We investigate the outcome of  Lotka-Volterra dynamics of ecological communities with random interaction coefficients and non-linear functional response . We show in simulations that the saturation of Holling type-II response stabilises the dynamics. This is confirmed in an analytical generating-functional approach to  Lotka-Volterra equations with piecewise linear saturating response. For such systems we are able to derive self-consistent relations governing the stable fixed-point phase, and to carry out a linear stability analysis to predict the onset of unstable behaviour. We investigate in detail the combined effects of the mean and variance of the random interaction coefficients, the cut-off parameter of the non-linear response , and a symmetry parameter . We find that stability and diversity increases with the introduction of functional response , where decreasing the functional response parameter has a similar effect to decreasing the symmetry parameter . We also find biomass and diversity to be less dependent on the symmetry of interactions with functional response, and co-operation to no longer have a detrimental effect on stability .
We investigate the outcome of generalised Lotka-Volterra dynamics of ecological communities with random interaction coefficients and non-linear feedback . We show in simulations that the saturation of non-linear feedback stabilises the dynamics. This is confirmed in an analytical generating-functional approach to generalised Lotka-Volterra equations with piecewise linear saturating response. For such systems we are able to derive self-consistent relations governing the stable fixed-point phase, and to carry out a linear stability analysis to predict the onset of unstable behaviour. We investigate in detail the combined effects of the mean , variance and co-variance of the random interaction coefficients, and the saturation value of the non-linear response . We find that stability and diversity increases with the introduction of non-linear feedback , where decreasing the saturation value has a similar effect to decreasing the co-variance . We also find co-operation to no longer have a detrimental effect on stability with non-linear feedback, and the order parameters mean abundance and diversity to be less dependent on the symmetry of interactions with stronger saturation .
A
generalised
R
functional response
feedback
R
Holling type-II response
non-linear feedback
A
generalised
R
and variance
, variance and co-variance
R
the cut-off parameter
and the saturation value
D
, and a symmetry parameter
R
functional response
non-linear feedback
R
functional response parameter
saturation value
R
symmetry parameter
co-variance
R
biomass and
co-operation to no longer have a detrimental effect on stability with non-linear feedback, and the order parameters mean abundance and
R
functional response, and co-operation to no longer have a detrimental effect on stability
stronger saturation