On feasible random ecosystems

Only a fraction of the total number of equilibrium solutions of the differential system which describes the populations of species in an ecosystem are feasible: that is only a fraction of the solutions give non-negative values for all the populations. The feasible equilibrium solutions of a generalized logistic equation are considered for the limiting cases of strongly and weakly interacting species. It is found that only about one third of all the possible species are generally expected to be present (i.e. to have non-zero populations) at any given equilibrium solution.     

Inference on system parameters in a model for interacting species

A system of p interacting species whose behaviour can be approximated by a Markovian model is considered. Estimates for system parameters are obtained by the method of moments, when the means, variances and covariances can be estimated from observed population sizes over a period of time. Further, approximate standard errors of these estimates are obtained using the -technique.     

Improving species distribution models using biotic interactions: a case study of parasites,pollinators and plants

Biotic interactions have been considered as an important factor to be included in species distribution modelling, but little is known about how different types of interaction or different strategies for modelling affect model performance. This study compares different methods for including interspecific interactions in distribution models for bees, their brood parasites, and the plants they pollinate. Host–parasite interactions among bumble bees (genus Bombus: generalist pollinators and brood parasites) and specialist plant–pollinator interactions between Centris bees and Krameria flowers were used as case studies. We used 7 different modelling algorithms available in the BIOMOD R package. For Bombus, the inclusion of interacting species distributions generally increased model predictive accuracy. The improvement was better when the interacting species was included with its raw distribution rather than with its modeled suitability. However, incorporating the distributions of non‐interacting species sometimes resulted in similarly increased model accuracy despite their being no significance of any interaction for the distribution. For the Centris‐Krameria system the best strategy for modelling biotic interactions was to include the interacting species model‐predicted values. However, the results were less consistent than those for Bombus species, and most models including biotic interactions showed no significant improvement over abiotic models. Our results are consistent with previous studies showing that biotic interactions can be important in structuring species distributions at regional scales. However, correlations between species distributions are not necessarily indicative of interactions. Therefore, choosing the correct biotic information, based on biological and ecological knowledge, is critical to improve the accuracy of species distribution models and forecast distribution change.     

Diversity as a product of inter-specific interactions

We demonstrate diversification rather than optimization for highly interacting organisms in a well-mixed biological system by means of a simple model of coevolution. We find the cause to be the complex network of interactions formed, allowing species that are less well adapted to an environment to succeed, instead of the 'best' species. This diversification can be considered as the construction of many coevolutionary niches by the network of interactions between species. The model predictions are discussed in relation to experimental work on dense communities of the bacteria Escherichia coli, which may coexist with their own mutants under certain conditions. We find that diversification only occurs above a certain threshold interaction strength, below which competitive exclusion occurs.     

Stochastic tunneling in the colonization of mutualistic organisms: Primary succession by mycorrhizal plants

In mutualism under spatial structure, asynchrony between the dispersions of the interacting species can be a key determinant of their dynamics. We focused on the plant-mycorrhizal fungi system to theoretically analyze the colonization process by calculating the probability of colony establishment under environmental fluctuation. This can be considered a joint process of two sub-processes before and after the association between the host plant and the mycorrhizal fungi in a novel habitat. When colony growth undergoes environmental fluctuation, the dynamics of colony size can be considered a combination of the two stochastic sub-processes that mediated the association event between the plant and the fungi. Therefore, properties of whole system are influenced by five parameters, means and variances of colony growth rates of two sub-systems, and a rate of association of plant and fungi. For the successful establishment of a colony, the second sub-process must start before the first sub-process finishes (i.e., extinction), which we refer to as “stochastic tunneling.” Our analysis of the establishment probability of a plant colony based on this concept revealed that (1) the mean colony growth rates of the host alone and the symbiotic association affect establishment probability in different ways, (2) the variance of colony growth rate of the symbiotic association reduces the establishment probability, although the variance of growth rate of the host alone facilitates the establishment probability when the mean growth rate of the host alone is negative, and (3) a trade-off between the mean colony growth rates of the host alone and the symbiotic association could result in the evolution of either a symbiotic or parasitic relationship, based on a host decision. The model we present is widely applicable to the colonization processes of both positive and negative species relationships, where the interacting species disperse independently.     

Phenologically explicit models for studying plant–pollinator interactions under climate change

Climate change is significantly influencing phenology. One potential effect is that historically interacting partners will respond to climate change at different rates, creating the potential for a phenological mismatch among previously synchronized interacting species, or even sexes of the same species. Focusing on plant demographics in a plant–pollinator interaction, we develop a hybrid dynamical model that uses a “non-autonomous” differential equation system (Zonneveld model) for within-season dynamics and discrete equations for season-to-season dynamics. Our model outlines how and when changes in the relative phenologies of an interacting species pair will alter the demographic outcome of the interaction. For our plant–pollinator system, we find that plant population growth rates are particularly sensitive to phenology mismatch when flowers are short-lived, when pollinators are short-lived, or when flowers and pollinators exhibit high levels of within-population synchrony in emergence or arrival dates. More generally, our aim is to introduce the use of hybrid dynamical models as a framework through which researchers can directly explore the demographic consequences of climatically driven phenological change.     

Keystone species and vulnerable species in ecological communities: strong or weak interactors?

The loss of a species from an ecological community can trigger a cascade of secondary extinctions. The probability of secondary extinction to take place and the number of secondary extinctions are likely to depend on the characteristics of the species that is lost--the strength of its interactions with other species--as well as on the distribution of interaction strengths in the whole community. Analysing the effects of species loss in model communities we found that removal of the following species categories triggered, on average, the largest number of secondary extinctions: (a) rare species interacting strongly with many consumers, (b) abundant basal species interacting weakly with their consumers and (c) abundant intermediate species interacting strongly with many resources. We also found that the keystone status of a species with given characteristics was context dependent, that is, dependent on the structure of the community where it was embedded. Species vulnerable to secondary extinctions were mainly species interacting weakly with their resources and species interacting strongly with their consumers.     

Loss of functionally unique species may gradually undermine ecosystems

Functionally unique species contribute to the functional diversity of natural systems, often enhancing ecosystem functioning. An abundance of weakly interacting species increases stability in natural systems, suggesting that loss of weakly linked species may reduce stability. Any link between the functional uniqueness of a species and the strength of its interactions in a food web could therefore have simultaneous effects on ecosystem functioning and stability. Here, we analyse patterns in 213 real food webs and show that highly unique species consistently tend to have the weakest mean interaction strength per unit biomass in the system. This relationship is not a simple consequence of the interdependence of both measures on body size and appears to be driven by the empirical pattern of size structuring in aquatic systems and the trophic position of each species in the web. Food web resolution also has an important effect, with aggregation of species into higher taxonomic groups producing a much weaker relationship. Food webs with fewer unique and less weakly interacting species also show significantly greater variability in their levels of primary production. Thus, the loss of highly unique, weakly interacting species may eventually lead to dramatic state changes and unpredictable levels of ecosystem functioning.     

Global Stability of a System of Two Interacting Species with Convective and Dispersive Migration

Using Liapunov's direct method, effects of convective and dispersive migration on the global stability of the equilibrium state of a system of two interacting species are investigated. It is shown that the stable equilibrium state without dispersal remains so with dispersal. Further, it is pointed out that stability or instability of the equilibrium state of the system is not affected by convective migration. These results are justified in cases of a system of mutualistic interactions of species and a prey-predator system with functional response.     

Heterospecific courtship,minority effects and niche separation between cryptic butterfly species

Species interacting in varied ecological conditions often evolve in different directions in different local populations. The butterflies of the cryptic Leptidea complex are sympatrically distributed in different combinations across their Eurasian range. Interestingly, the same species is a habitat generalist in some regions and a habitat specialist in others, where a sibling species has the habitat generalist role. Previous studies suggest that this geographically variable niche divergence is generated by local processes in different contact zones. By varying the absolute and relative densities of Leptidea sinapis and Leptidea juvernica in large outdoor cages, we show that female mating success is unaffected by conspecific density, but strongly negatively affected by the density of the other species. Whereas 80% of the females mated when a conspecific couple was alone in a cage, less than 10% mated when the single couple shared the cage with five pairs of the other species. The heterospecific courtships can thus affect the population fitness, and for the species in the local minority, the suitability of a habitat is likely to depend on the presence or absence of the locally interacting species. If the local relative abundance of the different species depends on the colonization order, priority effects might determine the ecological roles of interacting species in this system.     

Determination of the equilibrium constants of self-associating protein systems: XI. The application of C(r) in graphical analysis and the enumeration of interacting species in the ultracentrifuge

A greatly simplified procedure is proposed which employs C= f(r) as determined from sedimentation equilibrium measurements in graphical analysis of self-associating protein systems and in the enumeration of interacting species in the ultracentrifuge. Basic equations given here are applicable to any self-associating system. A procedure is outlined for enumeration of interacting components independent of non-ideal behavior, using principal component analysis.     

Transient-time analysis of substrate-channelling in interacting enzyme systems.

The kinetics of dynamically interacting enzyme systems is examined, in the light of increasing evidence attesting to the widespread occurrence of this mode of organization in vivo. The transient time, a key phenomenological parameter for the coupled reaction, is expressed as a function of the lifetime of the intermediate substrate. The relationships between the transient time and the pseudo-first-order rate constants for the coupled reaction by the complexed and uncomplexed enzyme species are indicative of the mechanism of intermediate transfer ('channelling'). In a dynamically interacting enzyme system these kinetic parameters are composite functions of those for the processes catalysed by the complex and by the separated enzymes. The mathematical paradigm can be extended to a linear sequence of N coupled reactions catalysed by dynamically (pair-wise) interacting enzymes.     

Le concept d'évolution polyphasée et ses implications

Analysis of allopatric speciation shows that it ispolyphased, each phase being characterized by populational and temporal modes organized into the following general sequence: phase 1 of desorganization of the gene pool; phase 2a of reorganization leading to reproductive isolation; phase 2b of adaptative reorganizational achievment. Depending on the circumstances, polyphased sequences are more or less complex and complete. Analysis of other models of speciation (Dumbbell, circular overlap, diachronic bottleneck) shows that anagenesis and cladogenesis can be no longer considered as two modes of evolution, they appear to be only patterns resulting in the occurrence of various modes of the sequential phases of speciation. Evolution appears as a result of species equilibria punctuated by desequilibria inducing polyphased sequences of various temporal and populational modes leading to new species equilibria through anagenetic or cladogenetic pattern. Phyletic gradualism versus punctualism polemics reflect distinct approaches by biologists and paleontologists at different integration levels and scales. In the new polyphasedsequence-speciation concept they are complementary in a coherent interacting system ensuring balance between species and environment.     

Evolution and coevolution in mutualistic networks

A major current challenge in evolutionary biology is to understand how networks of interacting species shape the coevolutionary process. We combined a model for trait evolution with data for twenty plant-animal assemblages to explore coevolution in mutualistic networks. The results revealed three fundamental aspects of coevolution in species-rich mutualisms. First, coevolution shapes species traits throughout mutualistic networks by speeding up the overall rate of evolution. Second, coevolution results in higher trait complementarity in interacting partners and trait convergence in species in the same trophic level. Third, convergence is higher in the presence of super-generalists, which are species that interact with multiple groups of species. We predict that worldwide shifts in the occurrence of super-generalists will alter how coevolution shapes webs of interacting species. Introduced species such as honeybees will favour trait convergence in invaded communities, whereas the loss of large frugivores will lead to increased trait dissimilarity in tropical ecosystems.     

A mathematical model of facultative mutualism with populations interacting in a food chain

Facultative mutualism with populations interacting in a food chain is modeled by a system of four autonomous ordinary differential equations. Two cases are considered: mutualism with the prey and mutualism with the first predator. In both cases persistence and extinction criteria are developed in terms of the invariant flows on the boundaries.     

Species abundance and asymmetric interaction strength in ecological networks

The strength of interactions among species in a network tends to be highly asymmetric. We evaluate the hypothesis that this asymmetry results from the distribution of abundance among species, so that species interactions occur randomly among individuals. We used a database on mutualistic and antagonistic bipartite quantitative interaction networks. We show that across all types of networks asymmetry was correlated with abundance, so that rare species were asymmetrically affected by their abundant partners, while pairs of interacting abundant species tended to exhibit more symmetric, reciprocally strong effects. A null model shows that abundance provides a sufficient explanation of the asymmetry structure in some networks, but suggests the role of additional factors in others. Although not universal, our hypothesis holds for a substantial fraction of networks analyzed here, and should be considered as a null model in all studies aimed at evaluating the ecological and evolutionary consequences of species interactions.     

Do rabbits eat voles? Apparent competition,habitat heterogeneity and large‐scale coexistence under mink predation

Habitat heterogeneity is predicted to profoundly influence the dynamics of indirect interspecific interactions; however, despite potentially significant consequences for multi-species persistence, this remains almost completely unexplored in large-scale natural landscapes. Moreover, how spatial habitat heterogeneity affects the persistence of interacting invasive and native species is also poorly understood. Here we show how the persistence of a native prey (water vole, Arvicola terrestris ) is determined by the spatial distribution of an invasive prey (European rabbit, Oryctolagus cuniculus ) and directly infer how this is defined by the mobility of a shared invasive predator (American mink, Neovison vison ). This study uniquely demonstrates that variation in habitat connectivity in large-scale natural landscapes creates spatial asynchrony, enabling coexistence between apparent competitive native and invasive species. These findings highlight that unexpected interactions may be involved in species declines, and also that in such cases habitat heterogeneity should be considered in wildlife management decisions.     

Intra- and interspecific tree diversity promotes multitrophic plant–Hemiptera–ant interactions in a forest diversity experiment

Interactions between species of different trophic levels have long been recognized as fundamental processes in ecology. Although mounting evidence indicates that plant species diversity (PSD) or plant genetic diversity (PGD) can influence the plant-associated arthropod community, these two fundamental levels of biodiversity are not often manipulated simultaneously to assess their effects on species interactions. We used a large tree diversity experiment (BEF-China), which manipulates PSD and PGD in a crossed design to test individual and combined effects of PSD and PGD on multitrophic interaction networks and interaction partner species richness and occurrence. We focused on two tree species, on which sap-sucking Hemiptera and interacting ant species commonly occur. This tri-trophic interaction can be divided into the antagonistic plant–Hemiptera interaction and the mutualistic Hemiptera–ant interaction, known as trophobioses. Qualitative evaluation of tri-trophic interaction networks at different PSD and PGD combinations showed increased interaction partner redundancy at high PSD and PGD. This was supported by increased Hemiptera species richness at high PSD and PGD. Furthermore, the data indicate higher occurrence of Hemiptera and trophobioses and higher trophobiotic ant species richness with increasing PSD and PGD. As no plant diversity component alone caused an effect we conclude that the combined effect of high PGD and high PSD might be additive. In summary, as plant genetic diversity, especially at low species richness, seems to increase the interaction partner redundancy in interaction networks and the diversity of interacting communities, we suggest that genetic diversity should be considered in forest conservation and restoration programs.     

Toward a more trait-centered approach to diffuse (co)evolution

How species evolve depends on the communities in which they are embedded. Here, we briefly review the ideas underlying concepts of diffuse coevolution, evolution, and selection. We discuss criteria to identify when evolution will be diffuse. We advocate a more explicitly trait-oriented approach to diffuse (co)evolution, and discuss how considering effects of interacting species on fitness alone tells us little about evolution. We endorse the view that diffuse evolution occurs whenever the response to selection by one interacting species on a given trait is altered by the presence of a second interacting species. Building on the work of others, we clarify and expand the criteria for diffuse evolution and present a simple experimental design that will allow the detection of diffuse selection. We argue that a greater focus on selection on specific traits and the evolutionary response to that selection will improve our conceptual understanding of how communities affect the evolution of species embedded within them.