Competition between phenotypes

Abstract

We present two models for phenotypic-dependent interspecific competition. In both cases the survivorship of individuals of one population depends on the entire phenotypic distribution of the other species. The first model considers a continuously varying metric trait, with assortative or random mating; the second model examines a character controlled by two alleles at a single locus. Pursuing the notion that each population maximizes its mean fitness we define a vector-optimum strategy using the concepts of cooperative and competitive optima. It is found that the dynamical constraints placed on the equations of motion by Mendelian genetics often prevent a population from evolving to a strategic optimum. However, for the single locus case with complete dominance, the competitive optimum always coincides with some dynamical equilibrium on the Hardy-Weinberg manifold.

The Evolution of the Use of Mathematics in Cancer Research

“…In this regard, the example of the optimal therapies we have analyzed is a clear exponent of this interpretation of an objective function. Nevertheless and as Rocklin and Oster (1976), Perelson et al (1976Perelson et al ( , 1978 and Perelson et al (1980) pointed out, there is a substantive logical and empirical evidence suggesting that, behind the notion of optimality, there exists an operational meaning for many biological systems. For instance, today it is widely accepted that natural selection is basically an optimizing process in which the objective function to maximize is the survival probability, and some biological phenomena and behaviors can be understood as the optimal solution for certain situations and/or tasks.…”

Emergence of multiple foraging strategies under competition

“…The optimal strategy for an isolated organism with full knowledge of the environment can be determined using the marginal value theorem [Stephens and Krebs, 1986; Parker and Smith, 1990]. This approach can be extended to competing organisms, but only when the birth and death rates for each are explicitly known [Chesson, 2000; Rocklin and Oster, 1976]. However, much less is known about how the environment and competition with other foragers shape the main phenotypic determinants of a foraging strategy: the ability to sense resources at a distance, and, the ability to move to the detected resource.…”

Quantitative character dynamics: Gametic model

“…A phenotypic model has appeared in a work by Slatkin (1970) (also Gimelfarb, 1970), and a rigorous and extensive treatment of models of this type was given in a series of papers by Karlin (1979a-d;1980a, b). Models of this type were applied by Rocklin and Oster (1976) to the problem of phenotype-dependent interspecific competition and by Slatkin and Lande (1976) to the problem of niche width in a fluctuating environment.…”

“…This brief discussion of the genie and zygotic/phenotypic models leads one to conclude that there is a definite gap between the two types. The zygotic/phenotypic "macro" models have actually no connections with the genie "micro" models (although an attempt has been made by Rocklin and Oster (1976) to derive a phenotypic model from a genie one). It is not clear whether and under what conditions the zygotic/phenotypic models may be considered as approximations of the genie ones.…”