Flexible components of functional responses

1. The functional response of predators describes the rate at which a predator consumes prey and is an important determinant of community dynamics. Despite the importance, most empirical studies have considered a limited number of models of functional response. In addition, the models often make strong assumptions about the pattern of predation processes, even though functional responses can potentially exhibit a wide variety of patterns. 2. In addition to the limited model consideration, model selections of functional response models cannot tease apart the components of predation (i.e. capture rate and handling time) when flexible traits are considered because it is always possible that many different combinations of the capture rate and handling time can lead to the same predation rate. 3. This study directly examined the capture rate and handling time of functional response in a mite community. To avoid the model selection problem, the searching and handling behaviour data were collected. The model selection was applied directly to these two components of predation data. Commonly used functional response models and models that allow for more flexible patterns were compared. 4. The results indicated that assumptions of the commonly used models were not supported by the data, and a flexible model was selected as the best model. These results suggest the need to consider a wider variety of predation patterns when characterizing a functional response. Without making a strong assumption (e.g. static handling time), model selections on functional response models cannot be used to make reliable inferences on the predation mechanisms.     

The loss in power when the test of differential expression is performed under a wrong scale.

One of the most common and important goals of microarray studies is to identify genes that are differentially expressed between cells of different conditions. T-test and ANOVA models on the expression data are common practices to gauge the significance of the observed difference in expression levels. Transformation of the microarray data is often applied in order to satisfy the model assumptions being entertained. However, the distributional properties of the expression are gene specific, and it is impractical to find a single transformation that is universally optimal for all the genes. This difficulty results in the situation that some genes have to violate the assumptions of the model (e.g., homogeneity in variance, normality). It is thus the interest of this paper to evaluate the impact on the inference of differential expression when the test is performed under an inappropriate scale. Particularly, we quantitatively assess the loss of power when the test is performed under a wrong scale. Normal distribution and log-normal distribution of the expression data are considered. The loss in power is investigated in two scenarios: a transformation is misused, or a transformation fails to be applied. Log transformation and power transformation are particularly considered due to the fact that Box-Cox types of transformation are commonly used in practice. The impact of using a wrong scale is investigated analytically and based on simulations. The loss in power is assessed both as a function of the degree to which the assumptions are violated and as a function of the effect size. Simulations are conducted to quantitatively assess the power loss when tests are performed under a wrong scale. A public experimental microarray dataset is used to illustrate the impact of transformation on the results of testing differential expression. The results show that the loss of power is a function of CV and fold-change (effect size). The loss in power depends on the true model and on how severely the assumptions are violated.     

A phylogeny of anisopterous dragonflies (Insecta,Odonata) using mtRNA genes and mixed nucleotide/doublet models

The application of mixed nucleotide/doublet substitution models has recently received attention in RNA‐based phylogenetics. Within a Bayesian approach, it was shown that mixed models outperformed analyses relying on simple nucleotide models. We analysed an mt RNA data set of dragonflies representing all major lineages of Anisoptera plus outgroups, using a mixed model in a Bayesian and parsimony (MP) approach. We used a published mt 16S rRNA secondary consensus structure model and inferred consensus models for the mt 12S rRNA and tRNA valine. Secondary structure information was used to set data partitions for paired and unpaired sites on which doublet or nucleotide models were applied, respectively. Several different doublet models are currently available of which we chose the most appropriate one by a Bayes factor test. The MP reconstructions relied on recoded data for paired sites in order to account for character covariance and an application of the ratchet strategy to find most parsimonious trees. Bayesian and parsimony reconstructions are partly differently resolved, indicating sensitivity of the reconstructions to model specification. Our analyses depict a tree in which the damselfly family Lestidae is sister group to a monophyletic clade Epiophlebia + Anisoptera, contradicting recent morphological and molecular work. In Bayesian analyses, we found a deep split between Libelluloidea and a clade ‘Aeshnoidea’ within Anisoptera largely congruent with Tillyard’s early ideas of anisopteran evolution, which had been based on evidently plesiomorphic character states. However, parsimony analysis did not support a clade ‘Aeshnoidea’, but instead, placed Gomphidae as sister taxon to Libelluloidea. Monophyly of Libelluloidea is only modestly supported, and many inter‐family relationships within Libelluloidea do not receive substantial support in Bayesian and parsimony analyses. We checked whether high Bayesian node support was inflated owing to either: (i) wrong secondary consensus structures; (ii) under‐sampling of the MCMC process, thereby missing other local maxima; or (iii) unrealistic prior assumptions on topologies or branch lengths. We found that different consensus structure models exert strong influence on the reconstruction, which demonstrates the importance of taxon‐specific realistic secondary structure models in RNA phylogenetics.     

A bayesian framework for parentage analysis: the value of genetic and other biological data

We develop fractional allocation models and confidence statistics for parentage analysis in mating systems. The models can be used, for example, to estimate the paternities of candidate males when the genetic mother is known or to calculate the parentage of candidate parent pairs when neither is known. The models do not require two implicit assumptions made by previous models, assumptions that are potentially erroneous. First, we provide formulas to calculate the expected parentage, as opposed to using a maximum likelihood algorithm to calculate the most likely parentage. The expected parentage is superior as it does not assume a symmetrical probability distribution of parentage and therefore, unlike the most likely parentage, will be unbiased. Second, we provide a mathematical framework for incorporating additional biological data to estimate the prior probability distribution of parentage. This additional biological data might include behavioral observations during mating or morphological measurements known to correlate with parentage. The value of multiple sources of information is increased accuracy of the estimates. We show that when the prior probability of parentage is known, and the expected parentage is calculated, fractional allocation provides unbiased estimates of the variance in reproductive success, thereby correcting a problem that has previously plagued parentage analyses. We also develop formulas to calculate the confidence interval in the parentage estimates, thus enabling the assessment of precision. These confidence statistics have not previously been available for fractional models. We demonstrate our models with several biological examples based on data from two fish species that we study, coho salmon (Oncorhychus kisutch) and bluegill sunfish (Lepomis macrochirus). In coho, multiple males compete to fertilize a single female's eggs. We show how behavioral observations taken during spawning can be combined with genetic data to provide an accurate calculation of each male's paternity. In bluegill, multiple males and multiple females may mate in a single nest. For a nest, we calculate the fertilization success and the 95% confidence interval of each candidate parent pair.     

Multiscale modeling and mechanics of filamentous actin cytoskeleton

The adaptive structure and functional changes of the actin cytoskeleton are induced by its mechanical behavior at various temporal and spatial scales. In particular, the mechanical behaviors at different scales play important roles in the mechanical functions of various cells, and these multiscale phenomena require clarification. To establish a milestone toward achieving multiscale modeling and simulation, this paper reviews mathematical analyses and simulation methods applied to the mechanics of the filamentous actin cytoskeleton. The actin cytoskeleton demonstrates characteristic behaviors at every temporal and spatial scale, and mathematical models and simulation methods can be applied to each level of actin cytoskeletal structure ranging from the molecular to the network level. This paper considers studies on mathematical models and simulation methods based on the molecular dynamics, coarse-graining, and continuum dynamics approaches. Every temporal and spatial scale of actin cytoskeletal structure is considered, and it is expected that discrete and continuum dynamics ranging from functional expression at the molecular level to macroscopic functional expression at the whole cell level will be developed and applied to multiscale modeling and simulation.     

On mathematical modeling of circadian rhythms, performance, and alertness

Mathematical models of neurobehavioral performance and alertness have both basic science and practical applications. These models can be especially useful in predicting the effect of different sleep-wake schedules on human neurobehavioral objective performance and subjective alertness under many conditions. Several relevant models currently exist in the literature. In principle, the development and refinement of any mathematical model should be based on an explicit modeling methodology, such as the Box modeling paradigm, that formally defines the model structure and calculates the set of parameters. While most mathematical models of neurobehavioral performance and alertness include homeostatic, circadian, and sleep inertia components and their interactions, there may be fundamental differences in the equations included in these models. In part, these may be due to differences in the assumptions of the underlying physiology. Because the choice of model equations can have a dramatic influence on the results, it is necessary to consider these differences in assumptions when examining the results from a model and when comparing results across models. This article presents principles of mathematical modeling and examples of how such procedures can be applied to the development and refinement of mathematical models of neurobehavioral performance and alertness. This article also presents several methods of testing and comparing these models, suggests different uses of the models, and discusses problems with current models.     

Biogeographic calibrations for the molecular clock

Molecular estimates of evolutionary timescales have an important role in a range of biological studies. Such estimates can be made using methods based on molecular clocks, including models that are able to account for rate variation across lineages. All clock models share a dependence on calibrations, which enable estimates to be given in absolute time units. There are many available methods for incorporating fossil calibrations, but geological and climatic data can also provide useful calibrations for molecular clocks. However, a number of strong assumptions need to be made when using these biogeographic calibrations, leading to wide variation in their reliability and precision. In this review, we describe the nature of biogeographic calibrations and the assumptions that they involve. We present an overview of the different geological and climatic events that can provide informative calibrations, and explain how such temporal information can be incorporated into dating analyses.     

Bayesian multiple index models for environmental mixtures

An important goal of environmental health research is to assess the risk posed by mixtures of environmental exposures. Two popular classes of models for mixtures analyses are response-surface methods and exposure-index methods. Response-surface methods estimate high-dimensional surfaces and are thus highly flexible but difficult to interpret. In contrast, exposure-index methods decompose coefficients from a linear model into an overall mixture effect and individual index weights; these models yield easily interpretable effect estimates and efficient inferences when model assumptions hold, but, like most parsimonious models, incur bias when these assumptions do not hold. In this paper, we propose a Bayesian multiple index model framework that combines the strengths of each, allowing for non-linear and non-additive relationships between exposure indices and a health outcome, while reducing the dimensionality of the exposure vector and estimating index weights with variable selection. This framework contains response-surface and exposure-index models as special cases, thereby unifying the two analysis strategies. This unification increases the range of models possible for analysing environmental mixtures and health, allowing one to select an appropriate analysis from a spectrum of models varying in flexibility and interpretability. In an analysis of the association between telomere length and 18 organic pollutants in the National Health and Nutrition Examination Survey (NHANES), the proposed approach fits the data as well as more complex response-surface methods and yields more interpretable results.     

Measuring the functional responses of farmland birds: an example for a declining seed-feeding bunting

1. Many farmland bird species have undergone significant declines. It is important to predict the effect of agricultural change on these birds and their response to conservation measures. This requirement could be met by mechanistic models that predict population size from the optimal foraging behaviour and fates of individuals within populations. A key component of these models is the functional response, the relationship between food and competitor density and feeding rate. 2. This paper describes a method for measuring functional responses of farmland birds, and applies this method to a declining farmland bird, the corn bunting Miliaria calandra L. We derive five alternative models to predict the functional responses of farmland birds and parameterize these for corn bunting. We also assess the minimum sample sizes required to predict accurately the functional response. 3. We show that the functional response of corn bunting can be predicted accurately from a few behavioural parameters (searching rate, handling time, vigilance time) that are straightforward to measure in the field. These parameters can be measured more quickly than the alternative of measuring the functional response directly. 4. While corn bunting violated some of the assumptions of Holling's disk equation (model 1 in our study), it still provided the most accurate fit to the observed feeding rates while remaining the most statistically simple model tested. Our other models may be more applicable to other species, or corn bunting feeding in other locations. 5. Although further tests are required, our study shows how functional responses can be predicted, simplifying the development of mechanistic models of farmland bird populations.     

Comparative performance of Bayesian and AIC-based measures of phylogenetic model uncertainty

Reversible-jump Markov chain Monte Carlo (RJ-MCMC) is a technique for simultaneously evaluating multiple related (but not necessarily nested) statistical models that has recently been applied to the problem of phylogenetic model selection. Here we use a simulation approach to assess the performance of this method and compare it to Akaike weights, a measure of model uncertainty that is based on the Akaike information criterion. Under conditions where the assumptions of the candidate models matched the generating conditions, both Bayesian and AIC-based methods perform well. The 95% credible interval contained the generating model close to 95% of the time. However, the size of the credible interval differed with the Bayesian credible set containing approximately 25% to 50% fewer models than an AIC-based credible interval. The posterior probability was a better indicator of the correct model than the Akaike weight when all assumptions were met but both measures performed similarly when some model assumptions were violated. Models in the Bayesian posterior distribution were also more similar to the generating model in their number of parameters and were less biased in their complexity. In contrast, Akaike-weighted models were more distant from the generating model and biased towards slightly greater complexity. The AIC-based credible interval appeared to be more robust to the violation of the rate homogeneity assumption. Both AIC and Bayesian approaches suggest that substantial uncertainty can accompany the choice of model for phylogenetic analyses, suggesting that alternative candidate models should be examined in analysis of phylogenetic data. [AIC; Akaike weights; Bayesian phylogenetics; model averaging; model selection; model uncertainty; posterior probability; reversible jump.].     

On the maintenance of genetic variation: global analysis of Kimura's continuum-of-alleles model

Methods of functional analysis are applied to provide an exact mathematical analysis of Kimura's continuum-of-alleles model. By an approximate analysis, Kimura obtained the result that the equilibrium distribution of allelic effects determining a quantitative character is Gaussian if fitness decreases quadratically from the optimum and if production of new mutants follows a Gaussian density. Lande extended this model considerably and proposed that high levels of genetic variation can be maintained by mutation even when there is strong stabilizing selection. This hypothesis has been questioned recently by Turelli, who published analyses and computer simulations of some multiallele models, approximating the continuum-of-alleles model, and reviewed relevant data. He found that the Kimura and Lande predictions overestimate the amount of equilibrium variance considerably if selection is not extremely weak or mutation rate not extremely high. The present analysis provides the first proof that in Kimura's model an equilibrium in fact exists and, moreover, that it is globally stable. Finally, using methods from quantum mechanics, estimates of the exact equilibrium variance are derived which are in best accordance with Turelli's results. This shows that continuum-of-alleles models may be excellent approximations to multiallele models, if analysed appropriately.     

Corroboration versus "Strongest Evidence"

Background knowledge comprises accepted (well-corroborated) theories and results. Such theories are taken to be true for the purpose of interpreting evidence when assessing the corroboration of a hypothesis currently in question. Accordingly, background knowledge does not properly include rejected theories, false assumptions, or null models. In particular, regarding a model of random character distribution as "background knowledge" would rule out corroboration of phylogenetic hypotheses, since it would make character data irrelevant to inferring phylogeny. The presence of homoplasy is not grounds for treating characters as if they were randomly distributed, since characters can show strong phylogenetic structure even when they show homoplasy. This means that clique (compatibility) analysis is unjustified, since that method depends crucially on the assumption that characters showing any homoplasy at all are unrelated to phylogeny. Although likelihood does not measure corroboration, corroboration is closely connected to likelihood: for given evidence and background, the most likely trees are also best corroborated. Most parsimonious trees are best corroborated; the apparent clash between parsimony and likelihood is an artifact of the use of unrealistic models in most "maximum likelihood" methods.     

Evaluating the Impact of Prior Assumptions in Bayesian Biostatistics

A common concern in Bayesian data analysis is that an inappropriately informative prior may unduly influence posterior inferences. In the context of Bayesian clinical trial design, well chosen priors are important to ensure that posterior-based decision rules have good frequentist properties. However, it is difficult to quantify prior information in all but the most stylized models. This issue may be addressed by quantifying the prior information in terms of a number of hypothetical patients, i.e., a prior effective sample size (ESS). Prior ESS provides a useful tool for understanding the impact of prior assumptions. For example, the prior ESS may be used to guide calibration of prior variances and other hyperprior parameters. In this paper, we discuss such prior sensitivity analyses by using a recently proposed method to compute a prior ESS. We apply this in several typical settings of Bayesian biomedical data analysis and clinical trial design. The data analyses include cross-tabulated counts, multiple correlated diagnostic tests, and ordinal outcomes using a proportional-odds model. The study designs include a phase I trial with late-onset toxicities, a phase II trial that monitors event times, and a phase I/II trial with dose-finding based on efficacy and toxicity.     

Uncertainty in assessing the impacts of global change with coupled dynamic species distribution and population models

Concern over rapid global changes and the potential for interactions among multiple threats are prompting scientists to combine multiple modelling approaches to understand impacts on biodiversity. A relatively recent development is the combination of species distribution models, land‐use change predictions, and dynamic population models to predict the relative and combined impacts of climate change, land‐use change, and altered disturbance regimes on species' extinction risk. Each modelling component introduces its own source of uncertainty through different parameters and assumptions, which, when combined, can result in compounded uncertainty that can have major implications for management. Although some uncertainty analyses have been conducted separately on various model components – such as climate predictions, species distribution models, land‐use change predictions, and population models – a unified sensitivity analysis comparing various sources of uncertainty in combined modelling approaches is needed to identify the most influential and problematic assumptions. We estimated the sensitivities of long‐run population predictions to different ecological assumptions and parameter settings for a rare and endangered annual plant species (Acanthomintha ilicifolia, or San Diego thornmint). Uncertainty about habitat suitability predictions, due to the choice of species distribution model, contributed most to variation in predictions about long‐run populations.     

Metabolic Engineering with power-law and linear-logarithmic systems

Metabolic Engineering aims to improve the performance of biotechnological processes through rational manipulation rather than random mutagenesis of the organisms involved. Such a strategy can only succeed when a mathematical model of the target process is available. Simplifying assumptions are often needed to cope with the complexity of such models in an efficient way, and the choice of such assumptions often leads to models that fall within a certain structural template or formalism. The most popular formalisms can be grouped in two categories: power-law and linear-logarithmic. As optimization and analysis of a model strongly depends on its structure, most methods in Metabolic Engineering have been defined within a given formalism and never used in any other.In this work, the four most commonly used formalisms (two power-law and two linear-logarithmic) are placed in a common framework defined within Biochemical Systems Theory. This framework defines every model as matrix equations in terms of the same parameters, enabling the formulation of a common steady state analysis and providing means for translating models and methods from one formalism to another. Several Metabolic Engineering methods are analysed here and shown to be variants of a single equation. Particularly, two problem solving philosophies are compared: the application of the design equation and the solution of constrained optimization problems. Generalizing the design equation to all the formalisms shows it to be interchangeable with the direct solution of the rate law in matrix form. Furthermore, optimization approaches are concluded to be preferable since they speed the exploration of the feasible space, implement a better specification of the problem and exclude unrealistic results.Beyond consolidating existing knowledge and enabling comparison, the systematic approach adopted here can fill the gaps between the different methods and combine their strengths.     

Family-based approaches: design,imputation, analysis,and beyond

Participants in the family-based analysis group at Genetic Analysis Workshop 19 addressed diverse topics, all of which used the family data. Topics addressed included questions of study design and data quality control (QC), genotype imputation to augment available sequence data, and linkage and/or association analyses. Results show that pedigree-based tests that are sensitive to genotype error may be useful for QC. Imputation quality improved with inclusion of small amounts of pedigree information used to phase the data in evaluation of 5 commonly used approaches for imputation in samples of (typically) unrelated subjects. It improved still further when pedigree-based imputation using larger pedigrees was also added. An important distinction was made between methods that do versus do not make use of Mendelian transmission in pedigrees, because this serves as a key difference between underlying models and assumptions. Methods that model relatedness generally had higher power in association testing than did analyses that carry out testing in the presence of a transmission model, but this may reflect details of implementation and/or ability of more general methods to jointly include data from larger pedigrees. In either case, for single nucleotide polymorphism–set approaches, weights that incorporate information on functional effects may be more useful than those that are based only on allele frequencies. The overall results demonstrate that family data continue to provide important information in the search for trait loci.     

New substitution models for rooting phylogenetic trees

The root of a phylogenetic tree is fundamental to its biological interpretation, but standard substitution models do not provide any information on its position. Here, we describe two recently developed models that relax the usual assumptions of stationarity and reversibility, thereby facilitating root inference without the need for an outgroup. We compare the performance of these models on a classic test case for phylogenetic methods, before considering two highly topical questions in evolutionary biology: the deep structure of the tree of life and the root of the archaeal radiation. We show that all three alignments contain meaningful rooting information that can be harnessed by these new models, thus complementing and extending previous work based on outgroup rooting. In particular, our analyses exclude the root of the tree of life from the eukaryotes or Archaea, placing it on the bacterial stem or within the Bacteria. They also exclude the root of the archaeal radiation from several major clades, consistent with analyses using other rooting methods. Overall, our results demonstrate the utility of non-reversible and non-stationary models for rooting phylogenetic trees, and identify areas where further progress can be made.     

cati: an R package using functional traits to detect and quantify multi‐level community assembly processes

Community ecologists are active in describing species by their functional traits, quantifying the functional structure of plant and animal assemblages and inferring community assembly processes with null‐model analyses of trait distribution and functional diversity indices. Intraspecific variation in traits and effects of spatial scale are potentially important in these analyses. Here, we introduce the R package cati (Community Assembly by Traits: Individuals and beyond) available on CRAN, for the analysis of community assembly with functional traits. cati builds on a recent approach to community assembly that explicitly incorporates individual differences in community assembly analyses and decomposes phenotypic variations across scales and organizational levels, based on three phenotypic variance ratios, termed the T‐statistics. More generally, the cati package 1) calculates a variety of single‐trait and multi‐trait indices from interspecific and intraspecific trait measures; 2) it partitions functional trait variation among spatial and taxonomic levels; 3) it implements a palette of flexible null models for detecting non‐random patterns of functional traits. These patterns can be used to draw inferences about hypotheses of community assembly such as environmental filtering and species interactions. The basic input for cati is a data frame in which columns are traits, rows are species or individuals, and entries are the measured trait values. The cati package can also incorporate a square distance matrix into analyses, which could include phylogenetic or genetic distances among individuals or species. Users select from a variety of functional trait metrics and analyze these relative to a null model that specifies trait distributions in a regional source pool.     

Multiscale Characterization of Land-Use Patterns in China

This article explores the pattern of land use in China to understand the relationships between land use and factors that can be used to predict it. Such understanding is important for development of comprehensive models of land-use dynamics. Correlation and regression analyses are used to identify the most important explanatory variables from a large set of factors generally considered important in predicting the distribution of land use. We found that the spatial distribution of all land-use types in China is best described by an integrated set of biophysical and socioeconomic factors. Specific attention is given to the influence of the scale of analysis on study results. Both data resolution and the extent of the study area influence the discovered relationships. Relationships obtained at a certain scale of analysis therefore may not be directly applied at other scales or in other areas. The relevance of the systematic and quantitative characterization of the land-use patterns in China for the parameterization of spatially explicit land-use models is discussed. Received 20 July 1999; accepted 10 March 2000.