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 Quantitative Biology , 2011, Abstract: We extend the Moran model with single-crossover recombination to include general recombination and mutation. We show that, in the case without resampling, the expectations of products of marginal processes defined via partitions of sites form a closed hierarchy, which is exhaustively described by a finite system of differential equations. One thus has the exceptional situation of moment closure in a nonlinear system. Surprisingly, this property is lost when resampling (i.e., genetic drift) is included.
 Mathematics , 2002, Abstract: It is well known that rather general mutation-recombination models can be solved algorithmically (though not in closed form) by means of Haldane linearization. The price to be paid is that one has to work with a multiple tensor product of the state space one started from. Here, we present a relevant subclass of such models, in continuous time, with independent mutation events at the sites, and crossover events between them. It admits a closed solution of the corresponding differential equation on the basis of the original state space, and also closed expressions for the linkage disequilibria, derived by means of M\"obius inversion. As an extra benefit, the approach can be extended to a model with selection of additive type across sites. We also derive a necessary and sufficient criterion for the mean fitness to be a Lyapunov function and determine the asymptotic behaviour of the solutions.
 Zhiying Wen Chinese Science Bulletin , 2001, DOI: 10.1007/BF02901155 Abstract: The purpose of this survey is to present Moran sets and Moran classes which generalize the classical selfsimilar sets from the following points: (i) The placements of the basic sets at each step of the constructions can be arbitrary; (ii) the contraction ratios may be different at each step; and (iii) the lower limit of the contraction ratios permits zero. In this discussion we will present geometrical properties and results of dimensions of these sets and classes, and discuss conformai Moran sets and random Moran sets as well.
 PLOS ONE , 2012, DOI: 10.1371/journal.pone.0043066 Abstract: Understanding linkage block size and molecular mechanisms of recombination suppression is important for plant breeding. Previously large linkage blocks ranging from 14 megabases to 27 megabases were observed around the rice blast resistance gene Pi-ta in rice cultivars and backcross progeny involving an indica and japonica cross. In the present study, the same linkage block was further examined in 456 random recombinant individuals of rice involving 5 crosses ranging from F2 to F10 generation, with and without Pi-ta containing genomic indica regions with both indica and japonica germplasm. Simple sequence repeat markers spanning the entire chromosome 12 were used to detect recombination break points and to delimit physical size of linkage blocks. Large linkage blocks ranging from 4.1 megabases to 10 megabases were predicted from recombinant individuals involving genomic regions of indica and japonica. However, a significantly reduced block from less than 800 kb to 2.1megabases was identified from crosses of indica with indica rice regardless of the existence of Pi-ta. These findings suggest that crosses of indica and japonica rice have significant recombination suppression near the centromere on chromosome 12.
 Mathematics , 2006, Abstract: Populations evolving under the joint influence of recombination and resampling (traditionally known as genetic drift) are investigated. First, we summarise and adapt a deterministic approach, as valid for infinite populations, which assumes continuous time and single crossover events. The corresponding nonlinear system of differential equations permits a closed solution, both in terms of the type frequencies and via linkage disequilibria of all orders. To include stochastic effects, we then consider the corresponding finite-population model, the Moran model with single crossovers, and examine it both analytically and by means of simulations. Particular emphasis is on the connection with the deterministic solution. If there is only recombination and every pair of recombined offspring replaces their pair of parents (i.e., there is no resampling), then the {\em expected} type frequencies in the finite population, of arbitrary size, equal the type frequencies in the infinite population. If resampling is included, the stochastic process converges, in the infinite-population limit, to the deterministic dynamics, which turns out to be a good approximation already for populations of moderate size.
 Mathematics , 2015, Abstract: We study the dimensional properties of Moran sets and Moran measures in doubling metric spaces. In particular, we consider local dimensions and $L^q$-dimensions. We generalize and extend several existing results in this area.