Effects of intraspecific cooperative interactions in large ecosystems

Abstract

We analyze the role of the Allee effect - a positive correlation between population density and mean individual fitness - for ecological communities formed by a large number of species. Our study is performed using the generalized Lotka-Volterra model with random interactions between species. We obtain the phase diagram and analyze the nature of the multiple equilibria phase. Remarkable differences emerge with respect to the logistic growth case, thus revealing the major role played by the functional response in determining aggregate behaviors of large ecosystems.

Antagonistic interactions can stabilise fixed points in heterogeneous linear dynamical systems

“…Another issue is that A is the Jacobian matrix, which is in general different from the interaction matrix. Nevertheless, studies in, among others, ecology [12][13][14] and neuroscience [2,3], show that nonlinear systems do exhibit regimes with one unique stationary fixed point and random matrix theory can provide insights on system stability in this regime. In the ecological context for symmetric interactions J i j = J ji , Refs.…”

“…Moreover, note that for symmetric interactions replica theory can be used to determine the leading eigenvalue of the Hessian, see Refs. [12,14,58], while for nonsymmetric interactions this is not possible.…”

“…Although one should be careful in drawing conclusions about the dynamics of nonlinear systems from the study of randomly coupled linear differential equations, random matrix theory has the advantage of providing analytical insights about the influence of interactions on linear stability. In fact, linear stability analyses with random matrix theory have been used to study the onset of chaos in random neural networks [2][3][4], the stability of ecosystems modelled by Lotka-Volterra equations with random interactions [8][9][10][11][12][13][14], economies [15], or gene regulatory networks [16]. Moreover, although traditionally random matrix models are fully connected, recently exact results have been derived for the stability of linear models defined on complex networks [17][18][19].…”

An Introduction to the Theory of Spin Glasses

“…In fact, theories based on disordered systems often reveal to be beneficial for the treatment of problems outside the domain of SGs. Heterogeneous systems, either with quenched or self-generated disorder, are much more general than it might be believed at first glance, ranging from neural networks and optimization problems [53,54,57,[187][188][189][190][191][192][193], signal reconstruction [194,195], random lasers [196,197], financial markets [198][199][200], supercooled liquids and jammed packings [201][202][203][204][205] and theoretical ecology [206][207][208][209][210][211][212][213][214], and thermodynamic and dynamic formalisms rooted in spin-glass theory can still be used to solve them.…”

Diversity begets stability: Sublinear growth and competitive coexistence across ecosystems

“…Applied to community ecology, this method consists in mapping the dynamical system to a disordered system at thermal equilibrium with HamiltonianH=140%true∑iVBi+140%true∑i<jAijBiBjwhere V represents self-regulation and temperature measures the strength of demographic fluctuations. Studying the corresponding free energy landscape, in particular the complex structure of its global and local minima using the “replica trick,” allows predictions of phase transitions in this system ( 94 , 95 ). We describe in supplementary materials, section S3.2 ( 54 ), how the boundary line between stable and unstable dynamics can be computed as a function of (μ, σ) in the GLV and sublinear models.…”