Global persistence despite local extinction in acarine predator-prey systems: Lessons from experimental and mathematical exercises.

Publisher Summary This chapter considers the main features of local dynamics in an acarine predator-prey system. It reviews the outcomes of a hierarchy of models of increasing complexity to answer questions such as which features are crucial to the understanding of metapopulation dynamics; whether it would suffice to represent local dynamics in terms of presence/absence of predators and prey, or whether it is crucial to incorporate the local dynamic processes. The chapter reviews some of the predictions that have been experimentally tested, and identifies some key predictions that still await rigorous tests and discusses whether the models under consideration are robust against structural changes and whether they are evolutionarily robust; this means that the models maintain essentially the same structure when exposed to long-term natural selection (for example, evolutionarily stable strategy). The chapter shows how experimental tests play a crucial role in deciding how to comply with evolutionary robustness. It reviews the most pertinent lessons drawn from combining theory and experiment.

[1]  S. Walde.  Immigration and the dynamics of a predator-prey interaction in biological control , 1994 .

[2]  Matthew James Keeling,et al.  Using individual‐based simulations to test the Levins metapopulation paradigm , 2002 .

[3]  William G. Wilson,et al.  Mobility versus density-limited predator-prey dynamics on different spatial scales , 1991, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[4]  B. Croft,et al.  Kin recognition and larval cannibalism by adult females in specialist predaceous mites , 2001, Animal Behaviour.

[5]  V. Jansen,et al.  The dynamics of two diffusively coupled predator-prey populations. , 2001, Theoretical population biology.

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

[7]  G. Nachman,et al.  Temporal and Spatial Dynamics of an Acarine Predator-Prey System , 1981 .

[8]  M. Sabelis,et al.  Evolution of Life-History Patterns in the Phytoseiidae , 1994 .

[9]  A. D. de Roos,et al.  Evolutionary Dynamics of Prey Exploitation in a Metapopulation of Predators , 2002, The American Naturalist.

[10]  M. Sabelis.  How to analyse prey preference when prey density varies? A new method to discriminate between effects of gut fullness and prey type composition , 1990, Oecologia.

[11]  O. Diekmann,et al.  The functional response of predatory mites to the density of two-spotted spider mites , 1986 .

[12]  M. Hassell,et al.  The effects of a pool of dispersers on host-parasitoid systems. , 1997, Journal of theoretical biology.

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

[14]  N. Gough.  Long-term stability in the interaction betweenTetranychus urticae andPhytoseiulus persimilis producing successful integrated control on roses in southeast Queensland , 1991, Experimental & applied acarology.

[15]  M. Holyoak,et al.  Persistence of an Extinction-Prone Predator-Prey Interaction Through Metapopulation Dynamics , 1996 .

[16]  G. Nachman,et al.  Dynamics of spatially structured spider mite populations , 1999 .

[17]  M. Holyoak,et al.  The role of dispersal in predator-prey metapopulation dynamics , 1996 .

[18]  O. Diekmann,et al.  The Dynamics of Physiologically Structured Populations , 1986 .

[19]  Laurence D. Mueller,et al.  Stability in Model Populations , 2000 .

[20]  M. Gilpin,et al.  Metapopulation Biology: Ecology, Genetics, and Evolution , 1997 .

[21]  V. Bailey,et al.  Interaction between hosts and parasites when some host individuals are more difficult to find than others , 1962 .

[22]  Han Olff,et al.  Herbivores Between Plants and Predators , 1999 .

[23]  Allan Stewart-Oaten,et al.  Aggregation by Parasitoids and Predators: Effects on Equilibrium and Stability , 1989, The American Naturalist.

[24]  Maurice W. Sabelis,et al.  The milker-killer dilemma in spatially structured predator-prey interactions , 1995 .

[25]  B. Croft,et al.  Hops as a metapopulation landscape for tetranychid-phytoseiid interactions: perspectives of intra- and interplant dispersal , 1999, Experimental & Applied Acarology.

[26]  Local and global cycles in an acarine predator-prey system: a frequency domain analysis , 1992, Experimental & Applied Acarology.

[27]  J. Metz,et al.  How should we define fitness in structured metapopulation models? Including an application to the calculation of evolutionarily stable dispersal strategies , 1999, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[28]  M. Hassell,et al.  Metapopulation structures affect persistence of predator–prey interactions , 2002 .

[29]  M. Hassell.  Parasitism in patchy environments: inverse density dependence can be stabilizing. , 1984, IMA journal of mathematics applied in medicine and biology.

[30]  R. Lingeman,et al.  Metapopulation dynamics of a persisting predator–prey system in the laboratory: time series analysis , 1997, Experimental & Applied Acarology.

[31]  G. Nachman.  Predator‐prey interactions in a nonequilibrium context: the metapopulation approach to modeling “hide‐and‐seek” dynamics in a spatially explicit tri‐trophic system , 2001 .

[32]  M. Sabelis,et al.  Kin recognition by the predatory mite Iphiseius degenerans: discrimination among own, conspecific, and heterospecific eggs , 2000 .

[33]  M. Baalen,et al.  The evolution of direct and indirect plant defence against herbivorous arthropods , 1999 .

[34]  O. Diekmann,et al.  Overall population stability despite local extinction: the stabilizing influence of prey dispersal from predator-invaded patches , 1988 .

[35]  Vincent A. A. Jansen,et al.  Metapopulation persistence despite local extinction: predator-prey patch models of the Lotka-Volterra type , 1991 .

[36]  O. Diekmann,et al.  Mathematical models of predator/prey/plant interactions in a patch environment , 2006, Experimental & Applied Acarology.

[37]  S. Levin.  Lectu re Notes in Biomathematics , 1983 .

[38]  Maurice W. Sabelis,et al.  Local dynamics, overexploitation and predator dispersal in an acarine predator-prey system , 1999 .

[39]  Experimental validation of a simulation model of the interaction between Phytoseiulus persimilis and Tetranychus urticae on cucumber , 1983 .

[40]  Bradford A. Hawkins,et al.  Theoretical Approaches to Biological Control , 2008 .

[41]  Michael P. Hassell,et al.  The Spatial and Temporal Dynamics of Host-Parasitoid Interactions , 2000 .

[42]  M. Sabelis,et al.  Local dynamics of the interaction between predatory mites and two-spotted spider mites , 1986 .

[43]  C. Huffaker.  Experimental studies on predation : dispersion factors and predator-prey oscillations , 1958 .

[44]  R. Lingeman,et al.  A demonstration of asynchronous local cycles in an acarine predator-prey system , 1992, Experimental & Applied Acarology.

[45]  Michael J. Crawley,et al.  Natural Enemies: The Population Biology of Predators, Parasites and Diseases , 1992 .

[46]  J. G. Charles,et al.  Airborne dispersal ofPhytoseiulus persimilis (Acarina:Phtyoseiidae) from a raspberry garden in New Zealand , 1988, Experimental & Applied Acarology.

[47]  L. Oksanen,et al.  Exploitation Ecosystems in Gradients of Primary Productivity , 1981, The American Naturalist.

[48]  Vincent A. A. Jansen,et al.  Regulation of predator-prey systems through spatial interactions:a possible solution to the paradox of enrichment. , 1995 .

[49]  Maurice W. Sabelis,et al.  Reflections and calculations on a prey-predator-patch problem , 1988 .

[50]  P. Hosseini,et al.  INFERRING COLONIZATION PROCESSES FROM POPULATION DYNAMICS IN SPATIALLY STRUCTURED PREDATOR–PREY SYSTEMS , 2000 .

[51]  L. Slobodkin,et al.  Community Structure, Population Control, and Competition , 1960, The American Naturalist.

[52]  M. Sabelis,et al.  Predators use volatiles to avoid prey patches with conspecifics , 1997 .

[53]  Maurice W. Sabelis,et al.  The Dynamics of Multiple Infection and the Evolution of Virulence , 1995, The American Naturalist.

[54]  C. Huffaker,et al.  Experimental studies on predation: Complex dispersion and levels of food in an acarine predator-prey interaction , 1963 .

[55]  V. Jansen,et al.  Phase locking: another cause of synchronicity in predator-prey systems. , 1999, Trends in ecology & evolution.

[56]  V. Jansen.  Effects of dispersal in a tri-trophic metapopulation model , 1995 .

[57]  P. W. Murphy,et al.  Acari: reproduction, development and life history strategies. , 1991 .

[58]  Peter Chesson,et al.  Aggregation of Risk: Relationships Among Host-Parasitoid Models , 1986, The American Naturalist.

[59]  M. Sabelis,et al.  Spider Mites Avoid Plants with Predators , 1999, Experimental & Applied Acarology.

[60]  K. Sigmund,et al.  Evolution of exploitation and defence in plant-herbivore-predator interactions. , 2002 .

[61]  Petra Klepac,et al.  Stabilizing dispersal delays in predator-prey metapopulation models. , 2002, Theoretical population biology.

[62]  M. Sabelis,et al.  Phytoseiid life-histories, local predator-prey dynamics, and strategies for control of tetranychid mites , 1992, Experimental & Applied Acarology.

[63]  M. Houck.  Mites: Ecological and Evolutionary Analyses of Life-History Patterns , 1993 .

[64]  R M Nisbet,et al.  Habitat structure and population persistence in an experimental community , 2001, Nature.

[65]  Robert M. May,et al.  HOST-PARASITOID SYSTEMS IN PATCHY ENVIRONMENTS: A PHENOMENOLOGICAL MODEL , 1978 .

[66]  R. May,et al.  Aggregation of Predators and Insect Parasites and its Effect on Stability , 1974 .