Eco-evolutionary modelling of microbial syntrophy indicates the robustness of cross-feeding over cross-facilitation.

Syntrophic cooperation among prokaryotes is ubiquitous and diverse. It relies on unilateral or mutual aid that may be both catalytic and metabolic in nature. Hypotheses of eukaryotic origins claim that mitochondrial endosymbiosis emerged from mutually beneficial syntrophy of archaeal and bacterial partners. However, there are no other examples of prokaryotic syntrophy leading to endosymbiosis. One potential reason is that when externalized products become public goods, they incite social conflict due to selfish mutants that may undermine any mutualistic interactions. To rigorously evaluate these arguments, here we construct a general mathematical framework of the ecology and evolution of different types of syntrophic partnerships. We do so both in a general microbial and in a eukaryogenetic context. Studying the case where partners cross-feed on each other's self-inhibiting waste, we show that cooperative partnerships will eventually dominate over selfish mutants. By contrast, systems where producers actively secrete enzymes that cross-facilitate their partners' resource consumption are not robust against cheaters over evolutionary time. We conclude that cross-facilitation is unlikely to provide an adequate syntrophic origin for endosymbiosis, but that cross-feeding mutualisms may indeed have played that role.

Coexistence of inertial competitors in chaotic flows.

We investigate the dynamics of inertial particles immersed in open chaotic flows. We consider the generic problem of competition between different species, e.g., phytoplankton populations in oceans. The strong influence from inertial effects is shown to result in the persistence of different species even in cases when the passively advected species cannot coexist. Multispecies coexistence in the ocean can be explained by the fact that the unstable manifold is different for each advected competitor of different size.

Stabilizing factors interact in promoting host-parasite coexistence.

Understanding the mechanisms that promote coexistence among species is a fundamental problem in evolutionary ecology. Such mechanisms include environmental noise, spatial population structure, density dependence, and genetic variation. In natural populations such factors may exert combined effects on coexistence. Thus, to disentangle the contribution of several factors to coexistence, their effects have to be considered simultaneously. Here we investigate the effects of Ricker-type density dependence, genetic variation, and the frequency of sex on host-parasite coexistence, using Nicholson-Bailey models with and without host density dependence. Interestingly, a low frequency of sex (and the genetic variation induced by sex) is the most important factor in explaining the stability of the host-parasite interaction. However, the carrying capacity K and the frequency of sex interact in affecting coexistence. If K is low (strong density regulation), coexistence is easily attained in the density-dependent model, independently of the frequency of sex. In contrast, for high values of K (weak density regulation), low frequencies of sex considerably improve coexistence. Thus, our results suggest that coexistence among species may strongly depend on interactions among several stabilizing factors. These results seem to be robust since they remain qualitatively unchanged if one assumes (1) Beverton-Holt-type or genotype-specific rather than Ricker-type density dependence in the host, or (2) different genotype-specific susceptibilities of hosts to their parasites, or if one adds (3) moderate levels of environmental stochasticity.

Data estimation and the colour of time series.

There has been a long debate on the source of temporal fluctuations in natural population densities. The difficulty is that unpredictable irregularities might be attributed either to external environmental factors or to chaotic dynamics of populations, or even to the interaction of these two factors. Some years ago Cohen (1995) pointed out that real time series follow redshifted Fourier power spectra, while the simplest chaotic population dynamical models are mostly blueshifted. Since then, the controversy has focused on comparisons of Fourier spectra originating from different models and data. Here, we show experimentally that estimation process by human observers shifts power spectra to the red. This result implies that because of estimation distortion, real population data must be less redshifted than many recorded time series suggest.

Survival of replicators with parabolic growth tendency and exponential decay.

The claim that the competition of parabolically growing self-replicators leads to dynamically stable coexistence was challenged by Lifson & Lifson [(1999). J. theor. Biol.199, 425-433]. They have shown that, if single- and double-strands are treated separately, and only single-strands undergo spontaneous decay, then there is natural selection rather than survival of everybody. We use their models to show that if double-strand decay is not neglected, then dynamical coexistence is still possible under a wide range of parameter values, in agreement with the chromatographized replicator model of von Kiedrowski & Szathmáry [(2000). Selection 1-3, 173-179]. Coexistence is always ensured above a critical resource (monomer) inflow rate. Recycling of decayed replicators into monomers further favours dynamical coexistence. The claim that parabolic growth invariably results in coexistence remains valid for the model for which it was meant to apply, namely for parabolic growth without template decay. Exponential decay acting on single- and double-strands, combined with parabolic growth, may or may not result in a dynamical coexistence of self-replicators.

Chaotic flow: the physics of species coexistence.

Hydrodynamical phenomena play a keystone role in the population dynamics of passively advected species such as phytoplankton and replicating macromolecules. Recent developments in the field of chaotic advection in hydrodynamical flows encourage us to revisit the population dynamics of species competing for the same resource in an open aquatic system. If this aquatic environment is homogeneous and well-mixed then classical studies predict competitive exclusion of all but the most perfectly adapted species. In fact, this homogeneity is very rare, and the species of the community (at least on an ecological observation time scale) are in nonequilibrium coexistence. We argue that a peculiar small-scale, spatial heterogeneity generated by chaotic advection can lead to coexistence. In open flows this imperfect mixing lets the populations accumulate along fractal filaments, where competition is governed by an "advantage of rarity" principle. The possibility of this generic coexistence sheds light on the enrichment of phytoplankton and the information integration in early macromolecule evolution.

Mesoscale vortices and the paradox of the plankton.

Coexistence of competitive species is severely limited by the availability of resources and the characteristics of the environment. In particular, the so-called 'competitive exclusion principle' states that, at equilibrium, the number of coexisting species cannot be larger than the number of resources for which they compete. However, many in situ observations have revealed prolonged coexistence of a large number of competitive plankton species, a phenomenon known as 'the paradox of the plankton'. Here we investigate this problem and show that ocean mesoscale vortices generate transport barriers and incomplete horizontal mixing, allowing for a prolonged survival of the less-fit species, even for fully homogeneous resource distributions. In such a situation, the temporarily less-fit plankton species are protected from competition by the action of the vortices.

Allee Effect Increases the Dynamical Stability of Populations.

The discrepancy between the frequent complex behaviour of simple population dynamical models and the relative dynamical simplicity of most experimental data encourages theoretical ecologists to revise the basic assumptions of the models. Among many other results, it has been shown recently that sexual reproduction increases dynamical stability, merely because population genetical process is introduced in the models. Here, we investigate another general consequence of sexual reproduction, the cost of rarity or the Allee effect, from a dynamical point of view. We show that the cost of rarity increases the stability of (the stable) fixed point in a broad class of one-dimensional difference equation systems. The strong stabilization due to the Allee effect is demonstrated by the numerical simulation of a host-microparasite model as well. Copyright 1999 Academic Press.

On the evolution of density dependent dispersal in a spatially structured population model.

A simple metapopulation lattice model of two competing phenotypes is presented, where one phenotype reacts more sensitively to overcrowding by migrating to neighbouring local habitats. The sensitivity is formulated by means of a threshold density of the subpopulations, above which dispersal is triggered off. If this threshold density is not very far from the local carrying capacity, an increased mobility provides benefits on the metapopulation level. At a surprisingly small difference between migrational triggering thresholds, the phenotype of larger mobility (or lower threshold) squeezes out the less mobile one from the whole system in a wide parameter range. Evolutionary considerations give an optimal threshold level for our model metapopulation.