Size of population required for artificial selection

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Abstract
It is widely acknowledged that genetic drift is an important source of variation in response to artificial directional selection. How large should a selection line be in order to reduce the effect of genetic drift to an acceptably low level?This paper investigates two criteria that can be used to answer this question in relation to short-term response to selection. The first criterion is coefficient of variation of response, and the second criterion is chance of success, where a successful selection programme is one in which the observed response is greater than a certain proportion, β, of expected response.For a simple mass selection programme with intensity i and heritability h2, the size of population required in order for the coefficient of variation of response to be γ after t generations, is approximately 2/(γih)2t, and the size required for the chance of success to be α after t generations is approximately 2{zα/(β−l)ih}2/t, where zα is the standard normal deviate corresponding to the probability α.As an example, suppose it is required that after t generations the coefficient of variation of response be 10% or that there be a 90% chance of achieving at least 9/10 of expected response. Since ih ≤ 2 in most selection programmes, the size of population required is at least 50/t or 82/t respectively. If ih ≤ 1, the corresponding sizes are 200/t and 328/t.Results are extended to enable the calculation of size of population required for any type of artificial directional selection programme, including those in which generations overlap.