a single population; (3) adaptation in two or more interacting species. We analyse a dynamic model of these adaptive scenarios in which the rate of change of the mean trait value is an increasing function of the fitness gradient (i.e. the rate of increase of individual fitness with the individual's trait value). Such models have been employed in evolutionary game theory and are often appropriate both for the evolution of quantitative genetic traits and for the behavioural adjustment of phenotypically plastic traits. The dynamics of the adaptation of several different ecologically important traits can result in characters that minimize individual fitness and can preclude evolution towards characters that maximize individual fitness. We discuss biological circumstances that are likely to produce such adaptive failures for situations involving foraging, predator avoidance, competition and coevolution. The results argue for greater attention to dynamical stability in models of the evolution of continuous traits.

Adaptive landscapes, genetic distance and the evolution of quantitative characters.

SummaryThe maintenance of polygenic variability by a balance between mutation and stabilizing selection has been analysed using two approximations: the ‘Gaussian’ and the ‘house of cards’. These lead to qualitatively different relationships between the equilibrium genetic variance and the parameters describing selection and mutation. Here we generalize these approximations to describe the dynamics of genetic means and variances under arbitrary patterns of selection and mutation. We incorporate genetic drift into the same mathematical framework.The effects of frequency-independent selection and genetic drift can be determined from the gradient of log mean fitness and a covariance matrix that depends on genotype frequencies. These equations describe an ‘adaptive landscape’, with a natural metric of genetic distance set by the covariance matrix. From this representation we can change coordinates to derive equations describing the dynamics of an additive polygenic character in terms of the moments (means, variances, …) of allelic effects at individual loci. Only under certain simplifying conditions, such as those derived from the Gaussian and house-of-cards approximations, do these general recursions lead to tractable equations for the first few phenotypic moments. The alternative approximations differ in the constraints they impose on the distributions of allelic effects at individual loci. The Gaussian-based prediction that evolution of the phenotypic mean does not change the genetic variance is shown to be a consequence of the assumption that the allelic distributions are never skewed. We present both analytical and numerical results delimiting the parameter values consistent with our approximations.