Mathematics and 21st Century Biology (2005) / Chapter Skim
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6 Understanding Populations
6 Understanding Populations
Pages 99-109
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From page 99... ...
These analyses strongly shaped our current understanding of natural selection in large, but finite, populations and guided experimental work. In recent years the emphasis has shifted from these deductive activities to inductive or retrospective approaches that address the question of what we can infer about evolutionary history and the nature of the evolutionary process from current patterns of genetic variation.
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From page 100... ...
The rapidly growing database of DNA polymorphism and divergence studies from a variety of organisms, including humans and other primates, provide an exciting opportunity to learn about the evolutionary history of populations and the evolutionary processes that have resulted in the patterns of variation that we observe in extant populations. The difficulty is that even very simple models of this process lead to challenging mathematical problems.
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From page 101... ...
The Wright-Fisher neutral model is a particular case of a more general class of neutral models in which all parents are equivalent; these are referred to as "exchangeable models." In these models, the distribution of offspring number need not be Poissonian. In the limit of large populations and a low mutation rate, the models' stationary properties depend on a single compound parameter, Nu/v, where u is the mutation rate and v is the variance of offspring number.
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From page 102... ...
method for obtaining quantities proportional to the sample probabilities. The main point here is that the sampling properties of sequence data under even this simplest, one-parameter, neutral model lead to recursions that are not analytically tractable.
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From page 103... ...
The focus thus far in this chapter has been on variation within species, but comparisons of sequences from different species can also be very informative, both about evolutionary relationships of species (the phylogenetic inference problem) and about evolutionary processes.
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From page 104... ...
and increased genetic complexity (heterogeneous recombination and mutation rates) , and with more complex types of natural selection (interaction between sites and spatial and temporal variation in selection coefficients)
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From page 105... ...
Much research is being devoted to anthropogenic impacts on natural and managed systems. Mathematical challenges include modeling and analysis of spatial aspects, temporal and spatial variation, demographic stochasticity (in particular when dealing with small populations)
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From page 106... ...
Many ecological interactions occur far away from equilibrium, and large-scale anthropogenic perturbations, such as land use change, species invasions, or alterations of nutrient or carbon cycles, exacerbate this problem. Land use change and the invasion of exotic species often result in rapid changes and thus have the potential to move a system far from equilibrium, with consequences for both ecological and evolutionary processes (see below)
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From page 107... ...
As an example of why one might wish to couple ecological and evolutionary processes, and of the mathematical challenges that result, consider the evolution of resistance. This is of importance, for instance, in understanding the ramifications of the use of transgenic Bt crops, which have been engineered to express a toxin from the soil bacterium Bacillus thuringiensis (Bt)
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From page 108... ...
2004. Bayesian Markov chain Monte Carlo sequence analysis reveals varying neutral substitution patterns in mammalian evolution.
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From page 109... ...
1995. Estimating effective population size and mutation rate from sequence data using Metropolis-Hastings sampling.
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