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Assortative mating may split a population even in the absence of natural selection. Here, we study when this happens if mating depends on one or two quantitative traits. Not surprisingly, the modes of assortative mating that can cause sympatric speciation without selection are rather strict. However, some of them may occur in nature. Slow elimination of… (More)

It has been shown that differences in fecundity variance can influence the probability of invasion of a genotype in a population; i.e., a genotype with lower variance in offspring number can be favored in finite populations even if it has a somewhat lower mean fitness than a competitor. In this article, Gillespie's results are extended to population genetic… (More)

The topological features of genotype spaces given a genetic operator have a substantial impact on the course of evolution. We explore the structure of the recombination spaces arising from four different unequal crossover models in the context of pretopological spaces. We show that all four models are incompatible with metric distance measures due to a lack… (More)

In this paper we present general results on aggregation of variables, specifically as it applies to decomposable (partitionable) dynamical systems. We show that a particular class of transition matrices, namely, those satisfying an equitable partitioning property, are aggregable under appropriate decomposition operators. It is also shown that equitable… (More)

It was shown by Gillespie [1974. Am. Nat. 108, 145-151], that if two genotypes produce the same average number of offspring on but have a different variance associated within each generation, the genotype with a lower variance will have a higher effective fitness. Specifically, the effective fitness is w(e)=w-sigma(2)/N, where w is the mean fitness,… (More)

For two genotypes that have the same mean number of offspring but differ in the variance in offspring number, naturalselection will favor the genotype with lower variance. In such cases, the average growth rate is not sufficient as a measure of fitness or as a predictor of fixation probability. However, the effect of variance in offspring number on the… (More)

Many dynamical systems are <i>aggregable</i> in the sense that we can divide their variables <i>x</i><inf>1</inf>,...,<i>x</i><inf><i>n</i></inf> into several (<i>k</i>) non-intersecting groups and find combinations <i>y</i><inf>1</inf>,...,<i>y<inf>k</inf></i> of variables from these groups (<i>macrovariables</i>) whose dynamics depend only on the initial… (More)

The number of extant individuals within a lineage, as exemplified by counts of species numbers across genera in a higher taxonomic category, is known to be a highly skewed distribution. Because the sublineages (such as genera in a clade) themselves follow a random birth process, deriving the distribution of lineage sizes involves averaging the solutions to… (More)

Many dynamical systems are decomposably aggregable in the sense that one can divide their (micro) variables x 1 ,. .. , x n into several (k) non-overlapping blocks and find combinations y1,. .. , y k of variables from these blocks (macrovari-ables) whose dynamics depend only on the initial values of the macrovariables. For example, the state of a biological… (More)