Neighborhood Models of Plant Population Dynamics. 4. Single-Species and Multispecies Models of Annuals with Dormant Seeds

Neighborhood population-dynamic models are developed for single-species and multispecies communities of annual plants with seeds that may lie dormant through one or more growing seasons. Dormancy-induced changes in lifetime germination successes affect the equilibrium densities of plants and the local stability of equilibria. Dormancy-induced population-dynamic time lags, in contrast, do not affect equilibrium densities of post-germination plants or the ability of an invader to successfully colonize a multispecies community. In single-species populations, time lags are never destabilizing but may be stabilizing. Specifically, some strategies of dormancy (a way to partition lifetime germination success among the various age classes of seeds) cause an otherwise oscillatory monoculture (eigenvalue less than negative one) to have a locally stable positive equilibrium. The maximum distance over which a plant of one species can interfere with a plant of another species is termed the neighborhood radius. The population-dynamic consequences of the sizes of the radii are examined in one- and two-species communities. The models in this paper are designed to be easily calibrated with experimental data. All results are illustrated with models calibrated for greenhouse communities of two species of annual weeds.

[1]  Stephen W. Pacala,et al.  Neighborhood models of plant population dynamics 3. Models with spatial heterogeneity in the physical environment , 1987 .

[2]  J. Harper Population Biology of Plants , 1979 .

[3]  P. H. Leslie SOME FURTHER NOTES ON THE USE OF MATRICES IN POPULATION MATHEMATICS , 1948 .

[4]  D. Cohen Optimizing reproduction in a randomly varying environment. , 1966, Journal of theoretical biology.

[5]  N. Macdonald,et al.  Models of an annual plant population with a seedbank , 1981 .

[6]  J M Cushing,et al.  Model stability and instability in age structured populations. , 1980, Journal of theoretical biology.

[7]  D. Levin,et al.  The Ecological and Genetic Consequences of Density-Dependent Regulation in Plants , 1980 .

[8]  R. Allen,et al.  Properties of Age Structure Models for Fish Populations , 1974 .

[9]  Morton E. Gurtin,et al.  Non-linear age-dependent population dynamics , 1974 .

[10]  M. Rotenberg Equilibrium and stability in populations whose interactions are age-specific. , 1975, Journal of theoretical biology.

[11]  R. May,et al.  Competition within and between species in a patchy environment: Relations between microscopic and macroscopic models , 1985 .

[12]  L. Lawlor,et al.  Growth Rate Projection and Life History Sensitivity for Annual Plants with a Seed Bank , 1983, The American Naturalist.

[13]  Local stability of a population with density-dependent fertility. , 1979, Theoretical population biology.

[14]  H. A. Roberts EMERGENCE AND LONGEVITY IN CULTIVATED SOIL OF SEEDS OF SOME ANNUAL WEEDS , 1964 .

[15]  K. Swick Stability and bifurcation in age-dependent population dynamics. , 1981, Theoretical population biology.

[16]  N. Macdonald Time lags in biological models , 1978 .

[17]  Robert M. May,et al.  Time delays, density-dependence and single-species oscillations , 1974 .

[18]  The joint evolution of seed dormancy and flowering time in annual plants living in variable environments , 1983 .

[19]  Stephen W. Pacala,et al.  Neighborhood models of plant population dynamics. 2. Multi-species models of annuals , 1986 .

[20]  S. Pacala,et al.  Neighborhood Models of Plant Population Dynamics. I. Single-Species Models of Annuals , 1985, The American Naturalist.

[21]  S. Levin Age-Structure and Stability in Multiple-Age Spawning Populations , 1981 .

[22]  D. Cohen A General Model of Optimal Reproduction in a Randomly Varying Environment , 1968 .

[23]  J. Guckenheimer,et al.  The dynamics of density dependent population models , 1977, Journal of mathematical biology.

[24]  William Gurney,et al.  Instability and complex dynamic behaviour in population models with long time delays , 1982 .

[25]  R. May,et al.  Bifurcations and Dynamic Complexity in Simple Ecological Models , 1976, The American Naturalist.

[26]  R M May,et al.  A note on difference-delay equations. , 1976, Theoretical population biology.

[27]  H. A. Roberts,et al.  Emergence and longevity of seeds of annual weeds in cultivated and undisturbed soil. , 1973 .

[28]  Yoh Iwasa,et al.  Demographic Theory for an Open Marine Population with Space-Limited Recruitment , 1985 .

[29]  J. Sarukhán Studies of plant demography : Ranunculus repens L., R. bulbosus L. and R. acris L. II. Reproductive strategies and seed population dynamics , 1974 .