Estimating primate divergence times by using conditioned birth-and-death processes

Mathematical Modelling of Parasite Dynamics: A Stochastic Simulation-Based Approach and Parameter Estimation via Modified Sequential-Type Approximate Bayesian Computation

The development of mathematical models for studying newly emerging and re-emerging infectious diseases has gained momentum due to global events. The gyrodactylid-fish system, like many host-parasite systems, serves as a valuable resource for ecological, evolutionary, and epidemiological investigations owing to its ease of experimental manipulation and long-term monitoring. Although this system has an existing individual-based model, it falls short in capturing information about species-specific microhabitat preferences and other biological details for different Gyrodactylus strains across diverse fish populations. This current study introduces a new individual-based stochastic simulation model that uses a hybrid τ -leaping algorithm to incorporate this essential data, enhancing our understanding of the complexity of the gyrodactylid-fish system. We compare the infection dynamics of three gyrodactylid strains across three host populations. A modified sequential-type approximate Bayesian computation (ABC) method, based on sequential Monte Carlo and sequential importance sampling, is developed. Additionally, we establish two penalised local-linear regression methods (based on L1 and L2 regularisations) for ABC post-processing analysis to fit our model using existing empirical data. With the support of experimental data and the fitted mathematical model, we address open biological questions for the first time and propose directions for future studies on the gyrodactylid-fish system. The adaptability of the mathematical model extends beyond the gyrodactylid-fish system to other host-parasite systems. Furthermore, the modified ABC methodologies provide efficient calibration for other multi-parameter models characterised by a large set of correlated or independent summary statistics.

Phylogenomic analyses reveal incongruences between divergence times and fossil records of freshwater snails in East Asia

Fossils provide important insight into our understanding of phylogenetic history by serving as calibration points for divergence time estimation. However, uncertainties in the fossil record due to parallel evolution and convergent evolution can critically affect estimates of node ages. Here, we compare and contrast estimates of phylogenetic divergence with geologic and fossil history for two freshwater snail genera of the family Viviparidae in East Asia (Cipangopaludina and Margarya). Cipangopaludina species are commonly widely distributed species in East Asia, but extant Margarya species are endemic to the ancient lakes in Yunnan, China. According to some previous studies, parallel evolution or convergent evolution of shell morphology has occurred in the family several times which may affect divergence time estimation using fossil records. In this study, we used SNP data derived from ddRAD-seq loci to investigate population demographic history of both genera. Our results show a common pattern of lake endemic lineages diversifying from widely distributed lineages in the Miocene, and multiple colonization to a single ancient lake occurred in the Pleistocene. Our results indicate substantial incongruence among estimated phylogenomic divergence times, some fossil records, and formation ages of ancient lakes. These findings suggest some fossil records may be misidentified in these groups and highlight the need to carefully evaluate geological evidence and fossil records when using these for divergence time estimation.

Estimation of parameters in biological species with several mating and reproduction alternatives

With the purpose of modeling the demographic dynamics of biological species in which different mating and reproduction alternatives are feasible, in Molina et al. (2014) we introduced a new mathematical model based on discrete-time branching processes. Assuming that the reproduction phase is governed by probability distributions belonging to the power series family, some reproductive parameters for such species were estimated. In this work, in a more general statistical context, we generalize this research. By considering observations, until a given generation, of the number of female and male individuals in each generation, we now investigate several inferential questions about the parameters of biological interest included in the mathematical model. We study such questions using procedures based on Bayesian statistical methodology. We apply the proposed methods to describe the dynamics of salmonid species.

Competing evolutionary paths in growing populations with applications to multidrug resistance

Investigating the emergence of a particular cell type is a recurring theme in models of growing cellular populations. The evolution of resistance to therapy is a classic example. Common questions are: when does the cell type first occur, and via which sequence of steps is it most likely to emerge? For growing populations, these questions can be formulated in a general framework of branching processes spreading through a graph from a root to a target vertex. Cells have a particular fitness value on each vertex and can transition along edges at specific rates. Vertices represent cell states, say genotypes or physical locations, while possible transitions are acquiring a mutation or cell migration. We focus on the setting where cells at the root vertex have the highest fitness and transition rates are small. Simple formulas are derived for the time to reach the target vertex and for the probability that it is reached along a given path in the graph. We demonstrate our results on several scenarios relevant to the emergence of drug resistance, including: the orderings of resistance-conferring mutations in bacteria and the impact of imperfect drug penetration in cancer.

How long does it take for a treatment naive, growing bacterial colony to be able to survive exposure to a cocktail of antibiotics? En route to multidrug resistance, what order did the drugs become impotent in? Questions such as these that pertain to the emergence of a significant cell type in a growing population arise frequently. They are often investigated via mathematical modelling but biologically insightful results are challenging to obtain. Here we outline a general framework of a stochastically growing population spreading through a graph to study such questions and provide simple formulas as answers. The significant cell type appears upon the population reaching a target vertex. Due to their simplicity, the derived formulas are widely accessible and can be used to guide and develop intuition on a range of biological scenarios. We demonstrate this on several settings including: how a region where drugs cannot penetrate affects the emergence of resistance, and, the ordering of mutations that leads to drugs being ineffective.

A mathematical model to describe the demographic dynamics of long-lived raptor species

Population viability analysis of threatened large and long-lived raptor species has strong limitations due to the restricted demographic information available for these species. In this work, we mathematically model the demographic dynamics of these raptor species through time-indexed branching processes. By assuming the more general non-parametric statistical setting, we determine accurate estimates for the most relevant reproductive parameters involved in the model. To this end, we propose an algorithm based on approximate Bayesian computations methods. As illustration, by using real data of counts of the number of pairs in the population, we apply the proposed statistical and computational methods to describe the demographic dynamics of the Eurasian black vulture colony located at National Park of Monfragüe (Spain), which appears to be both the largest and densest breeding colony worldwide. In the scenario of these data-poor species, the class of time-indexed branching processes introduced appears to be appropriate and a more cost-effective method to evaluate dynamics and viability of the populations, applicable to the conservation of these taxa.

Geomolecular Dating and the Origin of Placental Mammals

In modern evolutionary divergence analysis the role of geological information extends beyond providing a timescale, to informing molecular rate variation across the tree. Here I consider the implications of this development. I use fossil calibrations to test the accuracy of models of molecular rate evolution for placental mammals, and reveal substantial misspecification associated with life history rate correlates. Adding further calibrations to reduce dating errors at specific nodes unfortunately tends to transfer underlying rate errors to adjacent branches. Thus, tight calibration across the tree is vital to buffer against rate model errors. I argue that this must include allowing maximum bounds to be tight when good fossil records permit, otherwise divergences deep in the tree will tend to be inflated by the interaction of rate errors and asymmetric confidence in minimum and maximum bounds. In the case of placental mammals I sought to reduce the potential for transferring calibration and rate model errors across the tree by focusing on well-supported calibrations with appropriately conservative maximum bounds. The resulting divergence estimates are younger than others published recently, and provide the long-anticipated molecular signature for the placental mammal radiation observed in the fossil record near the 66 Ma Cretaceous-Paleogene extinction event.

Bayesian inference of sampled ancestor trees for epidemiology and fossil calibration

Phylogenetic analyses which include fossils or molecular sequences that are sampled through time require models that allow one sample to be a direct ancestor of another sample. As previously available phylogenetic inference tools assume that all samples are tips, they do not allow for this possibility. We have developed and implemented a Bayesian Markov Chain Monte Carlo (MCMC) algorithm to infer what we call sampled ancestor trees, that is, trees in which sampled individuals can be direct ancestors of other sampled individuals. We use a family of birth-death models where individuals may remain in the tree process after sampling, in particular we extend the birth-death skyline model [Stadler et al., 2013] to sampled ancestor trees. This method allows the detection of sampled ancestors as well as estimation of the probability that an individual will be removed from the process when it is sampled. We show that even if sampled ancestors are not of specific interest in an analysis, failing to account for them leads to significant bias in parameter estimates. We also show that sampled ancestor birth-death models where every sample comes from a different time point are non-identifiable and thus require one parameter to be known in order to infer other parameters. We apply our phylogenetic inference accounting for sampled ancestors to epidemiological data, where the possibility of sampled ancestors enables us to identify individuals that infected other individuals after being sampled and to infer fundamental epidemiological parameters. We also apply the method to infer divergence times and diversification rates when fossils are included along with extant species samples, so that fossilisation events are modelled as a part of the tree branching process. Such modelling has many advantages as argued in the literature. The sampler is available as an open-source BEAST2 package (https://github.com/CompEvol/sampled-ancestors).

A central goal of phylogenetic analysis is to estimate evolutionary relationships and the dynamical parameters underlying the evolutionary branching process (e.g. macroevolutionary or epidemiological parameters) from molecular data. The statistical methods used in these analyses require that the underlying tree branching process is specified. Standard models for the branching process which were originally designed to describe the evolutionary past of present day species do not allow one sampled taxon to be the ancestor of another. However the probability of sampling a direct ancestor is not negligible for many types of data. For example, when fossil and living species are analysed together to infer species divergence times, fossil species may or may not be direct ancestors of living species. In epidemiology, a sampled individual (a host from which a pathogen sequence was obtained) can infect other individuals after sampling, which then go on to be sampled themselves. The models that account for direct ancestors produce phylogenetic trees with a different structure from classic phylogenetic trees and so using these models in inference requires new computational methods. Here we developed a method for phylogenetic analysis that accounts for the possibility of direct ancestors.

The emergence of lobsters: phylogenetic relationships, morphological evolution and divergence time comparisons of an ancient group (decapoda: achelata, astacidea, glypheidea, polychelida)

Lobsters are a ubiquitous and economically important group of decapod crustaceans that include the infraorders Polychelida, Glypheidea, Astacidea and Achelata. They include familiar forms such as the spiny, slipper, clawed lobsters and crayfish and unfamiliar forms such as the deep-sea and "living fossil" species. The high degree of morphological diversity among these infraorders has led to a dynamic classification and conflicting hypotheses of evolutionary relationships. In this study, we estimated phylogenetic relationships among the major groups of all lobster families and 94% of the genera using six genes (mitochondrial and nuclear) and 195 morphological characters across 173 species of lobsters for the most comprehensive sampling to date. Lobsters were recovered as a non-monophyletic assemblage in the combined (molecular + morphology) analysis. All families were monophyletic, with the exception of Cambaridae, and 7 of 79 genera were recovered as poly- or paraphyletic. A rich fossil history coupled with dense taxon coverage allowed us to estimate and compare divergence times and origins of major lineages using two drastically different approaches. Age priors were constructed and/or included based on fossil age information or fossil discovery, age, and extant species count data. Results from the two approaches were largely congruent across deep to shallow taxonomic divergences across major lineages. The origin of the first lobster-like decapod (Polychelida) was estimated in the Devonian (∼409-372 Ma) with all infraorders present in the Carboniferous (∼353-318 Ma). Fossil calibration subsampling studies examined the influence of sampling density (number of fossils) and placement (deep, middle, and shallow) on divergence time estimates. Results from our study suggest including at least 1 fossil per 10 operational taxonomic units (OTUs) in divergence dating analyses. [Dating; decapods; divergence; lobsters; molecular; morphology; phylogenetics.].

Approximate Bayesian computation (ABC) gives exact results under the assumption of model error

Approximate Bayesian computation (ABC) or likelihood-free inference algorithms are used to find approximations to posterior distributions without making explicit use of the likelihood function, depending instead on simulation of sample data sets from the model. In this paper we show that under the assumption of the existence of a uniform additive model error term, ABC algorithms give exact results when sufficient summaries are used. This interpretation allows the approximation made in many previous application papers to be understood, and should guide the choice of metric and tolerance in future work. ABC algorithms can be generalized by replacing the 0-1 cut-off with an acceptance probability that varies with the distance of the simulated data from the observed data. The acceptance density gives the distribution of the error term, enabling the uniform error usually used to be replaced by a general distribution. This generalization can also be applied to approximate Markov chain Monte Carlo algorithms. In light of this work, ABC algorithms can be seen as calibration techniques for implicit stochastic models, inferring parameter values in light of the computer model, data, prior beliefs about the parameter values, and any measurement or model errors.

Dating primate divergences through an integrated analysis of palaeontological and molecular data

Estimation of divergence times is usually done using either the fossil record or sequence data from modern species. We provide an integrated analysis of palaeontological and molecular data to give estimates of primate divergence times that utilize both sources of information. The number of preserved primate species discovered in the fossil record, along with their geological age distribution, is combined with the number of extant primate species to provide initial estimates of the primate and anthropoid divergence times. This is done by using a stochastic forwards-modeling approach where speciation and fossil preservation and discovery are simulated forward in time. We use the posterior distribution from the fossil analysis as a prior distribution on node ages in a molecular analysis. Sequence data from two genomic regions (CFTR on human chromosome 7 and the CYP7A1 region on chromosome 8) from 15 primate species are used with the birth-death model implemented in mcmctree in PAML to infer the posterior distribution of the ages of 14 nodes in the primate tree. We find that these age estimates are older than previously reported dates for all but one of these nodes. To perform the inference, a new approximate Bayesian computation (ABC) algorithm is introduced, where the structure of the model can be exploited in an ABC-within-Gibbs algorithm to provide a more efficient analysis.

Approximate Bayesian Computation (ABC) in practice

Understanding the forces that influence natural variation within and among populations has been a major objective of evolutionary biologists for decades. Motivated by the growth in computational power and data complexity, modern approaches to this question make intensive use of simulation methods. Approximate Bayesian Computation (ABC) is one of these methods. Here we review the foundations of ABC, its recent algorithmic developments, and its applications in evolutionary biology and ecology. We argue that the use of ABC should incorporate all aspects of Bayesian data analysis: formulation, fitting, and improvement of a model. ABC can be a powerful tool to make inferences with complex models if these principles are carefully applied.