Relating individual behaviour to population dynamics

How do the behavioural interactions between individuals in an ecological system produce the global population dynamics of that system? Wepresent a stochastic individual–based model of the reproductive cycle of the mite Varroa jacobsoni, a parasite of honeybees. The model has the interesting property in that its population level behaviour is approximated extremely accurately by the exponential logistic equation or Ricker map. We demonstrated how this approximation is obtained mathematically and how the parameters of the exponential logistic equation can be written in terms of the parameters of the individual–based model. Our procedure demonstrates, in at least one case, how study of animal ecology at an individual level can be used to derive global models which predict population change over time.

[1]  Tamás Czárán,et al.  Spatiotemporal models of population and community dynamics , 1998 .

[2]  A. Łomnicki.  Individual-based models and the individual-based approach to population ecology , 1999 .

[3]  Robert A. Cheke,et al.  Complex dynamics of desert locust plagues , 1993 .

[4]  D J Sumpter,et al.  Ants and agents: A process algebra approach to modelling ant colony behaviour , 2001, Bulletin of mathematical biology.

[5]  N. Dung,et al.  Reproductive success of Varroa jacobsoni in brood of its original host, Apis cerana , in comparison to that of its new host, A. mellifera (Hymenoptera: Apidae) , 1997 .

[6]  Peter Turchin,et al.  Complex Dynamics in Ecological Time Series , 1992 .

[7]  M. Kot,et al.  8. Differential systems in ecology and epidemiology , 1986 .

[8]  Simon A. Levin,et al.  Stochastic Spatial Models: A User's Guide to Ecological Applications , 1994 .

[9]  A. Dixon,et al.  Population dynamics of a tree-dwelling aphid: individuals to populations , 1996 .

[10]  M. Hassell.  The dynamics of arthropod predator-prey systems. , 1979, Monographs in population biology.

[11]  N. Rashevsky,et al.  Mathematical biology , 1961, Connecticut medicine.

[12]  L. Oksanen,et al.  Are lemmings prey or predators? , 2000, Nature.

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

[14]  W. Rath.  Co-adaptation of Apis cerana Fabr. and Varroa jacobsoni Oud , 1999 .

[15]  Ricard V. Solé,et al.  Controlling chaos in ecology: From deterministic to individual-based models , 1999, Bulletin of mathematical biology.

[16]  W. Rath.  The key to Varroa: the drones of Apis cerana and their cell cap , 1992 .

[17]  W. Drescher,et al.  Response of Apis cerana Fabr. towards brood infested with Varroa jacobsoni Oud. and infestation rate of colonies in Thailand. , 1990 .

[18]  S. Martin.  A population model for the ectoparasitic mite Varroa jacobsoni in honey bee (Apis mellifera) colonies , 1998 .

[19]  Ian P. Woiwod,et al.  Detecting chaotic dynamics of insect populations from long‐term survey data , 1997 .

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

[21]  Pejman Rohani,et al.  Persistence, chaos and synchrony in ecology and epidemiology , 1998, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[22]  Y. Capowiez,et al.  Does the Spatial Distribution of the Parasitic Mite Varroa jacobsoni Oud. (Mesostigmata: Varroidae) in Worker Brood of Honey Bee Apis Mellifera L. (Hymenoptera: Apidae) Rely on an Aggregative Process? , 1999, Naturwissenschaften.

[23]  S. Camazine,et al.  Population dynamics of Varroa Jacobsoni: a model and a review , 1994 .

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

[25]  A. Nicholson.  An outline of the dynamics of animal populations. , 1954 .

[26]  David A. Rand,et al.  Correlation Equations and Pair Approximations for Spatial Ecologies , 1999 .

[27]  A. Dixon,et al.  Population dynamics of tree-dwelling aphids: the importance of seasonality and time scale , 1997 .