The effective size of annual plant populations: The interaction of a seed bank with fluctuating population size in maintaining genetic variation

Many annual plant populations undergo dramatic fluctuations in size. Such fluctuations can result in the loss of genetic variability. Here I formalize the potential for a seed bank to buffer against such genetic loss. The average time to seed germination (T) defines the generation time of annuals with a seed bank, and assuming random seed germination, I show that, under otherwise ideal conditions, a population's effective size (N-e) equals NT, where N is the number of adult plants. This result supports the general principle that lengthening the prereproductive period increases N-e. When adult numbers vary, N-e at any time depends on N and on the numbers contributing to the seed bank in previous seasons. Averaging these effects over time gives N-e approximate to N-h + (T - 1)N-a, where N-h and N-a are the harmonic e h a and arithmetic means of the adult population. Thus if T >>1, N-e is determined primarily by N-a. Simulations showed that until fluctuations in N are large (>25x) this relationship is accurate. I extended the theory to incorporate a selfing rate (S) and reproductive variance (I) through seed production (k), outcrossed pollen (m), and variation in selfing rate: N-c = NT(1 - S/2)/(1 + I) = NT/[(1 + F-IS)(1 + I)]. Reproductive variance (I) equals [I-k(1 + S)(2) + I-m (1 - S)(2) + 2(1 - S-2)I-km + (SIs)-I-2(1 + I-k)]/4, where I-j is the standardized variance (V-j/j(2)) of factor j and I-km is the standardized covariance between k and m. These results are applicable to other organisms with a similar life history, such as freshwater crustaceans with diapausing eggs (e. g., tadpole shrimp, clam shrimp, and fairy shrimp) and other semelparous species with discrete breeding seasons and a variable maturation time (e. g., Pacific salmon).