Mathematical population genetics

Ewens, W.J. 1979 Mathematical population genetics. Springer-Verlag, N.Y. 

HG] K. P. Hadeler and D. Glas (1983), Quasimonotone systems and convergence to equilibrium in a population genetic model, Journal of Mathematical Analysis and Applications 95 297-303. 

This book is unique in bringing together in one volume many, if not most, of the mathematical theories of population genetics presented in the past which are still valid and some of the current mathematical investigations. 

This concludes a discussion of exactly solvable second-order processes. As one can see, only a very few second-order cases can be solved exactly for their time dependence. The more complicated reversible reactions such as 2Apt C seem to lead to very complicated generating functions in terms of Lame functions and the like. This shows that even for reasonably simple second- and third-order reactions, approximate techniques are needed. This is not only true in chemical kinetic applications, but in others as well, such as population and genetic models. The actual models in these fields are beyond the scope of this review, but the mathematical problems are very similar. Reference 62 contains a discussion of many of these models. A few of the approximations that have been tried are discussed in Ref. 67. It should also be pointed out at this point that the application of these intuitive methods to chemical kinetics have never been justified at a fundamental level and so the results, although intuitively plausible, can be reasonably subject to doubt. 

MOGP is based on the more traditional optimisation method genetic programming (GP), which is a type of GA [53,54]. The main difference between GP and a GA is in the chromosome representation in a GA an individual is usually represented by a fixed-length linear string, whereas in GP individuals are represented by treelike structures hence, they can vary in shape and size as the population undergoes evolution. The internal nodes of the tree, typically represent mathematical operators, and the terminal nodes, typically represent variables and constant values thus, the chromosome can represent a mathematical expression as shown in Fig. 4. 

Brian Charlesworth Evolution in age-structured populations Stephen Childress Mechanics of swimming and flying C. Cannings and E. A. Thompson Genealogical and genetic structure Frank C. Hoppensteadt Mathematical methods of population biology... 

Cluster mathematics is a description technique, not a predictor. It measures correlation and correlation does not mean causation. In fact, the cluster diagram below shows Africa mathematically separated from the remainder of the world. Of course, humans in Africa share the same genes as humans elsewhere. There is simply more variance between Africans and Asians than between Caucasians and Asians. To complicate matters further, eighty-five percent of all variance occurs within populations and only fifteen percent among populations. This means there is usually far greater genetic diversity between members of a... 

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