Abstract
In his seminal work in the 1970s, Robert May suggested that there is an upper limit to the number of species that can be sustained in stable equilibrium by an ecosystem. This deduction was at odds with both intuition and the observed complexity of many natural ecosystems. The so-called stability-diversity debate ensued, and the discussion about the factors contributing to ecosystem stability or instability continues to this day. We show in this work that dispersal can be a destabilising influence. To do this, we combine ideas from Alan Turing’s work on pattern formation with May’s random-matrix approach. We demonstrate how a stable equilibrium in a complex ecosystem with trophic structure can become unstable with the introduction of dispersal in space, and we discuss the factors which contribute to this effect. Our work highlights that adding more details to the model of May can give rise to more ways for an ecosystem to become unstable. Making May’s simple model more realistic is therefore unlikely to entirely remove the upper bound on complexity.
Highlights
In his seminal work in the 1970s, Robert May suggested that there is an upper limit to the number of species that can be sustained in stable equilibrium by an ecosystem
We show that equilibria which would be stable without spatial effects can be destabilised by dispersal. We find that this dispersalinduced instability is possible in a linear model and in a non-linear system where the equilibrium is arrived at dynamically and is feasible by construction
We present simulation data of a complex ecosystem obeying non-linear Levin–Segel-type dynamics[31]
Summary
In his seminal work in the 1970s, Robert May suggested that there is an upper limit to the number of species that can be sustained in stable equilibrium by an ecosystem. This deduction was at odds with both intuition and the observed complexity of many natural ecosystems. For a fixed variance of interactions, there is an upper bound to the number of species and food web connections that the ecosystem can sustain This idea quickly became controversial and May’s work sparked the so-called complexity-stability (or diversity-stability) debate, which continues to this day[5,6,9]. It is understood that there are a number of senses in which an ecosystem can be unstable and, there are a number of ways one can define diversity[5,10]
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