Aggregation of variables and system decomposition: Applications to fitness landscape analysis.
Journal - Theory in biosciences = Theorie in den Biowissenschaften (Germany )
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 partitions have a natural application to the description of mutation-selection matrices (fitness landscapes) when their fitness functions have certain symmetries concordant with the neighborhood relationships in the underlying configuration space. We propose that the aggregate variable descriptions of mutation-selection systems offer a potential formal definition of units of selection and evolution.
A survey of unequal crossover systems and their mathematical properties.
Journal - Bulletin of mathematical biology (United States )
We present a model of gene duplication by means of unequal crossover (UCO) where the probability of any given pairing between homologous sequences scales as a penalty factor pz < or = 1, with z the number of mismatches due to asymmetric sequence alignment. From this general representation, we derive several limiting case models of UCO, some of which have been treated elsewhere in the literature. One limiting case is random unequal crossover (RUCO), obtained by setting p = 1 (corresponding to equiprobable pairings at each site). Another limiting case scenario (the 'Krueger-Vogel' model) proposes an optimal 'endpoint' alignment which strongly penalizes both overhang and deviations from endpoint matching positions. For both of these scenarios, we make use of the symmetry properties of the transition operator (together with the more general UCO properties of copy number conservation and equal parent-offspring mean copy number) to derive the stationary distribution of gene copy number generated by UCO. For RUCO, the stationary distribution of genotypes is shown to be a negative binomial, or alternatively, a convolution of geometric distributions on 'haplotype' frequencies. A different type of model derived from the general representation only allows recombination without overhang (internal UCO or IntUCO). This process has the special property of converging to a single copy length or a distribution on a pair of copy lengths in the absence of any other evolutionary forces. For UCO systems in general, we also show that selection can readily act on gene copy number in all of the UCO systems we investigate due to the perfect heritability (h 2 = 1) imposed by conservation of copy number. Finally, some preliminary work is presented which suggests that the more general models based on misalignment probabilities seem to also converge to stationary distributions, which are most likely functions of parameter value p.
|ISSN : ||0092-8240|
|Mesh Heading : ||Animals Crossing Over, Genetic Evolution, Molecular Gene Conversion Humans Recombination, Genetic genetics|
|Mesh Heading Relevant : ||Gene Duplication Models, Genetic genetics|
On the origin of species by means of assortative mating
Journal - Proceedings of the Royal Society B: Biological Sciences
Assortative mating may split a population even in the absenceof natural selection. Here, we study when this happens if matingdepends on one or two quantitative traits. Not surprisingly,the modes of assortative mating that can cause sympatric speciationwithout selection are rather strict. However, some of them mayoccur in nature. Slow elimination of intermediate individualscaused by the gradual tightening of assortative mating, whichevolves owing to relatively weak disruptive selection, providesthe alternative scenario for sympatric speciation, in additionto fast elimination of intermediate individuals as a resultof the direct action of strong disruptive selection under aninvariant mode of assortative mating. Even when assortativemating alone cannot split an initially coherent population,it may be able to prevent the merging of species after theirsecondary contact.
|Keywords : ||sympatric speciation • assortative mating • disruptive selection • multilocus traits|