Dynamical mechanism for coexistence of dispersing species

Synchronization within synchronization: transients and intermittency in ecological networks

Transients are fundamental to ecological systems with significant implications to management, conservation and biological control. We uncover a type of transient synchronization behavior in spatial ecological networks whose local dynamics are of the chaotic, predator–prey type. In the parameter regime where there is phase synchronization among all the patches, complete synchronization (i.e. synchronization in both phase and amplitude) can arise in certain pairs of patches as determined by the network symmetry—henceforth the phenomenon of  ‘synchronization within synchronization.’ Distinct patterns of complete synchronization coexist but, due to intrinsic instability or noise, each pattern is a transient and there is random, intermittent switching among the patterns in the course of time evolution. The probability distribution of the transient time is found to follow an algebraic scaling law with a divergent average transient lifetime. Based on symmetry considerations, we develop a stability analysis to understand these phenomena. The general principle of symmetry can also be exploited to explain previously discovered, counterintuitive synchronization behaviors in ecological networks.

Noise-enabled species recovery in the aftermath of a tipping point

The beneficial role of noise in promoting species coexistence and preventing extinction has been recognized in theoretical ecology, but previous studies were mostly concerned with low-dimensional systems. We investigate the interplay between noise and nonlinear dynamics in real-world complex mutualistic networks with a focus on species recovery in the aftermath of a tipping point. Particularly, as a critical parameter such as the mutualistic interaction strength passes through a tipping point, the system collapses and approaches an extinction state through a dramatic reduction in the species populations to near-zero values. We demonstrate the striking effect of noise: when the direction of parameter change is reversed through the tipping point, noise enables species recovery which otherwise would not be possible. We uncover an algebraic scaling law between the noise amplitude and the parameter distance from the tipping point to the recovery point and provide a physical understanding through analyzing the nonlinear dynamics based on an effective, reduced-dimension model. Noise, in the form of small population fluctuations, can thus play a positive role in protecting high-dimensional, complex ecological networks.

Persistent coexistence of cyclically competing species in spatially extended ecosystems

A fundamental result in the evolutionary-game paradigm of cyclic competition in spatially extended ecological systems, as represented by the classic Reichenbach-Mobilia-Frey (RMF) model, is that high mobility tends to hamper or even exclude species coexistence. This result was obtained under the hypothesis that individuals move randomly without taking into account the suitability of their local environment. We incorporate local habitat suitability into the RMF model and investigate its effect on coexistence. In particular, we hypothesize the use of "basic instinct" of an individual to determine its movement at any time step. That is, an individual is more likely to move when the local habitat becomes hostile and is no longer favorable for survival and growth. We show that, when such local habitat suitability is taken into account, robust coexistence can emerge even in the high-mobility regime where extinction is certain in the RMF model. A surprising finding is that coexistence is accompanied by the occurrence of substantial empty space in the system. Reexamination of the RMF model confirms the necessity and the important role of empty space in coexistence. Our study implies that adaptation/movements according to local habitat suitability are a fundamental factor to promote species coexistence and, consequently, biodiversity.

Two shoot-miners, Ceutorhynchus alliariae and Ceutorhynchus roberti, sharing the same fundamental niche on garlic mustard

A combination of observational and experimental methods, in both the laboratory and field, were used to assess niche partitioning between Ceutorhynchus alliariae Brisout and C. roberti Gyllenhal (Coleoptera: Curculionidae), two coexisting shoot-boring weevils on garlic mustard, Alliaria petiolata (M. Bieb.) Cavara and Grande (Brassicaceae). We compared their morphology, oviposition behavior, larval development, distribution, abundance, and attack rates in their sympatric range, and of C. alliariae when found alone and in sympatry with C. roberti. Results indicate only very small differences in the fundamental niches of the two species. Comparison of C. alliariae in the range it occurs alone with the range where it co-occurs with C. roberti revealed some evidence for competition between the two species, i.e., attack levels of C. alliariae were reduced in areas where it co-occurred with C. roberti. However, the study showed no character displacement in regard to adult size or shoot choice of C. alliariae and we found no indication for superiority of either of the two species. Clearly, manipulative experiments would be necessary to unambiguously test for competition between the two species. Our results, based on a subset of niche dimensions known to be important in other systems, suggest that C. alliariae and C. roberti may present one of the rare cases, in which niche differentiation is not the main mechanism underlying coexistence.

Synchrony in tritrophic food chain metacommunities

The synchronous behaviour of interacting communities is studied in this paper. Each community is described by a tritrophic food chain model, and the communities interact through a network with arbitrary topology, composed of patches and migration corridors. The analysis of the local synchronization properties (via the master stability function approach) shows that, if only one species can migrate, the dispersal of the consumer (i.e., the intermediate trophic level) is the most effective mechanism for promoting synchronization. When analysing the effects of the variations of demographic parameters, it is found that factors that stabilize the single community also tend to favour synchronization. Global synchronization is finally analysed by means of the connection graph method, yielding a lower bound on the value of the dispersion rate that guarantees the synchronization of the metacommunity for a given network topology.

Evolution of predator and prey movement into sink habitats

Mathematical models of predator-prey interactions in a patchy landscape are used to explore the evolution of dispersal into sink habitats. When evolution proceeds at a single trophic level (i.e., either prey or predator disperses), three evolutionary outcomes are observed. If predator-prey dynamics are stable in source habitats, then there is an evolutionarily stable strategy (ESS) corresponding to sedentary phenotypes residing in source habitats. If predator-prey dynamics are sufficiently unstable, then either an ESS corresponding to dispersive phenotypes or an evolutionarily stable coalition (ESC) between dispersive and sedentary phenotypes emerges. Dispersive phenotypes playing an ESS persist despite exhibiting, on average, a negative per capita growth rate in all habitats. ESCs occur if dispersal into sink habitats can stabilize the predator-prey interactions. When evolution proceeds at both trophic levels, any combination of monomorphic or dimorphic phenotypes at one or both trophic levels is observed. Coevolution is largely top-down driven. At low predator mortality rates in sink habitats, evolution of predator movement into sink habitats forestalls evolution of prey movement into sink habitats. Only at intermediate mortality rates is there selection for predator and prey movement. Our results also illustrate an evolutionary paradox of enrichment, in which enriching source habitats can reduce phenotypic diversity.

npr-1 Regulates foraging and dispersal strategies in Caenorhabditis elegans

Wild isolates of Caenorhabditis elegans differ in their tendency to aggregate on food [1, 2]. Most quantitative variation in this behavior is explained by a polymorphism at a single amino acid in the G protein-coupled receptor NPR-1: gregarious strains carry the 215F allele, and solitary strains carry the 215V allele [2]. Although npr-1 regulates a behavioral syndrome with potential adaptive implications, the evolutionary causes and consequences of this natural polymorphism remain unclear. Here we show that npr-1 regulates two behaviors that can promote coexistence of the two alleles. First, gregarious and solitary worms differ in their responses to food such that they can partition a single, continuous patch of food. Second, gregarious worms disperse more readily from patch to patch than do solitary worms, which can cause partitioning of a fragmented resource. The dispersal propensity of both gregarious and solitary worms increases with density. npr-1-dependent dispersal is independent of aggregation and could be part of a food-searching strategy. The gregarious allele is favored in a fragmented relative to a continuous food environment in competition experiments. We conclude that the npr-1 polymorphism could be maintained by a trade-off between dispersal and competitive ability.

Transients: the key to long-term ecological understanding?

Ecological theory has been dominated by a focus on long-term or asymptotic behavior as a way to understand natural systems. Yet experiments are done on much shorter timescales, and the relevant timescales for ecological systems can also be relatively short. Thus, there is a mismatch between the timescales of most experiments and the timescales of many theoretical investigations. However, recent work has emphasized the importance of transient dynamics rather than long-term behavior in ecological systems, enabling the examination of forces that allow coexistence on ecological timescales. Through an examination of what leads to transients in ecological systems, a deeper appreciation of the forces leading to persistence or coexistence in ecological systems emerges, as well as a general understanding of how population levels can change through time.

Remarks on metacommunity synchronization with application to prey-predator systems

The problem of synchronization of metacommunities is investigated in this article with reference to a rather general model composed of a chaotic environmental compartment driving a biological compartment. Synchronization in the absence of dispersal (i.e., the so-called Moran effect) is first discussed and shown to occur only when there is no biochaos. In other words, if the biological compartment is reinforcing environmental chaos, dispersal must be strictly above a specified threshold in order to synchronize population dynamics. Moreover, this threshold can be easily determined from the model by computing a special Lyapunov exponent. The application to prey-predator metacommunities points out the influence of frequency and coherence of the environmental noise on synchronization and agrees with all experimental studies performed on the subject.

Density-dependent migration and synchronism in metapopulations

A spatially explicit metapopulation model with density-dependent dispersal is proposed in order to study the stability of synchronous dynamics. A stability criterion is obtained based on the computation of the transversal Liapunov number of attractors on the synchronous invariant manifold. We examine in detail a special case of density-dependent dispersal rule where migration does not occur if the patch density is below a certain critical density, while the fraction of individuals that migrate to other patches is kept constant if the patch density is above the threshold level. Comparisons with density-independent migration models indicate that this simple density-dependent dispersal mechanism reduces the stability of synchronous dynamics. We were able to quantify exactly this loss of stability through the frequency that synchronous trajectories are above the critical density.

Beneficial role of noise in promoting species diversity through stochastic resonance

There is an increasing recognition that patterns in species diversity cannot be understood without reference to nonequilibrial or unstable dynamics. Recently, through a realistic ecological model that involves dispersal, we have addressed the positive role of noise in promoting species coexistence [Phys. Rev. Lett. 94, 038102 (2005)]. Here we present a physical theory to account for the main scaling law responsible for this phenomenon.

Noise promotes species diversity in nature

Species diversity in nature is accomplished by coexistence. In a spatial environment, inferior but rapidly moving species can coexist with superior but relatively stationary species. Recent work showed that chaotic dynamics can provide the spatiotemporal variation in the fitness required for coexistence, via the dynamical mechanism of synchronization and intermittency. Utilizing a realistic model that consists of two interacting species in a two-patch environment, we discovered a stochastic-resonance phenomenon where noise can significantly enhance the coexistence and thereby promote species diversity.