Effective size of fluctuating populations with two sexes and overlapping generations

We derive formulas that can be applied to estimate the effective population size N-e for organisms with two sexes reproducing once a year and having constant adult mean vital rates independent of age. Temporal fluctuations in population size are generated by demographic and environmental stochasticity. For populations with even sex ratio at birth, no deterministic population growth and identical mean vital rates for both sexes, the key parameter determining N-e is simply the mean value of the demographic variance for males and females considered separately. In this case Crow and Kimura's generalization of Wright's formula for N-e with two sexes, in terms of the effective population sizes for each sex, is applicable even for fluctuating populations with different stochasticity in vital rates for males and females. If the mean vital rates are different for the sexes then a simple linear combination of the demographic variances determines N-e, further extending Wright's formula. For long-lived species an expression is derived for N-e involving the generation times for both sexes. In the general case with nonzero population growth and uneven sex ratio of newborns, we use the model to investigate numerically the effects of different population parameters on N-e. We also estimate the ratio of effective to actual population size in six populations of house sparrows on islands off the coast of northern Norway. This ratio showed large interisland variation because of demographic differences among the populations. Finally, we calculate how N-e in a growing house sparrow population will change over time.