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Models of microsatellite evolution
 Statistical Methods in Molecular Evolution, Series: Statistics for Biology and Health
, 2004
"... Microsatellites are simple sequence repeats in DNA, for example the motif AT repeated twentyfive times in a row. Microsatellites mutate by changing the number of their repeats, for example the (AT)25 mentioned in the previous sentence might become an (AT)24 or (AT)26 in that individual’s offspring. ..."
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Microsatellites are simple sequence repeats in DNA, for example the motif AT repeated twentyfive times in a row. Microsatellites mutate by changing the number of their repeats, for example the (AT)25 mentioned in the previous sentence might become an (AT)24 or (AT)26 in that individual’s offspring.
Unequal Crossover Dynamics in Discrete and Continuous Time
, 2003
"... We analyze a class of models for unequal crossover (UC) of sequences containing sections with repeated units that may differ in length. In these, the probability of an ‘imperfect’ alignment, in which the shorter sequence has d units without a partner in the longer one, scales like q^d as compared to ..."
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We analyze a class of models for unequal crossover (UC) of sequences containing sections with repeated units that may differ in length. In these, the probability of an ‘imperfect’ alignment, in which the shorter sequence has d units without a partner in the longer one, scales like q^d as compared to ‘perfect’ alignments where all these copies are paired. The class is parameterized by this penalty factor. An effectively infinite population size and thus deterministic dynamics is assumed. For the extreme cases q = 0 and q = 1 and any initial distribution whose moments satisfy certain conditions, we prove the convergence to one of the known fixed points, uniquely determined by the mean copy number, in both discrete and continuous time. For the intermediate parameter values, the existence of fixed points is shown.
Microsatellite evolution: Markov transition functions for a suite of models
 Theor. Popul. Biol
, 2007
"... This paper takes from the collection of models considered by Whittaker et. al. (2003) derived from direct observation of microsatellite mutation in parentchild pairs and provides analytical expressions for the probability distributions for the change in number of repeats over any given number of ge ..."
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This paper takes from the collection of models considered by Whittaker et. al. (2003) derived from direct observation of microsatellite mutation in parentchild pairs and provides analytical expressions for the probability distributions for the change in number of repeats over any given number of generations. The mathematical framework for this analysis is the theory of Markov processes. We find these expressions using two approaches, approximating by circulant matrices and solving a partial differential equation satisfied by the generating function. The impact of the differing choice of models is examined using likelihood estimates for time to most recent common ancestor. The analysis presented here may play a role in elucidating the connections between these two approaches and shows promise in reconciling differences between estimates for mutation rates based on Whittaker’s approach and methods based on phylogenetic analyses. Key words and phrases: microsatellites, Markov process, generating functions 1.
REPEAT DISTRIBUTIONS FROM UNEQUAL CROSSOVERS
, 803
"... Abstract. It is a wellknown fact that genetic sequences may contain sections with repeated units, called repeats, that differ in length over a population, with a length distribution of geometric type. A simple class of recombination models with single crossovers is analysed that result in equilibri ..."
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Abstract. It is a wellknown fact that genetic sequences may contain sections with repeated units, called repeats, that differ in length over a population, with a length distribution of geometric type. A simple class of recombination models with single crossovers is analysed that result in equilibrium distributions of this type. Due to the nonlinear and infinitedimensional nature of these models, their analysis requires some nontrivial tools from measure theory and functional analysis, which makes them interesting also from a mathematical point of view. In particular, they can be viewed as quadratic, hence nonlinear, analogues of Markov chains.
Mapping Unequal Crossing over Hotspot Region of Simple Sequence Repeat in
"... Abstract: The polymorphism of simple sequence repeat (SSR) in biological genome is one result of unequal crossing over for homologous chromosomes; therefore it has theoretical importance in clarifying the hotspot regions of unequal crossing over. A set of recombinant inbred lines (RILs) population t ..."
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Abstract: The polymorphism of simple sequence repeat (SSR) in biological genome is one result of unequal crossing over for homologous chromosomes; therefore it has theoretical importance in clarifying the hotspot regions of unequal crossing over. A set of recombinant inbred lines (RILs) population that derived form an elite hybrid Yuyu 22 was used in this study, its genetic components of the population was analyzed by means of SSR analysis, and 40 unequal crossing over SSR markers were found. The frequency of the unequal crossing over in the RIL population was 0.34–14.63%, with 10−2–10−1 frequency per generation, and the (AG)n repeat SSR markers accounted for 58.3%. There were 31 unequal crossing over markers locating on 11 chromosomal hotspot regions, distributing on 10 chromosomes except for chromosome 9, including two unequal crossing over hotspot regions each
Unequal Crossover Dynamics in Discrete and Continuous Time
, 2003
"... Abstract. We analyze a class of models for unequal crossover (UC) of sequences containing sections with repeated units that may differ in length. In these, the probability of an ‘imperfect ’ alignment, in which the shorter sequence has d units without a partner in the longer one, scales like q d as ..."
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Abstract. We analyze a class of models for unequal crossover (UC) of sequences containing sections with repeated units that may differ in length. In these, the probability of an ‘imperfect ’ alignment, in which the shorter sequence has d units without a partner in the longer one, scales like q d as compared to ‘perfect ’ alignments where all these copies are paired. The class is parameterized by this penalty factor q. An effectively in£nite population size and thus deterministic dynamics is assumed. For the extreme cases q = 0 and q = 1 and any initial distribution whose moments satisfy certain conditions, we prove the convergence to one of the known £xed points, uniquely determined by the mean copy number, in both discrete and continuous time. For the intermediate parameter values, the existence of £xed points is shown. 1.
Open Access
"... Do patients adhere to overthecounter artemisinin combination therapy for malaria? evidence from an intervention study in Uganda ..."
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Do patients adhere to overthecounter artemisinin combination therapy for malaria? evidence from an intervention study in Uganda