My project aims to model population dynamics of a 3 trophic levels system: primary producers, herbivores and predator. I try to predict how changes in the vegetation abundance might affect higher trophic levels. My herbivores are described through juvenile and adults compartments, with the first "supplying" the other, after a maturation time. My predator only has an "adult" life stage.

Currently, I'm a bit struggling, because no matter what vegetation biomass or initial densities I put in the system, it always converges toward the same densities. The system reaches an equilibrium stable point, no matter the amount of food available for my herbivores, which is quite a problem for my study.

Could anyone enlighten me with some ideas of what to test/look for to resolve my issue?

Of course, I can give more details about my simulations (done with R and Rstudio, with the deSolve package) and the structure of my equations (Lotka-Volterra).

Thanks a lot in advance.

  • $\begingroup$ If you're still interested in the answer, can you edit your questions to include the actual equations (either a R code or as mathematical notation, ideally in LaTeX but text would be OK -- just not an image/screenshot in either case) you're working with? $\endgroup$
    – Ben Bolker
    Feb 25 at 19:02
  • $\begingroup$ Hi @BenBolker, Yes I'm still interested! I'll try to edit my post as soon as possible. Thanks a lot $\endgroup$
    – Rachel
    Mar 2 at 0:27

1 Answer 1


In a deterministic system, there are 2 options: equilibrium or collapse. It sounds like you've found an equilibrium. This is probably expected!

Classic Lotka-Volterra makes specific deterministic claims about the equilibrium population levels:

Secondly, the population equilibrium of this model has the property that the prey equilibrium density (given by $x=\gamma /\delta$) depends on the predator's parameters, and the predator equilibrium density (given by $y=\alpha /\beta$) on the prey's parameters.

As long as your inputs are consistent with the model (e.g. nonzero), they should come to equilibrium. You are basically finding the abundance states where change in frequency over time is zero.

I don't know much about the deSolve implementation, but I'd suggest varying not the initial densities but the other parameters ($\alpha, \beta, \delta, \gamma$) to see how that changes your solution.

If you are interested in exploring error bounds beyond the classic model, I'd suggest exploring a stochastic version of the model or a different modeling regime.


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