Dispersal in a metapopulation neighbourhood model of an annual plant with a seedbank

1 A metapopulation neighbourhood model of an annual plant species in a harsh environment is derived. It includes the effects of seed survival, dormancy, competition, dispersal, spatial and temporal heterogeneity, and stochastic local extinctions. 2 The model contained the following assumptions: (i) the time step is 1 year; (ii) competition is density-dependent via a Hassell-type submodel; (iii) each local population is regulated separately within a hexagonal cell, 1 m across, and the cells form a tessellated array; (iv) dispersal is from a parent cell to its neighbours and declines exponentially with distance; (v) the harshness of the environment is a value set for each cell; spatial and temporal heterogeneity are introduced by altering this value; (vi) each local population is rounded to give an integer number of individuals at the end of each generation so that those with density below unity may become extinct, with a probability inversely proportional to density. 3 In spatially homogeneous and heterogeneous harsh environments with moderate levels of density-dependent competition, all populations persisted and dispersal aided metapopulation growth when the population growth rate was sufficiently large. When the population growth rate was smaller, dispersal increased the risk of, and speeded up the time to, metapopulation extinction. Metapopulation growth was faster when the heterogeneity was at a larger-scale spatial pattern. 4 Temporal heterogeneity had an adverse effect when added to the existing spatial heterogeneity; strongly dispersing metapopulations were affected only slightly, while those with only moderate or no dispersal became extinct. The more frequently the environment changed, the greater was the probability of extinction. 5 The model simulations in 2-4 were repeated for more-severe density-dependence. In the spatially homogeneous environment dispersal prevented metapopulation extinction, while lack of dispersal encouraged it. Dispersal aided metapopulation growth in the spatially heterogeneous unchanging environment. The addition of temporal heterogeneity had little effect on populations with strong dispersal but the effect on the other metapopulations was catastrophic.

[1]  J. González-Andújar,et al.  The effect of dispersal between chaotic and non-chaotic populations within a metapopulation , 1993 .

[2]  R. May,et al.  Biological populations obeying difference equations: stable points, stable cycles, and chaos. , 1975, Journal of theoretical biology.

[3]  U. Motro.  Optimal rates of dispersal II. Diploid populations , 1982 .

[4]  Jonathan Silvertown,et al.  Modularity, reproductive thresholds and plant population dynamics , 1991 .

[5]  C. Fernández-Quintanilla.  Studying the population dynamics of weeds , 1988 .

[6]  M. Gilpin,et al.  Metapopulation dynamics: a brief his-tory and conceptual domain , 1991 .

[7]  J. Perry.  Some models for spatial variability of animal species. , 1988 .

[8]  B. A. Auld,et al.  INVADE: Towards the simulation of plant spread , 1990 .

[9]  David Tilman,et al.  Oscillations and chaos in the dynamics of a perennial grass , 1991, Nature.

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

[11]  M. Crawley,et al.  Growth, reproduction and population dynamics , 1989 .

[12]  Andrew R. Watkinson,et al.  Density-dependence in single-species populations of plants , 1980 .

[13]  James F. Quinn,et al.  Correlated environments and the persistence of metapopulations , 1989 .

[14]  Robert M. May,et al.  Patterns of Dynamical Behaviour in Single-Species Populations , 1976 .

[15]  S. Moss,et al.  The seed cycle of Alopecurus myosuroides in winter cereals: a quantitative analysis. , 1990 .

[16]  Michael P. Hassell,et al.  DENSITY-DEPENDENCE IN SINGLE-SPECIES POPULATIONS , 1975 .

[17]  Ilkka Hanski,et al.  Single‐species metapopulation dynamics: concepts, models and observations , 1991 .

[18]  H. Hanski,et al.  Cross-correlation in population dynamics and the slope of spatial variance-mean regressions , 1987 .

[19]  Jacob Weiner,et al.  A Neighborhood Model of Annual‐Plant Interference , 1982 .

[20]  C. Ballaré,et al.  The demography of Datura ferox (L.) in soybean crops , 1987 .

[21]  Richard H. Elderkin.  Seed dispersal in a patchy environment with global age dependence , 1982 .

[22]  Jacob Weiner,et al.  Dispersal and neighborhood effects in an annual plant competition model , 1981 .

[23]  Jonathan Silvertown,et al.  Cellular Automaton Models of Interspecific Competition for Space--The Effect of Pattern on Process , 1992 .

[24]  G. W. Cussans,et al.  The dispersal of weeds: seed movement in arable agriculture , 1991 .

[25]  Claudio M. Ghersa,et al.  The population ecology of Datura ferox in soybean crops. A simulation approach incorporating seed dispersal , 1987 .

[26]  Bruce D. Maxwell,et al.  The Influence of Weed Seed Dispersion Versus the Effect of Competition on Crop Yield , 1992, Weed Technology.

[27]  J. Metz,et al.  An Explanation for Low Dispersal Rates: a Simulation Experiment , 1982 .

[28]  J. Conn.  Seed Viability and Dormancy of 17 Weed Species After Burial for 4.7 Years in Alaska , 1990, Weed Science.

[29]  T. Czárán,et al.  Spatiotemporal dynamic models of plant populations and communities. , 1992, Trends in ecology & evolution.

[30]  E. Marshall.  DISTRIBUTION PATTERNS OF PLANTS ASSOCIATED WITH ARABLE FIELD EDGES , 1989 .

[31]  J. Perry,et al.  A new index of aggregation for animal counts. , 1991, Biometrics.

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

[33]  Alan Hastings,et al.  Dispersal strategies in patchy environments , 1984 .

[34]  P. Gould,et al.  On robust weed population models , 1989 .

[35]  J. Perry.  Effects of spatial heterogeneity on Jones's model for cyst-nematode population dynamics and crop root damage. , 1983 .

[36]  P. Brain,et al.  Long‐term stability of distribution of Alopecurus myosuroides Huds. within cereal fields , 1991 .

[37]  R. Levins.  Some Demographic and Genetic Consequences of Environmental Heterogeneity for Biological Control , 1969 .

[38]  Joel s. Brown,et al.  The Selective Interactions of Dispersal, Dormancy, and Seed Size as Adaptations for Reducing Risk in Variable Environments , 1988, The American Naturalist.

[39]  J. Metz,et al.  Life history tactics of annual organisms: The joint effects of dispersal and delayed germination , 1987 .

[40]  José Luis González-Andújar,et al.  Chaos, metapopulations and dispersal , 1993 .

[41]  C. Fernández-Quintanilla,et al.  Seedling recruitment and age-specific survivorship and reproduction in populations of Avena sterilis L. ssp. ludoviciana (Durieu) Nyman. , 1986 .

[42]  T. E. Thórhallsdóttir,et al.  The dynamics of five grasses and white clover in a simulated mosaic sward. , 1990 .

[43]  John L. Harper,et al.  INTERFERENCE IN DUNE ANNUALS: SPATIAL PATTERN AND NEIGHBOURHOOD EFFECTS , 1977 .

[44]  L. R. Taylor,et al.  Aggregation, migration and population mechanics , 1977, Nature.

[45]  P. J. Boer,et al.  Spreading of risk and stabilization of animal numbers , 1968 .

[46]  L. Taylor,et al.  Synoptic Dynamics, Migration and the Rothamsted Insect Survey: Presidential Address to the British Ecological Society, December 1984 , 1986 .

[47]  R. May,et al.  STABILITY IN INSECT HOST-PARASITE MODELS , 1973 .

[48]  Robert M. May,et al.  Dispersal in stable habitats , 1977, Nature.

[49]  C. Horvitz,et al.  Seed dispersal and environmental heterogeneity in a neotropical herb: a model of population and patch dynamics , 1986 .