The Lotka Volterra model is the basic model for predator-prey interactions. Is it also used for herbivore-plant interactions or is there a different, equivalently standard model for herbivore-plant interactions? And has there been research on using the Lotka Volterra model with an additional carrying capacity for the prey?
If you are going to include plant density dependence (as the Lotka-Volterra does) as well as herbivore effects on plants and plant effects on herbivores, be aware that there are better ways to model density-dependence among plants than the logistic/Lotka-Volterra. We (and many others) have found that found that the type of function described by Firbank and Watkinson 1985 (N2 = N1 * 1/(1 + constant*N1)) gives a much better fit (Fowler and Pease 2010) for density-dependence in plants than the logistic (the logistic is just the LV without other species). This consideration is relevant whether or not you are using an individual-based model.
There are a number of excellent studies that have modeled plant-herbivore interactions. For example, Buckley et al. 2005. Stable coexistence of an invasive plant and biocontrol agent: a parameterized coupled plant–herbivore model. Or Abbott and Dwyer 2007 (Food limitation and insect outbreaks: complex dynamics in plant–herbivore models) who, as we did, compared different algebraic functions
See also the review by Maron and Crone 2006 (Herbivory: effects on plant abundance, distribution and population growth).
A final note: if you use an individual-based model where each plant occupies a different cell in a cellular automata-type map, you will be including density-dependence implicitly and therefore probably do not need to worry about the shape of the density-dependent function.
Good luck!
See: Alternatives to Lotka-Volterra competition: Models of intermediate complexity, http://dx.doi.org/10.1016/0040-5809(76)90022-8 for alternatives.
I hope this helps!
Andrew :-)
Instead of the LV model, you can use the Nicholson-Bailey model which is originally a host-parasite model but that works well for a plant-herbivore system as well. See for example https://math.la.asu.edu/~dieter/papers/herbivore.pdf
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