The shape of ecological networks

We study the statistics of ecosystems with a variable number of co-evolving species. The species interact in two ways: by prey-predator relationships and by direct competition with similar kinds. The interaction coefficients change slowly through successful adaptations and speciations. We treat them as quenched random variables. These interactions determine long-term topological features of the species network, which are found to agree with those of biological systems.Comment: 4 pages, 2 figure

Interplay of spatial dynamics and local adaptation shapes species lifetime distributions and species-area relationships

The distributions of species lifetimes and species in space are related, since species with good local survival chances have more time to colonize new habitats and species inhabiting large areas have higher chances to survive local disturbances. Yet, both distributions have been discussed in mostly separate communities. Here, we study both patterns simultaneously using a spatially explicit, evolutionary community assembly approach. We present and investigate a metacommunity model, consisting of a grid of patches, where each patch contains a local food web. Species survival depends on predation and competition interactions, which in turn depend on species body masses as the key traits. The system evolves due to the migration of species to neighboring patches, the addition of new species as modifications of existing species, and local extinction events. The structure of each local food web thus emerges in a self-organized manner as the highly non-trivial outcome of the relative time scales of these processes. Our model generates a large variety of complex, multi-trophic networks and therefore serves as a powerful tool to investigate ecosystems on long temporal and large spatial scales. We find that the observed lifetime distributions and species-area relations resemble power laws over appropriately chosen parameter ranges and thus agree qualitatively with empirical findings. Moreover, we observe strong finite-size effects, and a dependence of the relationships on the trophic level of the species. By comparing our results to simple neutral models found in the literature, we identify the features that are responsible for the values of the exponents.Comment: Theor Ecol (2019

Species assembly in model ecosystems, II: Results of the assembly process

In the companion paper of this set (Capitan and Cuesta, 2010) we have developed a full analytical treatment of the model of species assembly introduced in Capitan et al. (2009). This model is based on the construction of an assembly graph containing all viable configurations of the community, and the definition of a Markov chain whose transitions are the transformations of communities by new species invasions. In the present paper we provide an exhaustive numerical analysis of the model, describing the average time to the recurrent state, the statistics of avalanches, and the dependence of the results on the amount of available resource. Our results are based on the fact that the Markov chain provides an asymptotic probability distribution for the recurrent states, which can be used to obtain averages of observables as well as the time variation of these magnitudes during succession, in an exact manner. Since the absorption times into the recurrent set are found to be comparable to the size of the system, the end state is quickly reached (in units of the invasion time). Thus, the final ecosystem can be regarded as a fluctuating complex system where species are continually replaced by newcomers without ever leaving the set of recurrent patterns. The assembly graph is dominated by pathways in which most invasions are accepted, triggering small extinction avalanches. Through the assembly process, communities become less resilient (e.g., have a higher return time to equilibrium) but become more robust in terms of resistance against new invasions.Comment: 14 pages, 13 figures. Revised versio

Species assembly in model ecosystems, I: Analysis of the population model and the invasion dynamics

Recently we have introduced a simplified model of ecosystem assembly (Capitan et al., 2009) for which we are able to map out all assembly pathways generated by external invasions in an exact manner. In this paper we provide a deeper analysis of the model, obtaining analytical results and introducing some approximations which allow us to reconstruct the results of our previous work. In particular, we show that the population dynamics equations of a very general class of trophic-level structured food-web have an unique interior equilibrium point which is globally stable. We show analytically that communities found as end states of the assembly process are pyramidal and we find that the equilibrium abundance of any species at any trophic level is approximately inversely proportional to the number of species in that level. We also find that the per capita growth rate of a top predator invading a resident community is key to understand the appearance of complex end states reported in our previous work. The sign of these rates allows us to separate regions in the space of parameters where the end state is either a single community or a complex set containing more than one community. We have also built up analytical approximations to the time evolution of species abundances that allow us to determine, with high accuracy, the sequence of extinctions that an invasion may cause. Finally we apply this analysis to obtain the communities in the end states. To test the accuracy of the transition probability matrix generated by this analytical procedure for the end states, we have compared averages over those sets with those obtained from the graph derived by numerical integration of the Lotka-Volterra equations. The agreement is excellent.Comment: 16 pages, 8 figures. Revised versio

On the interplay of speciation and dispersal: An evolutionary food web model in space

We introduce an evolutionary metacommunity of multitrophic food webs on several habitats coupled by migration. In contrast to previous studies that focus either on evolutionary or on spatial aspects, we include both and investigate the interplay between them. Locally, the species emerge, interact and go extinct according to the rules of the well-known evolutionary food web model proposed by Loeuille and Loreau in 2005. Additionally, species are able to migrate between the habitats. With random migration, we are able to reproduce common trends in diversity-dispersal relationships: Regional diversity decreases with increasing migration rates, whereas local diversity can increase in case of a low level of dispersal. Moreover, we find that the total biomasses in the different patches become similar even when species composition remains different. With adaptive migration, we observe species compositions that differ considerably between patches and contain species that are descendant from ancestors on both patches. This result indicates that the combination of spatial aspects and evolutionary processes affects the structure of food webs in different ways than each of them alone.Comment: under review at JT

Mutual information in the Tangled Nature Model

We consider the concept of mutual information in ecological networks, and use this idea to analyse the Tangled Nature model of co-evolution. We show that this measure of correlation has two distinct behaviours depending on how we define the network in question: if we consider only the network of viable species this measure increases, whereas for the whole system it decreases. It is suggested that these are complimentary behaviours that show how ecosystems can become both more stable and better adapted.Comment: 7 pages, 5 figures. To appear in Ecological Modellin

Ecological criteria for evaluation candidate sites for marine reserves

Several schemes have been developed to help select the locations of marine reserves. All of them combine social, economic, and biological criteria, and few offer any guidance as to how to prioritize among the criteria identified. This can imply that the relative weights given to different criteria are unimportant. Where two sites are of equal value ecologically, then socioeconomic criteria should dominate the choice of which should be protected. However, in many cases, socioeconomic criteria are given equal or greater weight than ecological considerations in the choice of sites. This can lead to selection of reserves with little biological value that fail to meet many of the desired objectives. To avoid such a possibility, we develop a series of criteria that allow preliminary evaluation of candidate sites according to their relative biological values in advance of the application of socioeconomic criteria. We include criteria that, while not strictly biological, have a strong influence on the species present or ecological processes. Our scheme enables sites to be assessed according to their biodiversity, the processes which underpin that diversity, and the processes that support fisheries and provide a spectrum of other services important to people. Criteria that capture biodiversity values include biogeographic representation, habitat representation and heterogeneity, and presence of species or populations of special interest (e.g., threatened species). Criteria that capture sustainability of biodiversity and fishery values include the size of reserves necessary to protect viable habitats, presence of exploitable species, vulnerable life stages, connectivity among reserves, links among ecosystems, and provision of ecosystem services to people. Criteria measuring human and natural threats enable candidate sites to be eliminated from consideration if risks are too great, but also help prioritize among sites where threats can be mitigated by protection. While our criteria can be applied to the design of reserve networks, they also enable choice of single reserves to be made in the context of the attributes of existing protected areas. The overall goal of our scheme is to promote the development of reserve networks that will maintain biodiversity and ecosystem functioning at large scales. The values of ecosystem goods and services for people ultimately depend on meeting this objective

A bio-economic model for the ecosystem-based management of the coastal fishery in French Guiana

This paper offers a theoretical and empirical modeling for ecosystem-based fishery management (EBFM). A multi-species and multi-fleets model integrating Lokta-Volterra trophic dynamics and profit functions is developed for the coastal fishery of French Guiana. This small-case fishery constitutes a challenging example with high fish biodiversity, several non selective fleets and a potentially increasing local food demand due to demographic pressure. The dynamic model is calibrated with thirteen species and four fleets using catch and effort data on a monthly basis from 2006 to 2009. Several contrasting fishing scenarios including status quo, total closure, economic and viable strategies are simulated and compared from both biodiversity preservation and socio-economic performance viewpoints. We show that fishing outputs including food supply and profitability of fleets can be sustained although a significant loss of biodiversity cannot be avoided.Small-scale fishery, biodiversity, sustainability, profitability, food security, multi-species, multi-fleets