Max Shpak

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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)
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)
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)
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)
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)
In this paper, we investigate fitness landscapes (under point mutation and recombination) from the standpoint of whether the induced evolutionary dynamics have a "fast-slow" time scale associated with the differences in relaxation time between local quasi-equilibria and the global equilibrium. This dynamical hevavior has been formally described in the(More)
In most sexually reproducing species, including humans, mitochondria and other cytoplasmic elements are uniparentally (usually maternally) inherited. This phenomenon is of broad interest as a mechanism for countering the proliferation of selfish mitochondria. Uniparental inheritance can be enforced either by the female gametes excluding male cytoplasm or(More)
Many biologically relevant dynamical systems are aggregable, in the sense that one can divide their microvariables x 1 ,. .. , x n into several (k) non-intersecting groups and find functions y1,. .. , y k (k < n) from these groups (macrovariables) whose dynamics only depend on the initial state of the macrovari-able. For example, the state of a population(More)