Modelling the Coexistence of Annual and Perennial Plants in Temporally Varying Environments*

Abstract The long-term growth and coexistence of species with large mixed populations in varying environments were modelled for representative environments and life-history characteristics of annual and perennial plants. The effects of the relationships between the means, variances, and covariances of seed yield, establishment, and survival, were explored by Taylor's expansion. The main findings are: 1. Individual variation in reproductive success within generations has no effect on long-term growth, which is determined only by the mean growth rate of the individuals of the species. 2. In annual species with nonoverlapping generations and without seed banks, the species with the largest mean log of the annual growth rate Y, that is the product of the average seed yield per plant and the establishment probability per seed, will win in competition with other species, independent of the correlations between the growth rates of the different species. In this case there is a negative tradeoff between the mean and the variance. 3. In perennial species with a lottery type of equal access to vacant sites, a high annual survival probability allows stable coexistence between perennial species with independent or negatively correlated variance in their mean annual product of seed production and establishment Y. 4. The coexistence range and the likely number of coexisting perennial species increase as a function of the variance of the common species, and is decreased by the variance of the rare species. The coexistence range is decreased by the covariance between the growth rates of the species, and between the survival of the rare species and its growth rate. 5. If mortality in the community of long-lived perennials is synchronized, the generations become nonoverlapping, and the competitive dynamics become similar to that of annuals. 6. Coexistence between annual and perennial species is promoted if the covariances between the annual survival and the relative yield of perennials, and between the yields of perennials and annuals, decrease and become more negative. 7. Selection for seed yield and establishment in different conditions in annuals favours a generalist strategy with low variance between years which provides a moderate yield and establishment over a wide range of environmental conditions. In perennial plants, long-term growth rate is determined by the lifetime seed yield and establishment. Because of strong competition with annuals in the more common conditions, selection in perennials favours instead a specialist strategy, with a high seed yield and establishment at relatively rare occasions in space and time, in which there is only weak competition with annuals. 8. Coexistence of annual species with a long-lived seed bank in the soil is also made possible by independent variation in different years of the germination, seed yield and establishment of different species, analogous to the situation of perennial plants.