Fundamentals of natural selection

6.1 Natural selection

• Translating Darwin's ideas into a model.

• Natural selection as differential population growth.

• Natural selection with clonal reproduction.

• Natural selection with sexual reproduction and its assumptions.

simple population growth model. If a population is assumed to have no upper limit in its size, the number of individuals one generation in the future (Nt+1) is a product of the number of individuals present now (Nt) multiplied by the finite rate of increase of the population X (pronounced "lambda") to give the expression:

Charles Darwin's (1859) statement of the process of natural selection can be summarized as three basic observations about populations:

• all species have more offspring than can possibly survive and reproduce,

• individual organisms vary in phenotypes that influence their ability to survive and reproduce, and

• within each generation, the individuals possessing phenotypes that confer greater survival and reproduction will contribute more offspring to the next generation.

The result is that phenotypes which cause a predictably greater chance of survival and reproduction will increase in frequency over generations to the extent that such traits have a genetic basis. Darwin's observations initially served as a qualitative model, since an accurate model of genetic inheritance was lacking until Mendel's results were recognized. Once particulate inheritance was understood, the unification of genetics with the principle of natural selection took place in what is now called the modern synthesis or neo-Darwinian synthesis of evolutionary biology. The major challenge in the modern synthesis for population genetics was to develop expectations for the genetic changes that are caused by natural selection. This section of the chapter develops these basic population genetic expectations for natural selection.

Natural selection with clonal reproduction

In this equation for unbounded population growth, X is a multiplier that represents the net difference between the number of individuals lost from the population due to death and the number of new individuals recruited to the population by reproduction each generation. If the number of births and deaths are exactly equal then X is one and the population does not change in size. If there are more births than deaths then X> 1.0 and the population grows whereas if there are more deaths than births then X < 1.0 and the population shrinks. The population growth rate can be thought of as the chance that an individual contributes one offspring to the next generation.

Natural selection is really just a special case of this basic population growth model where each genotype has its own growth rate. To see how this works, let's consider a population composed of two genotypes of an asexual organism like a bacterial species that reproduces only by clonal division over discrete generations. Call the two genotypes A and B with genotype-specific growth rates or absolute fitnesses of XA and XB. The proportions of each genotype in the total population in any generation are:

At its core natural selection is actually a process of population growth, so let's start off by examining a

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