32 research outputs found
Species Abundance Patterns in Complex Evolutionary Dynamics
An analytic theory of species abundance patterns (SAPs) in biological
networks is presented. The theory is based on multispecies replicator dynamics
equivalent to the Lotka-Volterra equation, with diverse interspecies
interactions. Various SAPs observed in nature are derived from a single
parameter. The abundance distribution is formed like a widely observed
left-skewed lognormal distribution. As the model has a general form, the result
can be applied to similar patterns in other complex biological networks, e.g.
gene expression.Comment: 4 pages, 3 figures. Physical Review Letters, in pres
Statistical mechanics and stability of a model eco-system
We study a model ecosystem by means of dynamical techniques from disordered
systems theory. The model describes a set of species subject to competitive
interactions through a background of resources, which they feed upon.
Additionally direct competitive or co-operative interaction between species may
occur through a random coupling matrix. We compute the order parameters of the
system in a fixed point regime, and identify the onset of instability and
compute the phase diagram. We focus on the effects of variability of resources,
direct interaction between species, co-operation pressure and dilution on the
stability and the diversity of the ecosystem. It is shown that resources can be
exploited optimally only in absence of co-operation pressure or direct
interaction between species.Comment: 23 pages, 13 figures; text of paper modified, discussion extended,
references adde
Rank abundance relations in evolutionary dynamics of random replicators
We present a non-equilibrium statistical mechanics description of rank
abundance relations (RAR) in random community models of ecology. Specifically,
we study a multi-species replicator system with quenched random interaction
matrices. We here consider symmetric interactions as well as asymmetric and
anti-symmetric cases. RARs are obtained analytically via a generating
functional analysis, describing fixed-point states of the system in terms of a
small set of order parameters, and in dependence on the symmetry or otherwise
of interactions and on the productivity of the community. Our work is an
extension of Tokita [Phys. Rev. Lett. {\bf 93} 178102 (2004)], where the case
of symmetric interactions was considered within an equilibrium setup. The
species abundance distribution in our model come out as truncated normal
distributions or transformations thereof and, in some case, are similar to
left-skewed distributions observed in ecology. We also discuss the interaction
structure of the resulting food-web of stable species at stationarity, cases of
heterogeneous co-operation pressures as well as effects of finite system size
and of higher-order interactions.Comment: 12 pages, 14 figures; text amended, minor corrections/modifications
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