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Register a new userEfficient recycled algorithms for quantitative trait models on phylogenies
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We present an efficient and flexible method for computing likelihoods of phenotypic traits on a phylogeny. The method does not resort to Monte-Carlo computation but instead blends Felsensteins discrete character pruning algorithm with methods for numerical quadrature. It is not limited to Gaussian models and adapts readily to model uncertainty in the observed trait values. We demonstrate the framework by developing efficient algorithms for likelihood calculation and ancestral state reconstruction under Wrights threshold model, applying our methods to a dataset of trait data for extrafloral nectaries (EFNs) across a phylogeny of 839 Labales species.
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Ecologists have long suspected that species are more likely to interact if their traits match in a particular way. For example, a pollination interaction may be more likely if the proportions of a bees tongue fit a plants flower shape. Empirical estimates of the importance of trait-matching for determining species interactions, however, vary significantly among different types of ecological networks. Here, we show that ambiguity among empirical trait-matching studies may have arisen at least in parts from using overly simple statistical models. Using simulated and real data, we contrast conventional generalized linear models (GLM) with more flexible Machine Learning (ML) models (Random Forest, Boosted Regression Trees, Deep Neural Networks, Convolutional Neural Networks, Support Vector Machines, naive Bayes, and k-Nearest-Neighbor), testing their ability to predict species interactions based on traits, and infer trait combinations causally responsible for species interactions. We find that the best ML models can successfully predict species interactions in plant-pollinator networks, outperforming GLMs by a substantial margin. Our results also demonstrate that ML models can better identify the causally responsible trait-matching combinations than GLMs. In two case studies, the best ML models successfully predicted species interactions in a global plant-pollinator database and inferred ecologically plausible trait-matching rules for a plant-hummingbird network, without any prior assumptions. We conclude that flexible ML models offer many advantages over traditional regression models for understanding interaction networks. We anticipate that these results extrapolate to other ecological network types. More generally, our results highlight the potential of machine learning and artificial intelligence for inference in ecology, beyond standard tasks such as image or pattern recognition.
In a recent paper, Klaere et al. modeled the impact of substitutions on arbitrary branches of a phylogenetic tree on an alignment site by the so-called One Step Mutation (OSM) matrix. By utilizing the concept of the OSM matrix for the four-state nucleotide alphabet, Nguyen et al. presented an efficient procedure to compute the minimal number of substitutions needed to translate one alignment site into another.The present paper delivers a proof for this computation.Moreover, we provide several mathematical insights into the generalization of the OSM matrix to multistate alphabets.The construction of the OSM matrix is only possible if the matrices representing the substitution types acting on the character states and the identity matrix form a commutative group with respect to matrix multiplication. We illustrate a means to establish such a group for the twenty-state amino acid alphabet and critically discuss its biological usefulness.
Genetic studies of human traits have revolutionized our understanding of the variation between individuals, and opened the door for numerous breakthroughs in biology, medicine and other scientific fields. And yet, the ultimate promise of this area of research is still not fully realized. In this review, we highlight the major open problems that need to be solved to improve our understanding of the genetic variation underlying human traits, and by discussing these challenges provide a primer to the field. Our focus is on concrete analytical problems, both conceptual and technical in nature. We cover general issues in genetic studies such as population structure, epistasis and gene-environment interactions, data-related issues such as ethnic diversity and rare genetic variants, and specific challenges related to heritability estimates, genetic association studies and polygenic risk scores. We emphasize the interconnectedness of these open problems and suggest promising avenues to address them.
We first generalise ideas discussed by Kiss et al. (2015) to prove a theorem for generating exact closures (here expressing joint probabilities in terms of their constituent marginal probabilities) for susceptible-infectious-removed (SIR) dynamics on arbitrary graphs (networks). For Poisson transmission and removal processes, this enables us to obtain a systematic reduction in the number of differential equations needed for an exact `moment closure representation of the underlying stochastic model. We define `transmission blocks as a possible extension of the block concept in graph theory and show that the order at which the exact moment closure representation is curtailed is the size of the largest transmission block. More generally, approximate closures of the hierarchy of moment equations for these dynamics are typically defined for the first and second order yielding mean-field and pairwise models respectively. It is frequently implied that, in principle, closed models can be written down at arbitrary order if only we had the time and patience to do this. However, for epidemic dynamics on networks, these higher-order models have not been defined explicitly. Here we unambiguously define hierarchies of approximate closed models that can utilise subsystem states of any order, and show how well-known models are special cases of these hierarchies.
We propose a novel probabilistic method for detection of objects in noisy images. The method uses results from percolation and random graph theories. We present an algorithm that allows to detect objects of unknown shapes in the presence of random noise. The algorithm has linear complexity and exponential accuracy and is appropriate for real-time systems. We prove results on consistency and algorithmic complexity of our procedure.
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