Pattern of functional extinctions in ecological networks with a variety of interaction types

Stability-instability transition in tripartite merged ecological networks

Although ecological networks are typically constructed based on a single type of interaction, e.g. trophic interactions in a food web, a more complete picture of ecosystem composition and functioning arises from merging networks of multiple interaction types. In this work, we consider tripartite networks constructed by merging two bipartite networks, one mutualistic and one antagonistic. Taking the interactions within each sub-network to be distributed randomly, we consider the stability of the dynamics of the network based on the spectrum of its community matrix. In the asymptotic limit of a large number of species, we show that the spectrum undergoes an eigenvalue phase transition, which leads to an abrupt destabilisation of the network as the ratio of mutualists to antagonists is increased. We also derive results that show how this transition is manifest in networks of finite size, as well as when disorder is introduced in the segregation of the two interaction types. Our random-matrix results will serve as a baseline for understanding the behaviour of merged networks with more realistic structures and/or more detailed dynamics.

The Sixth Mass Extinction: fact, fiction or speculation?

There have been five Mass Extinction events in the history of Earth's biodiversity, all caused by dramatic but natural phenomena. It has been claimed that the Sixth Mass Extinction may be underway, this time caused entirely by humans. Although considerable evidence indicates that there is a biodiversity crisis of increasing extinctions and plummeting abundances, some do not accept that this amounts to a Sixth Mass Extinction. Often, they use the IUCN Red List to support their stance, arguing that the rate of species loss does not differ from the background rate. However, the Red List is heavily biased: almost all birds and mammals but only a minute fraction of invertebrates have been evaluated against conservation criteria. Incorporating estimates of the true number of invertebrate extinctions leads to the conclusion that the rate vastly exceeds the background rate and that we may indeed be witnessing the start of the Sixth Mass Extinction. As an example, we focus on molluscs, the second largest phylum in numbers of known species, and, extrapolating boldly, estimate that, since around AD 1500, possibly as many as 7.5-13% (150,000-260,000) of all ~2 million known species have already gone extinct, orders of magnitude greater than the 882 (0.04%) on the Red List. We review differences in extinction rates according to realms: marine species face significant threats but, although previous mass extinctions were largely defined by marine invertebrates, there is no evidence that the marine biota has reached the same crisis as the non-marine biota. Island species have suffered far greater rates than continental ones. Plants face similar conservation biases as do invertebrates, although there are hints they may have suffered lower extinction rates. There are also those who do not deny an extinction crisis but accept it as a new trajectory of evolution, because humans are part of the natural world; some even embrace it, with a desire to manipulate it for human benefit. We take issue with these stances. Humans are the only species able to manipulate the Earth on a grand scale, and they have allowed the current crisis to happen. Despite multiple conservation initiatives at various levels, most are not species oriented (certain charismatic vertebrates excepted) and specific actions to protect every living species individually are simply unfeasible because of the tyranny of numbers. As systematic biologists, we encourage the nurturing of the innate human appreciation of biodiversity, but we reaffirm the message that the biodiversity that makes our world so fascinating, beautiful and functional is vanishing unnoticed at an unprecedented rate. In the face of a mounting crisis, scientists must adopt the practices of preventive archaeology, and collect and document as many species as possible before they disappear. All this depends on reviving the venerable study of natural history and taxonomy. Denying the crisis, simply accepting it and doing nothing, or even embracing it for the ostensible benefit of humanity, are not appropriate options and pave the way for the Earth to continue on its sad trajectory towards a Sixth Mass Extinction.

Spatial resolution and location impact group structure in a marine food web

Ecological processes in food webs depend on species interactions. By identifying broad-scaled interaction patterns, important information on species' ecological roles may be revealed. Here, we use the group model to examine how spatial resolution and proximity influence group structure. We examine a data set from the Barents Sea, with food webs described for both the whole region and 25 subregions. We test how the group structure in the networks differ comparing (1) the regional metaweb to subregions and (2) subregion to subregion. We find that more than half the species in the metaweb change groups when compared to subregions. Between subregions, networks with similar group structure are spatially related. Interestingly, although species overlap is important for similarity in group structure, there are notable exceptions. Our results highlight that species ecological roles vary depending on fine-scaled differences in the patterns of interactions, and that local network characteristics are important to consider.

The effect of multiple biotic interaction types on species persistence

No species can persist in isolation from other species, but how biotic interactions affect species persistence is still a matter of inquiry. Is persistence more likely in communities with higher proportion of competing species, or in communities with more positive interactions? How do different components of community structure mediate this relationship? We address these questions using a novel simulation framework that generates realistic communities with varying numbers of species and different proportions of biotic interaction types within and across trophic levels. We show that when communities have fewer species, persistence is more likely if positive interactions-such as mutualism and commensalism-are prevalent. In species-rich communities, the disproportionate effect of positive interactions on persistence is diluted and different combinations of biotic interaction types can coexist without affecting persistence significantly. We present the first theoretical examination of how multiple-interaction networks with varying architectures relate to local species persistence, and provide insight about the underlying causes of stability in communities.

Significance evaluation in factor graphs

BACKGROUND

Factor graphs provide a flexible and general framework for specifying probability distributions. They can capture a range of popular and recent models for analysis of both genomics data as well as data from other scientific fields. Owing to the ever larger data sets encountered in genomics and the multiple-testing issues accompanying them, accurate significance evaluation is of great importance. We here address the problem of evaluating statistical significance of observations from factor graph models.

RESULTS

Two novel numerical approximations for evaluation of statistical significance are presented. First a method using importance sampling. Second a saddlepoint approximation based method. We develop algorithms to efficiently compute the approximations and compare them to naive sampling and the normal approximation. The individual merits of the methods are analysed both from a theoretical viewpoint and with simulations. A guideline for choosing between the normal approximation, saddle-point approximation and importance sampling is also provided. Finally, the applicability of the methods is demonstrated with examples from cancer genomics, motif-analysis and phylogenetics.

CONCLUSIONS

The applicability of saddlepoint approximation and importance sampling is demonstrated on known models in the factor graph framework. Using the two methods we can substantially improve computational cost without compromising accuracy. This contribution allows analyses of large datasets in the general factor graph framework.

Stability of an adaptive hybrid community

Contrary to stable natural ecosystems, the classical ecological theory predicts that complex ecological communities are fragile. The adaptive switching of interaction partners was proposed as a key factor to resolve the complexity–stability problem. However, this theory is based on the food webs that comprise predator–prey interactions alone; thus, the manner in which adaptive behavior affects the dynamics of hybrid communities with multiple interaction types remains unclear. Here, using a bipartite community network model with antagonistic and mutualistic interactions, I show that adaptive partner shifts by both antagonists and mutualists are crucial to the persistence of communities. The results show that adaptive behavior destabilizes the dynamics of communities with a single interaction type; however, the hybridity of multiple interaction types within a community greatly improves the stability. Moreover, adaptive behavior does not create a positive complexity–stability relationship in communities with a single interaction type but it does in the hybrid community. The diversity of interaction types is predicted to play a crucial role in community maintenance in an adaptive world.