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Spatial modeling of predator- assisted dispersal Carl Leth Tanner Hill Nichole Zimmerman Colorado State University FEScUE Program, Summer 2008.

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Presentation on theme: "Spatial modeling of predator- assisted dispersal Carl Leth Tanner Hill Nichole Zimmerman Colorado State University FEScUE Program, Summer 2008."— Presentation transcript:

1 Spatial modeling of predator- assisted dispersal Carl Leth Tanner Hill Nichole Zimmerman Colorado State University FEScUE Program, Summer 2008

2 Lines of Logic Spatial dispersal of prey species Predator preference We propose to couple these two ideas through predator-assisted dispersal

3 Results from Dispersal Studies Local dispersal has been found to promote the persistence of interacting populations 1 Wave-like patterns can occur by dispersing predators and prey 2 1.Comins and Hassell 1996 2.Savill and Hogeweg 1999

4 Results from Preference Studies Predator preference with switching has been found to promote stability and persistence in some cases 1 Preference switching lags behind the optimum for changing prey densities 2 Variable interaction strengths can help stabilize a system 3 1.Bonsall and Hassell 1999 3. McCann et al. 1998 2.Abrams and Matsuda 2004

5 Predator-Assisted Dispersal Combines dispersal and predator preference Predators may carry their prey to different spatial locations and deposit them there Empirical studies show that this occurs in nature

6 Example of Predator-Assisted Dispersal Dromph looked at collembolans dispersing entomopathogenic fungi http://en.wikipedia.org/wiki/Image:Isotoma_Habitus.jpgDromph 2001

7 Empirical Studies: Fungi Dispersal Aided by their Predators Rodents were found likely to be important in the dispersal of vesicular- arbuscular mycorrhizal (VAM) fungus spores 1 Australian mammals feeding on hypogeous fungi increased spore dispersal 2 1.Janos and Sahley 1995 2.Johnson 1995

8 Empirical Studies: Fungi Dispersal Aided by their Predators Mammals were observed to disperse spores of ectomycorrhizal fungi 1 Grasshoppers and small mammals transported fungal spores 2 1.Cázares and Trappe 1994 2.Warner, Allen, and MacMahon 1987

9 Our Proposal We will model predator-assisted dispersal of a two prey system with predator preference Preliminary results Intended studies

10 A Brief Overview of the Model Use spatially explicit mathematical model Program simulations in Matlab Simplify model to validate simulation and examine underlying mechanisms

11 Spatial Model Modeled as a rectangular grid Prey are dispersed locally

12 Spatial Model Predators have very high mobility relative to prey, can feed from any patch at any time

13 Predator-Assisted Dispersal Prey have a chance to be carried by predators foraging in their patch Predators deposit prey in a random patch

14 Questions 1. Given predator-assisted dispersal, how does predator preference affect the final densities of the prey species? 2. How does predator-assisted dispersal affect the resistance of static prey densities in the face of a spatial disturbance? 3. How does predator-assisted dispersal affect the resilience of the system in the face of prey-specific infection?

15 Question 1 Hypotheses Given predator-assisted dispersal, how does predator preference affect the final densities of the prey species? High preference decreases fitness due to increased consumption High preference increases fitness due to increased dispersal There is an optimal degree of preference for fitness that balances mortality due to consumption with dispersal

16 Investigating Question 1: Benefits of Preference Give predators a constant predation rate between the two species Vary degree of preference for one species Measure changes in final densities

17 Question 2 Hypotheses How does predator-assisted dispersal affect the resistance of static prey densities in the face of a spatial disturbance? There is no effect Densities are more resistant to change than in control cases Densities are less resistant to change than in control cases

18 Investigating Question 2: Spatial Disturbance Vary size and distribution of disturbance Measure recovery time and prey densities after recovery

19 Question 3 Hypotheses How does predator-assisted dispersal affect the resilience of the system in the face of prey-specific infection? No effect Resilience is decreased because the predators carry infected individuals Resilience is increased because it causes patchiness

20 Patchiness

21 Investigating Question 3: Infection Allow prey to fully colonize habitat Introduce a species-specific infection using an SIR model Measure resilience by how virulent the infection must be to cause extinction of a species

22 The Model

23 The Model: Mortality

24 Dispersal Prey undergo local dispersal with reflective boundary Comins & Hassell 1996

25 SIR Model

26

27 Simplifications of the Model Two competing species in absence of a predator One species in presence of a predator Two competing species in presence of a predator Predator preference, no assisted dispersal Predator-assisted dispersal of a single prey species

28 The Model: Mortality

29 Two competing species in absence of a predator

30 Predator preference, no assisted dispersal Allows us to measure only the negative effect of preference Possible outcomes Exclusion due to preference Decreased final density

31 Predator preference, no assisted dispersal

32 Predator-assisted dispersal of a single prey species Allows us to examine the simplest case of predator-assisted dispersal Possible outcomes Similar outcomes to single predator-prey simplification Increases the speed of colonization

33 Predator-assisted dispersal of a single prey species

34 Complete Model: Predator- assisted dispersal of two prey

35

36 Summary Predator-assisted dispersal combines independent dispersal models with predator preference There is a gap in knowledge at the intersection of these two ideas We propose a mathematical model which investigates these dynamics

37 Future Work Other Models Poisson process Alternate equations Discrete time models Empirical Studies Preference studies Collembolla and fungus

38 Acknowledgements FEScUE and NSF Michael Antolin, Dan Cooley, Don Estep, Sheldon Lee, Stephanie McMahonn, John Moore, Simon Tavener, Colleen Webb

39 References Abrams, P.A., Hiroyuki Matsuda. 2004. Consequences of behavioral dynamics for the population dynamics of predator- prey systems with switching. Popul Ecol 46:13-25. Bonsall, Michael B. Michael P. Hassell. 1999. Parasitiod- mediated effects: apparent competition and the persistence of host-parasitiod assemblages. Res Popul Ecol 41:59-68. Cázares, Efrén, James M. Trappe. 1994. Spore dispersal of ectomycorrhizal fungi on a glacier forefront by mammal mycophagy. Mycologia 86:507-510. Comins, H.N., M.P. Hassell. 1996. Persisence of Multispecies Host-Parasitoid Interactions in Spatially Distributed Models with Local Dispersal. J. theor. Biol. 183:19-28. Dromph, Karsten M., 2001. Dispersal of entomopathogenic fungi by collembolans. Soil Biology & Biochemistry 33:2047-2051.

40 References Continued… Janos, David P., Catherine T. Sahley. 1995. Rodent Dispersal of Vesicular-Arbuscular Mycorrhizal Fungi in Amasonian Peru. Ecology 76:1852-1858. Johnson, C.N., 1995. Interactions between fire, mycophagous mammals, and dispersal of ectromycorrhizal fungi in Eucalyptus forests. Oecologia 104:467-475. Krause, A. E., K. A. Frank, D. M. Mason, R. E. Ulanowicz, W. W. Taylor. 2003. Compartments revealed in food-web structure. Nature 426:282- 285. McCann, Kevin, Alan Hastings, Gary R. Huxel. 1998. Weak trophic interactions and the balance of nature. Nature 395: 794-797. Savill, Nicholas J., Paulien Hogeweg. 1999. Competition and Dispersal in Predator-Prey Waves. Theoretical Population Biology 56: 243-263. Waren, Nancy J., Michael F. Allen, James A. MacMahon. 1987. Dispersal Agents of Vesicular-Arbuscular Mycorrhizal Fungi in a disturbed Arid Ecosystem. Mycologia 79:721-730.


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