Evolving dispersal and age at death

Traditional, and often competing, theories on ageing agree that a programmed age at death must have arisen as a side effect of natural selection, and that it can have no adaptive value of its own. However, theoretical models suggest that ageing and programmed death can be adaptive. Travis J. M. J. suggested that if fecundity declines with age, a programmed age of death evolves through kin selection and that the nature of dispersal is crucial as it determines the degree of spatial structure and hence the strength of kin selection. Here, using a similar model, we consider the interplay between dispersal and age of death. We incorporate more realistic dispersal kernels and allow both dispersal and age of death to evolve. Our results show each trait can evolve in response to the other: earlier age of death evolves when individuals disperse less and greater dispersal distances evolve when individuals are programmed to die later. When we allow dispersal and age of death to evolve at the same time we typically find that dispersal evolves more rapidly, and that ageing then evolves in response to the new dispersal regime. The cost of dispersal is crucial in determining the evolution of both traits. We argue both that ageing is an overlooked ecological process, and that the field of gerontology could learn a lot from evolutionary ecology. We suggest that it is time to develop the field of ecological gerontology and we highlight a few areas where future work might be particularly rewarding.     

Evolutionary model selection with a genetic algorithm: a case study using stem RNA

The choice of a probabilistic model to describe sequence evolution can and should be justified. Underfitting the data through the use of overly simplistic models may miss out on interesting phenomena and lead to incorrect inferences. Overfitting the data with models that are too complex may ascribe biological meaning to statistical artifacts and result in falsely significant findings. We describe a likelihood-based approach for evolutionary model selection. The procedure employs a genetic algorithm (GA) to quickly explore a combinatorially large set of all possible time-reversible Markov models with a fixed number of substitution rates. When applied to stem RNA data subject to well-understood evolutionary forces, the models found by the GA 1) capture the expected overall rate patterns a priori; 2) fit the data better than the best available models based on a priori assumptions, suggesting subtle substitution patterns not previously recognized; 3) cannot be rejected in favor of the general reversible model, implying that the evolution of stem RNA sequences can be explained well with only a few substitution rate parameters; and 4) perform well on simulated data, both in terms of goodness of fit and the ability to estimate evolutionary rates. We also investigate the utility of several distance measures for comparing and contrasting inferred evolutionary models. Using widely available small computer clusters, our approach allows, for the first time, to evaluate the performance of existing RNA evolutionary models by comparing them with a large pool of candidate models and to validate common modeling assumptions. In addition, the new method provides the foundation for rigorous selection and comparison of substitution models for other types of sequence data.     

The consequences of direct versus indirect species interactions to selection on traits: pollination and nectar robbing in Ipomopsis aggregata

Organisms experience a complex suite of species interactions. Although the ecological consequences of direct versus indirect species interactions have received attention, their evolutionary implications are not well understood. I examined selection on floral traits through direct versus indirect pathways of species interactions using the plant Ipomopsis aggregata and its pollinators and nectar robber. Using path analysis and structural equation modeling, I tested competing hypotheses comparing the relative importance of direct (pollinator-mediated) versus indirect (robber-mediated) interactions to trait selection through female plant function in 2 years. The hypothesis that provided the best fit to the observed data included robbing and pollination, suggesting that both interactors are important in driving selection on some traits; however, the direction and intensity of selection through robbing versus pollination varied between years. I then increased my scope of inference by assessing traits and species interactions across more years. I found that the potential for temporal variation in the direction and intensity of selection was pronounced. Taken together, results suggest that assessing the broader context in which organisms evolve, including both direct and indirect interactions and across multiple years, can provide increased mechanistic understanding of the diversity of ways that animals shape floral and plant evolution.     

An analytically tractable model for competitive speciation

Several recent models have shown that frequency-dependent disruptive selection created by intraspecific competition can lead to the evolution of assortative mating and, thus, to competitive sympatric speciation. However, since most of these results rely on limited numerical analyses, their generality has been debated. Here, we consider one of the standard models (the so-called Roughgarden model) with a simplified genetics where the selected trait is determined by a single diallelic locus. This model is sufficiently complex to maintain key properties of the general multilocus case but simple enough to allow for comprehensive analytical treatment by means of invasion fitness arguments. Depending on (1) the strength and (2) the shape of stabilizing selection, (3) the strength and (4) the shape of pairwise competition, (5) the shape of the mating function, and (6) whether assortative mating leads to sexual selection, we find five different evolutionary regimes. In one of these regimes, complete reproductive isolation can evolve through arbitrarily small steps in the strength of assortative mating. Our approach provides a mechanistic understanding of several phenomena that have been found in previous models. The results demonstrate how even in a simple model, the evolutionary outcome depends in a complex way on ecological and genetic parameters.     

Divergent life histories among populations of the fish Brachyrhaphis rhabdophora: detecting putative agents of selection by candidate model analysis

Studies of natural selection in the wild almost always begin by examining patterns of association between phenotypic adaptations and environmental factors thought to shape evolutionary change. Unfortunately, many studies pay little attention to the effects of model selection on the evolutionary inferences drawn from such correlative data. In this study, I employed a candidate model analysis to examine four potential causes of life-history evolution in the livebearing fish Brachyrhaphis rhabdophora . Combining factor analysis with path analysis, I constructed a nested set of 17 models that represent the hypothetical effects of four putative selective agents (mortality, density, resource availability, and habitat stability) on life-history evolution in this species. These models represent both direct and indirect effects of selection on the life history. Using the Akaike Information Criterion to distinguish among models, I found that simple models that contained only single selective agents most parsimoniously explained life-history divergence among 27 B. rhabdophora populations. Surprisingly, the four putative selective agents could not be distinguished, suggesting that the selective environment could be composed of a single selective agent confounded with other environmental factors, or could be composed of a suite of environmental factors that act in concert to shape the life history. In addition, comparisons among more complex models indicated that direct effects of selective agents appear to have primacy over combinations of indirect selective interactions in explaining intraspecific variation in B. rhabdophora life histories.     

A hybrid approach to survival model building using integration of clinical and molecular information in censored data

In medical society, the prognostic models, which use clinicopathologic features and predict prognosis after a certain treatment, have been externally validated and used in practice. In recent years, most research has focused on high dimensional genomic data and small sample sizes. Since clinically similar but molecularly heterogeneous tumors may produce different clinical outcomes, the combination of clinical and genomic information, which may be complementary, is crucial to improve the quality of prognostic predictions. However, there is a lack of an integrating scheme for clinic-genomic models due to the P ≥ N problem, in particular, for a parsimonious model. We propose a methodology to build a reduced yet accurate integrative model using a hybrid approach based on the Cox regression model, which uses several dimension reduction techniques, L? penalized maximum likelihood estimation (PMLE), and resampling methods to tackle the problem. The predictive accuracy of the modeling approach is assessed by several metrics via an independent and thorough scheme to compare competing methods. In breast cancer data studies on a metastasis and death event, we show that the proposed methodology can improve prediction accuracy and build a final model with a hybrid signature that is parsimonious when integrating both types of variables.     

Reducing model complexity of the general Markov model of evolution

The selection of an optimal model for data analysis is an important component of model-based molecular phylogenetic studies. Owing to the large number of Markov models that can be used for data analysis, model selection is a combinatorial problem that cannot be solved by performing an exhaustive search of all possible models. Currently, model selection is based on a small subset of the available Markov models, namely those that assume the evolutionary process to be globally stationary, reversible, and homogeneous. This forces the optimal model to be time reversible even though the actual data may not satisfy these assumptions. This problem can be alleviated by including more complex models during the model selection. We present a novel heuristic that evaluates a small fraction of these complex models and identifies the optimal model.     

Selfishness versus functional cooperation in a stochastic protocell model

How to design an “evolvable” artificial system capable to increase in complexity? Although Darwin’s theory of evolution by natural selection obviously offers a firm foundation, little hope of success seems to be expected from the explanatory adequacy of modern evolutionary theory, which does a good job at explaining what has already happened but remains practically helpless at predicting what will occur. However, the study of the major transitions in evolution clearly suggests that increases in complexity have occurred on those occasions when the conflicting interests between competing individuals were partly subjugated. This immediately raises the issue about “levels of selection” in evolutionary biology, and the idea that multi-level selection scenarios are required for complexity to emerge. After analyzing the dynamical behaviour of competing replicators within compartments, we show here that a proliferation of differentiated catalysts and/or improvement of catalytic efficiency of ribozymes can potentially evolve in properly designed artificial cells where the strong internal competition between the different species of replicators is somewhat prevented (i.e., by choosing them with equal probability). Experimental evolution in these systems will likely stand as beautiful examples of artificial adaptive systems, and will provide new insights to understand possible evolutionary paths to the evolution of metabolic complexity.     

A mixed branch length model of heterotachy improves phylogenetic accuracy

Evolutionary relationships are typically inferred from molecular sequence data using a statistical model of the evolutionary process. When the model accurately reflects the underlying process, probabilistic phylogenetic methods recover the correct relationships with high accuracy. There is ample evidence, however, that models commonly used today do not adequately reflect real-world evolutionary dynamics. Virtually all contemporary models assume that relatively fast-evolving sites are fast across the entire tree, whereas slower sites always evolve at relatively slower rates. Many molecular sequences, however, exhibit site-specific changes in evolutionary rates, called "heterotachy." Here we examine the accuracy of 2 phylogenetic methods for incorporating heterotachy, the mixed branch length model--which incorporates site-specific rate changes by summing likelihoods over multiple sets of branch lengths on the same tree--and the covarion model, which uses a hidden Markov process to allow sites to switch between variable and invariable as they evolve. Under a variety of simple heterogeneous simulation conditions, the mixed model was dramatically more accurate than homotachous models, which were subject to topological biases as well as biases in branch length estimates. When data were simulated with strong versions of the types of heterotachy observed in real molecular sequences, the mixed branch length model was more accurate than homotachous techniques. Analyses of empirical data sets confirmed that the mixed branch length model can improve phylogenetic accuracy under conditions that cause homotachous models to fail. In contrast, the covarion model did not improve phylogenetic accuracy compared with homotachous models and was sometimes substantially less accurate. We conclude that a mixed branch length approach, although not the solution to all phylogenetic errors, is a valuable strategy for improving the accuracy of inferred trees.     

Statistical analysis of synaptic transmission: model discrimination and confidence limits.

Procedures for discriminating between competing statistical models of synaptic transmission, and for providing confidence limits on the parameters of these models, have been developed. These procedures were tested against simulated data and were used to analyze the fluctuations in synaptic currents evoked in hippocampal neurones. All models were fitted to data using the Expectation-Maximization algorithm and a maximum likelihood criterion. Competing models were evaluated using the log-likelihood ratio (Wilks statistic). When the competing models were not nested, Monte Carlo sampling of the model used as the null hypothesis (H0) provided density functions against which H0 and the alternate model (H1) were tested. The statistic for the log-likelihood ratio was determined from the fit of H0 and H1 to these probability densities. This statistic was used to determine the significance level at which H0 could be rejected for the original data. When the competing models were nested, log-likelihood ratios and the chi 2 statistic were used to determine the confidence level for rejection. Once the model that provided the best statistical fit to the data was identified, many estimates for the model parameters were calculated by resampling the original data. Bootstrap techniques were then used to obtain the confidence limits of these parameters.     

An evolutionary model for protein-coding regions with conserved RNA structure

Here we present a model of nucleotide substitution in protein-coding regions that also encode the formation of conserved RNA structures. In such regions, apparent evolutionary context dependencies exist, both between nucleotides occupying the same codon and between nucleotides forming a base pair in the RNA structure. The overlap of these fundamental dependencies is sufficient to cause "contagious" context dependencies which cascade across many nucleotide sites. Such large-scale dependencies challenge the use of traditional phylogenetic models in evolutionary inference because they explicitly assume evolutionary independence between short nucleotide tuples. In our model we address this by replacing context dependencies within codons by annotation-specific heterogeneity in the substitution process. Through a general procedure, we fragment the alignment into sets of short nucleotide tuples based on both the protein coding and the structural annotation. These individual tuples are assumed to evolve independently, and the different tuple sets are assigned different annotation-specific substitution models shared between their members. This allows us to build a composite model of the substitution process from components of traditional phylogenetic models. We applied this to a data set of full-genome sequences from the hepatitis C virus where five RNA structures are mapped within the coding region. This allowed us to partition the effects of selection on different structural elements and to test various hypotheses concerning the relation of these effects. Of particular interest, we found evidence of a functional role of loop and bulge regions, as these were shown to evolve according to a different and more constrained selective regime than the nonpairing regions outside the RNA structures. Other potential applications of the model include comparative RNA structure prediction in coding regions and RNA virus phylogenetics.     

Model selection in ecology and evolution

Recently, researchers in several areas of ecology and evolution have begun to change the way in which they analyze data and make biological inferences. Rather than the traditional null hypothesis testing approach, they have adopted an approach called model selection, in which several competing hypotheses are simultaneously confronted with data. Model selection can be used to identify a single best model, thus lending support to one particular hypothesis, or it can be used to make inferences based on weighted support from a complete set of competing models. Model selection is widely accepted and well developed in certain fields, most notably in molecular systematics and mark-recapture analysis. However, it is now gaining support in several other areas, from molecular evolution to landscape ecology. Here, we outline the steps of model selection and highlight several ways that it is now being implemented. By adopting this approach, researchers in ecology and evolution will find a valuable alternative to traditional null hypothesis testing, especially when more than one hypothesis is plausible.     

Phylogenetic models and model selection for noncoding DNA

Awareness of the complex structure and evolutionary dynamics of noncoding DNA has improved both noncoding sequence alignment and the use of microstructural changes as characters in phylogenetic analysis. The next step is to consider improvements in the use and selection of phylogenetic models for noncoding sequence data. Models of character evolution are central to phylogeny estimation, but the use of an inadequate model can mislead topology selection and branch length estimations. This is particularly likely when sequence divergence is either limited (nearly invariable, as in population-level or species-level studies) or extreme (nearly saturated, as in deep-level studies that focus on conserved secondary structures). Noncoding data sets are often at these extremes, and they can be particularly awkward for model definition and model selection. This paper introduces the goals of model use in phylogenetics and identifies ten issues that arise from the application of models to noncoding sequence data. It is concluded that most of these issues derive from small data set sizes, very low or very high sequence variability, limitations of current phylogenetic models, and possibly character definition and nonindependence. Recommendations are made that should help to improve alignment, character quality, model selection, and phylogeny estimation based on noncoding sequence data.     

Improving sequence-based fold recognition by using 3D model quality assessment

MOTIVATION: The ability of a simple method (MODCHECK) to determine the sequence-structure compatibility of a set of structural models generated by fold recognition is tested in a thorough benchmark analysis. Four Model Quality Assessment Programs (MQAPs) were tested on 188 targets from the latest LiveBench-9 automated structure evaluation experiment. We systematically test and evaluate whether the MQAP methods can successfully detect native-like models. RESULTS: We show that compared with the other three methods tested MODCHECK is the most reliable method for consistently performing the best top model selection and for ranking the models. In addition, we show that the choice of model similarity score used to assess a model's similarity to the experimental structure can influence the overall performance of these tools. Although these MQAP methods fail to improve the model selection performance for methods that already incorporate protein three dimension (3D) structural information, an improvement is observed for methods that are purely sequence-based, including the best profile-profile methods. This suggests that even the best sequence-based fold recognition methods can still be improved by taking into account the 3D structural information. CONTACT: d.jones@cs.ucl.ac.uk     

Modeling invasive species spread in Lake Champlain via evolutionary computations

We use a reaction diffusion equation, together with a genetic algorithm approach for model selection to develop a general modeling framework for biological invasions. The diffusion component of the reaction diffusion model is generalized to include dispersal and advection. The reaction component is generalized to include both linear and non-linear density dependence, and Allee effect. A combination of the reaction diffusion and genetic algorithm is able to evolve the most parsimonious model for invasive species spread. Zebra mussel data obtained from Lake Champlain, which demarcates the states of New York and Vermont, is used to test the appropriateness of the model. We estimate the minimum wave spread rate of Zebra mussels to be 22.5 km/year. In particular, the evolved models predict an average northward advection rate of 60.6 km/year (SD ± 1.9), which compares very well with the rate calculated from the known hydrologic residence time of 60 km/year. A combination of a reaction diffusion model and a genetic algorithm is, therefore, able to adequately describe some of the hydrodynamic features of Lake Champlain and the spread of a typical invasive species—Zebra mussels within the lake.     

The effects of nucleotide substitution model assumptions on estimates of nonparametric bootstrap support

The use of parameter-rich substitution models in molecular phylogenetics has been criticized on the basis that these models can cause a reduction both in accuracy and in the ability to discriminate among competing topologies. We have explored the relationship between nucleotide substitution model complexity and nonparametric bootstrap support under maximum likelihood (ML) for six data sets for which the true relationships are known with a high degree of certainty. We also performed equally weighted maximum parsimony analyses in order to assess the effects of ignoring branch length information during tree selection. We observed that maximum parsimony gave the lowest mean estimate of bootstrap support for the correct set of nodes relative to the ML models for every data set except one. For several data sets, we established that the exact distribution used to model among-site rate variation was critical for a successful phylogenetic analysis. Site-specific rate models were shown to perform very poorly relative to gamma and invariable sites models for several of the data sets most likely because of the gross underestimation of branch lengths. The invariable sites model also performed poorly for several data sets where this model had a poor fit to the data, suggesting that addition of the gamma distribution can be critical. Estimates of bootstrap support for the correct nodes often increased under gamma and invariable sites models relative to equal rates models. Our observations are contrary to the prediction that such models cause reduced confidence in phylogenetic hypotheses. Our results raise several issues regarding the process of model selection, and we briefly discuss model selection uncertainty and the role of sensitivity analyses in molecular phylogenetics.     

Generalized F accelerated failure time model for mapping survival trait loci

As the two most popular models in survival analysis, the accelerated failure time (AFT) model can more easily fit survival data than the Cox proportional hazards model (PHM). In this study, we develop a general parametric AFT model for identifying survival trait loci, in which the flexible generalized F distribution, including many commonly used distributions as special cases, is specified as the baseline survival distribution. EM algorithm for maximum likelihood estimation of model parameters is given. Simulations are conducted to validate the flexibility and the utility of the proposed mapping procedure. In analyzing survival time following hyperoxic acute lung injury (HALI) of mice in an F(2) mating population, the generalized F distribution performed best among the six competing survival distributions and detected four QTLs controlling differential HALI survival.     

Adaptive Dynamics of Altruistic Cooperation in a Metapopulation: Evolutionary Emergence of Cooperators and Defectors or Evolutionary Suicide?

We investigate the evolution of public goods cooperation in a metapopulation model with small local populations, where altruistic cooperation can evolve due to assortment and kin selection, and the evolutionary emergence of cooperators and defectors via evolutionary branching is possible. Although evolutionary branching of cooperation has recently been demonstrated in the continuous snowdrift game and in another model of public goods cooperation, the required conditions on the cost and benefit functions are rather restrictive, e.g., altruistic cooperation cannot evolve in a defector population. We also observe selection for too low cooperation, such that the whole metapopulation goes extinct and evolutionary suicide occurs. We observed intuitive effects of various parameters on the numerical value of the monomorphic singular strategy. Their effect on the final coexisting cooperator–defector pair is more complex: changes expected to increase cooperation decrease the strategy value of the cooperator. However, at the same time the population size of the cooperator increases enough such that the average strategy does increase. We also extend the theory of structured metapopulation models by presenting a method to calculate the fitness gradient in a general class of metapopulation models, and try to make a connection with the kin selection approach.     

Bayesian model averaging for evaluation of candidate gene effects

Statistical assessment of candidate gene effects can be viewed as a problem of variable selection and model comparison. Given a certain number of genes to be considered, many possible models may fit to the data well, each including a specific set of gene effects and possibly their interactions. The question arises as to which of these models is most plausible. Inference about candidate gene effects based on a specific model ignores uncertainty about model choice. Here, a Bayesian model averaging approach is proposed for evaluation of candidate gene effects. The method is implemented through simultaneous sampling of multiple models. By averaging over a set of competing models, the Bayesian model averaging approach incorporates model uncertainty into inferences about candidate gene effects. Features of the method are demonstrated using a simulated data set with ten candidate genes under consideration.