Trait-mediated interaction leads to structural emergence in mutualistic networks

As asymmetric structures of mutualistic networks can potentially contribute to system resilience, elucidating drivers behind the emergence of particular network architectures remains a major endeavour in ecology. Here, using an eco-evolutionary model for bipartite mutualistic networks with trait-mediated interactions, we explore how particular levels of connectance, nestedness and modularity are affected by three network assembly forces: resource accessibility, tolerance to trait difference between mutualistic pairs and competition intensity. We found that a moderate accessibility to intra-trophic resources and cross-trophic mutualistic support can result in a highly nested web, while low tolerance to trait difference between interacting pairs leads to a high level of modularity. Network-level trait complementarity leads to low connectance and high modularity, while network-level specialization can result in nested structures. Consequently, we argue that the interplay of ecological and evolutionary processes through trait-mediated interactions can explain these widely observed architectures in mutualistic networks.     

Implementation of a Markov model for phylogenetic trees

A recently developed mathematical model for the analysis of phylogenetic trees is applied to comparative data for 48 species. The model represents a return to fundamentals and makes no hypothesis with respect to the reversibility of the process. The species have been analysed in all subsets of three, and a measure of reliability of the results is provided. The numerical results of the computations on 17,296 triples of species are made available on the Internet. These results are discussed and the development of reliable tree structures for several species is illustrated. It is shown that, indeed, the Markov model is capable of considerably more interesting predictions than has been recognized to date.     

An interaction switch predicts the nested architecture of mutualistic networks

Nested architecture is distinctive in plant-animal mutualistic networks. However, to date an integrative and quantitative explanation has been lacking. It is evident that species often switch their interactive partners in real-world mutualistic networks such as pollination and seed-dispersal networks. By incorporating an interaction switch into a novel multi-population model, we show that the nested architecture rapidly emerges from an initially random network. The model allowing interaction switches between partner species produced predictions which fit remarkably well with observations from 81 empirical networks. Thus, the nested architecture in mutualistic networks could be an intrinsic physical structure of dynamic networks and the interaction switch is likely a key ecological process that results in nestedness of real-world networks. Identifying the biological processes responsible for network structures is thus crucial for understanding the architecture of ecological networks.     

Bayesian phylogenetic model selection using reversible jump Markov chain Monte Carlo

A common problem in molecular phylogenetics is choosing a model of DNA substitution that does a good job of explaining the DNA sequence alignment without introducing superfluous parameters. A number of methods have been used to choose among a small set of candidate substitution models, such as the likelihood ratio test, the Akaike Information Criterion (AIC), the Bayesian Information Criterion (BIC), and Bayes factors. Current implementations of any of these criteria suffer from the limitation that only a small set of models are examined, or that the test does not allow easy comparison of non-nested models. In this article, we expand the pool of candidate substitution models to include all possible time-reversible models. This set includes seven models that have already been described. We show how Bayes factors can be calculated for these models using reversible jump Markov chain Monte Carlo, and apply the method to 16 DNA sequence alignments. For each data set, we compare the model with the best Bayes factor to the best models chosen using AIC and BIC. We find that the best model under any of these criteria is not necessarily the most complicated one; models with an intermediate number of substitution types typically do best. Moreover, almost all of the models that are chosen as best do not constrain a transition rate to be the same as a transversion rate, suggesting that it is the transition/transversion rate bias that plays the largest role in determining which models are selected. Importantly, the reversible jump Markov chain Monte Carlo algorithm described here allows estimation of phylogeny (and other phylogenetic model parameters) to be performed while accounting for uncertainty in the model of DNA substitution.     

Coevolution can stabilize a mutualistic interaction

Interspecific mutualisms are ubiquitous in nature, despite their ecological and evolutionary instability. Recent studies have developed coevolutionary theory of mutualisms, which coupled population and evolutionary dynamics, to resolve the longstanding puzzle. However, earlier studies assumed a time-scale separation between these dynamics, leaving an unanswered question of how a relaxation in the time-scale separation affects the coevolutionary dynamics of mutualism. Here I relax the strong assumption to theoretically show that ecological and evolutionary dynamics occurring in a similar time scale can stabilize an otherwise unstable mutualism. I show that the coevolutionary dynamics can cause a stable limit cycle or stable equilibrium in the population sizes, even if the population sizes increase unbounded in the absence of evolutionary adaptation. In contrast, coevolution can also cause stable limit cycle even if the population dynamics is stable in the absence of evolutionary adaptation. Furthermore, the model predicts that the population dynamics is likely to converge to equilibrium when the evolutionary speed of two species is similar and fast or highly dissimilar. The results suggest that the ease of the evolutionary ‘arms race’ is of crucial importance to maintain mutualism.     

Detecting conserved interaction patterns in biological networks.

Molecular interaction data plays an important role in understanding biological processes at a modular level by providing a framework for understanding cellular organization, functional hierarchy, and evolutionary conservation. As the quality and quantity of network and interaction data increases rapidly, the problem of effectively analyzing this data becomes significant. Graph theoretic formalisms, commonly used for these analysis tasks, often lead to computationally hard problems due to their relation to subgraph isomorphism. This paper presents an innovative new algorithm, MULE, for detecting frequently occurring patterns and modules in biological networks. Using an innovative graph simplification technique based on ortholog contraction, which is ideally suited to biological networks, our algorithm renders these problems computationally tractable and scalable to large numbers of networks. We show, experimentally, that our algorithm can extract frequently occurring patterns in metabolic pathways and protein interaction networks from the KEGG, DIP, and BIND databases within seconds. When compared to existing approaches, our graph simplification technique can be viewed either as a pruning heuristic, or a closely related, but computationally simpler task. When used as a pruning heuristic, we show that our technique reduces effective graph sizes significantly, accelerating existing techniques by several orders of magnitude! Indeed, for most of the test cases, existing techniques could not even be applied without our pruning step. When used as a stand-alone analysis technique, MULE is shown to convey significant biological insights at near-interactive rates. The software, sample input graphs, and detailed results for comprehensive analysis of nine eukaryotic PPI networks are available at www.cs.purdue.edu/homes/koyuturk/mule.     

Detecting overlapping protein complexes in protein-protein interaction networks

We introduce clustering with overlapping neighborhood expansion (ClusterONE), a method for detecting potentially overlapping protein complexes from protein-protein interaction data. ClusterONE-derived complexes for several yeast data sets showed better correspondence with reference complexes in the Munich Information Center for Protein Sequence (MIPS) catalog and complexes derived from the Saccharomyces Genome Database (SGD) than the results of seven popular methods. The results also showed a high extent of functional homogeneity.     

Detecting distant homologs using phylogenetic tree-based HMMs

It is often desired to identify further homologs of a family of biological sequences from the ever-growing sequence databases. Profile hidden Markov models excel at capturing the common statistical features of a group of biological sequences. With these common features, we can search the biological database and find new homologous sequences. Most general profile hidden Markov model methods, however, treat the evolutionary relationships between the sequences in a homologous group in an ad-hoc manner. We hereby introduce a method to incorporate phylogenetic information directly into hidden Markov models, and demonstrate that the resulting model performs better than most of the current multiple sequence-based methods for finding distant homologs.     

Protein secondary structure prediction using three neural networks and a segmental semi Markov model

Prediction of protein secondary structure is an important step towards elucidating its three dimensional structure and its function. This is a challenging problem in bioinformatics. Segmental semi Markov models (SSMMs) are one of the best studied methods in this field. However, incorporating evolutionary information to these methods is somewhat difficult. On the other hand, the systems of multiple neural networks (NNs) are powerful tools for multi-class pattern classification which can easily be applied to take these sorts of information into account.To overcome the weakness of SSMMs in prediction, in this work we consider a SSMM as a decision function on outputs of three NNs that uses multiple sequence alignment profiles. We consider four types of observations for outputs of a neural network. Then profile table related to each sequence is reduced to a sequence of four observations. In order to predict secondary structure of each amino acid we need to consider a decision function. We use an SSMM on outputs of three neural networks. The proposed SSMM has discriminative power and weights over different dependency models for outputs of neural networks. The results show that the accuracy of our model in predictions, particularly for strands, is considerably increased.     

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.     

Statistical estimation of parameters in a phylogenetic tree using a dynamic model of the substitutional process

Using a modified version of the substitutional process proposed by Neyman, we estimate the parameters of the phylogenetic tree made up of three species (or groups of species). The parameters estimated are the rate of substitution of amino acids along a protein and the ratio of the times of divergence of the species (or group of species). A method is given for determining the tree structure when it is not known. Both the maximum likelihood and Bayes methods are used in the estimation. The basic model of the substitutional process within the proteins is validated by showing that the estimates of the ratio of the times of divergence of three species computed from two different protein molecules (haemoglobin α and fibrinopeptides) are within one standard deviation of each other. Next we consider the construction of the correct phylogenetic tree made up of three or more taxonomic categories like phyla or class utilizing the structure of the various types of protein molecules of the species in the three categories. The generalization of the procedure for the construction of the entire phylogenetic tree is also indicated. The main advantage of this method of tree construction over the traditional method is that the latter method can use the information of only one type of protein (for example cytochrome c) while the method of this paper can use all the available data from the different molecules. We also discuss the recent controversy over the constancy of the molecular clock.     

Modelling phylogenetic relationships using reticulated networks

Makarenkov, V., Legendre, P. & Desdevises, Y. (2004). Modelling phylogenetic relationships using reticulated networks. —  Zoologica Scripta , 33 , 89–96.
Most traditional methods of phylogenetic analysis assume that species evolution can be represented by means of a bifurcating tree model. In many phylogenetic situations, however, some of the evolutionary links between species are due to reticulate evolution. For instance, reticulate models can adequately describe such complicated mechanisms as lateral gene transfer in bacteria or species hybridization. The theoretical concepts of reticulate evolution developed in the 1980s and 1990s need to be supported by appropriate analytical tools and software. In this paper, we present the main features of a new distance-based method for modelling phylogenetic relationships among species by means of reticulated networks (RNs). The method uses the least-squares model to build a RN by gradually improving upon the solution provided by a phylogenetic tree. A computer program facilitating the reconstruction and visualization of reticulate phylogenies is made available to researchers. In the application section, we illustrate the usefulness of the method by studying the evolution of honeybees (genus Apis ). The method for reconstructing RNs has been included in the T-Rex ( Tree and Reticulogram Reconstruction ) package recently developed by the first-named author.     

On the inference of complex phylogenetic networks by Markov Chain Monte-Carlo

For various species, high quality sequences and complete genomes are nowadays available for many individuals. This makes data analysis challenging, as methods need not only to be accurate, but also time efficient given the tremendous amount of data to process. In this article, we introduce an efficient method to infer the evolutionary history of individuals under the multispecies coalescent model in networks (MSNC). Phylogenetic networks are an extension of phylogenetic trees that can contain reticulate nodes, which allow to model complex biological events such as horizontal gene transfer, hybridization and introgression. We present a novel way to compute the likelihood of biallelic markers sampled along genomes whose evolution involved such events. This likelihood computation is at the heart of a Bayesian network inference method called SnappNet, as it extends the Snapp method inferring evolutionary trees under the multispecies coalescent model, to networks. SnappNet is available as a package of the well-known beast 2 software.Recently, the MCMC_BiMarkers method, implemented in PhyloNet, also extended Snapp to networks. Both methods take biallelic markers as input, rely on the same model of evolution and sample networks in a Bayesian framework, though using different methods for computing priors. However, SnappNet relies on algorithms that are exponentially more time-efficient on non-trivial networks. Using simulations, we compare performances of SnappNet and MCMC_BiMarkers. We show that both methods enjoy similar abilities to recover simple networks, but SnappNet is more accurate than MCMC_BiMarkers on more complex network scenarios. Also, on complex networks, SnappNet is found to be extremely faster than MCMC_BiMarkers in terms of time required for the likelihood computation. We finally illustrate SnappNet performances on a rice data set. SnappNet infers a scenario that is consistent with previous results and provides additional understanding of rice evolution.     

Asymmetries in specialization in ant-plant mutualistic networks

Mutualistic networks involving plants and their pollinators or frugivores have been shown recently to exhibit a particular asymmetrical organization of interactions among species called nestedness: a core of reciprocal generalists accompanied by specialist species that interact almost exclusively with generalists. This structure contrasts with compartmentalized assemblage structures that have been verified in antagonistic food webs. Here we evaluated whether nestedness is a property of another type of mutualism-the interactions between ants and extrafloral nectary-bearing plants--and whether species richness may lead to differences in degree of nestedness among biological communities. We investigated network structure in four communities in Mexico. Nested patterns in ant-plant networks were very similar to those previously reported for pollination and frugivore systems, indicating that this form of asymmetry in specialization is a common feature of mutualisms between free-living species, but not always present in species-poor systems. Other ecological factors also appeared to contribute to the nested asymmetry in specialization, because some assemblages showed more extreme asymmetry than others even when species richness was held constant. Our results support a promising approach for the development of multispecies coevolutionary theory, leading to the idea that specialization may coevolve in different but simple ways in antagonistic and mutualistic assemblages.     

Missing and forbidden links in mutualistic networks

Ecological networks are complexes of interacting species, but not all potential links among species are realized. Unobserved links are either missing or forbidden. Missing links exist, but require more sampling or alternative ways of detection to be verified. Forbidden links remain unobservable, irrespective of sampling effort. They are caused by linkage constraints. We studied one Arctic pollination network and two Mediterranean seed-dispersal networks. In the first, for example, we recorded flower-visit links for one full season, arranged data in an interaction matrix and got a connectance C of 15 per cent. Interaction accumulation curves documented our sampling of interactions through observation of visits to be robust. Then, we included data on pollen from the body surface of flower visitors as an additional link ‘currency’. This resulted in 98 new links, missing from the visitation data. Thus, the combined visit–pollen matrix got an increased C of 20 per cent. For the three networks, C ranged from 20 to 52 per cent, and thus the percentage of unobserved links (100 − C) was 48 to 80 per cent; these were assumed forbidden because of linkage constraints and not missing because of under-sampling. Phenological uncoupling (i.e. non-overlapping phenophases between interacting mutualists) is one kind of constraint, and it explained 22 to 28 per cent of all possible, but unobserved links. Increasing phenophase overlap between species increased link probability, but extensive overlaps were required to achieve a high probability. Other kinds of constraint, such as size mismatch and accessibility limitations, are briefly addressed.     

Detecting social learning using networks: a users guide

Controversy over claims of cultures in nonhuman primates and other animals has led to a call for quantitative methods that are able to infer social learning from freely interacting groups of animals. Network-based diffusion analysis (NBDA) is such a method that infers social transmission of a behavioral trait when the pattern of acquisition follows the social network. As, relative to other animals, primates may be unusual in their heavy reliance on social learning, with learning frequently directed along pathways of association; in this study, we draw attention to the significance of this method for primatologists. We provide a "users guide" to NBDA methodology, discussing the choice of NBDA model and social network, and suggest model selection procedures. We also present the results of simulations that suggest that NBDA works well even when the assumptions of the underlying model are violated.     

Predicting abundances of plants and pollinators using a simple compartmental mutualistic model

Key gaps to be filled in population and community ecology are predicting the strength of species interactions and linking pattern with process to understand species coexistence and their relative abundances. In the case of mutualistic webs, like plant–pollinator networks, advances in understanding species abundances are currently limited, mainly owing to the lack of methodological tools to deal with the intrinsic complexity of mutualisms. Here, we propose an aggregation method leading to a simple compartmental mutualistic population model that captures both qualitatively and quantitatively the size-segregated populations observed in a Mediterranean community of nectar-producing plant species and nectar-searching animal species. We analyse the issue of optimal aggregation level and its connection with the trade-off between realism and overparametrization. We show that aggregation of both plants and pollinators into five size classes or compartments leads to a robust model with only two tunable parameters. Moreover, if, in each compartment, (i) the interaction coefficients fulfil the condition of weak mutualism and (ii) the mutualism is facultative for at least one party of the compartment, then the interactions between different compartments are sufficient to guarantee global stability of the equilibrium population.     

Varieties of mutualistic interaction in population models

A Lotka-Volterra model of mutalism indicates eight possible cases, of which two lead to survival of both populations, two indicate inevitable extinction, and four are indeterminate, the result depending on the initial population sizes. Conventional neighborhood stability analysis is a poor indicator of the biological result expected. Modification of the Lotka-Volterra model to give non-linear isoclines is necessary to obtain a minimum of biological realism; this modified model is illustrated with an analysis of a legume-Rhizobium mutualism.