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A basic assumption of population genetics is that all individuals have an equal probability of reproducing and the actual number of (surviving to reproduction) offpsring are Poisson distributed with an average of two in a population of constant size. However, there is evidence that many natural populations have very unequal probabilities of reproduction. This reduces the effective population size below the census size because alleles are inherited through a smaller number of individuals. Culver et al. (2008) cite Lande & Barrowclough (1987) and give the following relationships for females (f) and males (m), which are likely to have different reproductive probabilities.

k is the average number of offpsring per individual and V_k is the variance in the number of offpsring.

In an ideal population of constant size k=2 and V_k=2. N_e,f = (2N_f-1)/(2-1+2/2) = (2N_f-1)/(2) = N_f - 1/2

References

• Culver, M., Hedrick, P. W., Murphy, K., O'Brien, S., & Hornocker, M. G. (2008). Estimation of the bottleneck size in Florida panthers. Animal Conservation, 11(2), 104–110. https://zslpublications.onlinelibrary.wiley.com/doi/abs/10.1111/j.1469-1795.2007.00154.x
• Lande, R. & Barrowclough, G.F. (1987). Effective population size, genetic variation, and their use in population management. In Viable populations for conservation: 87–124. Soule, M. (Ed.). Cambridge: Cambridge University Press.

Followup Reading List

• Harris, R. B., & Allendorf, F. W. (1989). Genetically effective population size of large mammals: an assessment of estimators. Conservation Biology, 3(2), 181–191. Note equation B-11.
• Kelly, M. J. (2001). Lineage loss in Serengeti cheetahs: consequences of high reproductive variance and heritability of fitness on effective population size. Conservation Biology, 15(1), 137–147. See Table 2.