Past states of continuous-time Markov models for ecological communities

Discrete-time Markov chains are often used to model communities of sessile organisms. The community is described by a set of discrete states, which may represent species or groups of species. Transitions between states are modelled using a stochastic matrix. A recent study showed how the time-reversal of such a Markov chain can be used to estimate the distribution of time since the last occurrence of some state of interest (such as empty space) at a point, given the current state of the point. However, if the underlying process operates in continuous time but is observed at regular intervals, this distribution describes the time since the last possible observation of the state of interest, rather than the time since its last occurrence. We show how to obtain the distribution of time since the last occurrence of a state of interest for a continuous-time homogeneous Markov chain. The expected time since the last occurrence of an initial state can be interpreted as a measure of the successional rank of a state. We show how to distinguish between different ways in which a state can have high successional rank. We apply our results to a marine subtidal community.     

Bayesian selection of continuous-time Markov chain evolutionary models

We develop a reversible jump Markov chain Monte Carlo approach to estimating the posterior distribution of phylogenies based on aligned DNA/RNA sequences under several hierarchical evolutionary models. Using a proper, yet nontruncated and uninformative prior, we demonstrate the advantages of the Bayesian approach to hypothesis testing and estimation in phylogenetics by comparing different models for the infinitesimal rates of change among nucleotides, for the number of rate classes, and for the relationships among branch lengths. We compare the relative probabilities of these models and the appropriateness of a molecular clock using Bayes factors. Our most general model, first proposed by Tamura and Nei, parameterizes the infinitesimal change probabilities among nucleotides (A, G, C, T/U) into six parameters, consisting of three parameters for the nucleotide stationary distribution, two rate parameters for nucleotide transitions, and another parameter for nucleotide transversions. Nested models include the Hasegawa, Kishino, and Yano model with equal transition rates and the Kimura model with a uniform stationary distribution and equal transition rates. To illustrate our methods, we examine simulated data, 16S rRNA sequences from 15 contemporary eubacteria, halobacteria, eocytes, and eukaryotes, 9 primates, and the entire HIV genome of 11 isolates. We find that the Kimura model is too restrictive, that the Hasegawa, Kishino, and Yano model can be rejected for some data sets, that there is evidence for more than one rate class and a molecular clock among similar taxa, and that a molecular clock can be rejected for more distantly related taxa.     

Understanding ecological community succession: Causal models and theories,a review

Critical review of explanations for patterns of natural succession suggests a strong, common basis for theoretical understanding, but also suggests that several well known models are incomplete as explanations of succession. A universal, general cause for succession is unlikely, since numerous aspects of historical and environmental circumstances will impinge on the process in a unique manner. However, after disturbance, occupation of a site by any species causes changes in the conditions at the site. Sorting of species may result, since different species are adapted to different regions of environmental gradients. Such sorting can generate several patterns of species abundance in time, but commonly results in sequential replacements of species adapted to the varying conditions. This may be due to constraints on species' strategies, or life history traits, placed by the limited resources available to the organism. These constraints often result in inverse correlation between traits which confer success during early and late stages of succession. Facilitatory or inhibitory effects of species on each other are best understood in terms of these life history interactions, perhaps as restrictions on, or as moderation of, these processes.Strong support for the importance of correlations in life history traits stems from comparisons of simulated succession with and without these correlations. These simulations are reviewed in some detail, and followed by brief reviews of other prominent models for succession. Several aspects of the confusion and controversies in the successional literature are then discussed, with a view to a more optimistic synthesis and direction for successional ecology.     

Bacteriocins: ecological and evolutionary significance

Bacteriocins are compounds that are produced by bacteria and are antagonistic to other bacteria. Although they have been known for many years, recent interest in these compounds has increased because of their potential use as natural food preservatives. Although most of this research has been directed at the molecular level, a clearer picture of the ecological role played by bacteriocins in natural environments is beginning to emerge. In addition, the importance and practical implications of evolutionary aspects of bacteriocins and bacteriocin resistance are now being assessed.     

The analysis of plant growth in ecological and evolutionary studies

Plant growth rate is often assumed to be an ecologically important life history trait. However, conventional plant growth analysis, while providing a useful accounting of rates of weight gain and its components, is ill-suited for testing relationships between growth and fitness, particularly in natural populations. Two new approaches that are suitable for testing such relationships have evolved over the past several years. The first - the population biology of plant parts, or 'modular demography' - permits non-destructive measures of growth rate in natural field populations. When modular demography is performed using matrix population models, controls over growth rate can be examined, as well as consequences of growth variation for reproduction. The second - demographic growth analysis - provides growth parameters analogous to those of conventional growth analysis, but can be performed in natural field populations. Demographic growth analysis allows measures of individual growth-rate variation, which, in turn, can be related to plant performance.     

Cooperation: integrating evolutionary and ecological perspectives

Putting a competitive squeeze on a cooperative group has long been considered to encourage cheats. Now we learn that competition, by driving diversification among cooperators, can create groups that are both more productive and more resistant to defection.     

Species borders: ecological and evolutionary perspectives

Recent ecological studies on species borders have used a number of approaches to establish causation for specific environmental factors and to identify the traits involved. These include interspecific comparisons, detailed investigations of marginal populations, and experimental manipulation. Species borders continue to be largely ignored in evolutionary biology, although some work suggests that marginal populations may often be relatively better-adapted to unfavourable conditions but perform poorly under most other conditions.     

Applying socioendocrinology to evolutionary models: Fatherhood and physiology

Owing to humans' unique life history pattern, particularly comparatively short interbirth intervals, early weaning, and prolonged support of multiple dependents, human females have greater reproductive value and higher lifetime fertility, on average, than do their Great Ape counterparts. 1 - 4 As hominin females began weaning their young early and “stacking” dependents of various ages, they must have had cooperative allomaternal care partners already in place or been successful at concurrently soliciting help to ensure a high rate of survival of their offspring. 1 - 6 Following Hrdy, I define allomaternal care (and its derivatives, such as “allomothers” and “allomothering”) as “care from anyone other than the mother,” which thus encompasses a wide range of individuals, including fathers. 7 Who the likely allomother candidates mothers were and what form that cooperation took remain intriguing, difficult‐to‐answer questions, which are limited, in some capacity, by the lines of evidence available to us. Here, I present a framework for the ways in which we can integrate neurobiological‐endocrine and social‐behavioral data (“socioendocrinology”) 8 to contribute to this dialogue in terms of evaluating fathers' roles.     

Rules of thumb for judging ecological theories

An impressive fit to historical data suggests to biologists that a given ecological model is highly valid. Models often achieve this fit at the expense of exaggerated complexity that is not justified by empirical evidence. Because overfitted theories complement the traditional assumption that ecology is 'messy', they generally remain unquestioned. Using predation theory as an example, we suggest that a fit-driven appraisal of model value is commonly misdirected; although fit to historical data can be important, the simplicity and generality of a theory--and thus its ecological value--are of comparable importance. In particular, we argue that theories whose complexity greatly exceeds the complexity of the problem that they address should be rejected. We suggest heuristics for distinguishing between valuable ecological theories and their overfitted brethren.     

Testing evolutionary theories of menopause

Why do women cease fertility rather abruptly through menopause at an age well before generalized senescence renders child rearing biologically impossible? The two main evolutionary hypotheses are that menopause serves either (i) to protect mothers from rising age-specific maternal mortality risks, thereby protecting their highly dependent younger children from death if the mother dies or (ii) to provide post-reproductive grandmothers who enhance their inclusive fitness by helping to care and provide for their daughters'' children. Recent theoretical work indicates that both factors together are necessary if menopause is to provide an evolutionary advantage. However, these ideas need to be tested using detailed data from actual human life histories lived under reasonably ‘natural’ conditions; for obvious reasons, such data are extremely scarce. We here describe a study based on a remarkably complete dataset from The Gambia. The data provided quantitative estimates for key parameters for the theoretical model, which were then used to assess the actual effects on fitness. Empirically based numerical analysis of this nature is essential if the enigma of menopause is to be explained satisfactorily in evolutionary terms. Our results point to the distinctive (and perhaps unique) role of menopause in human evolution and provide important support for the hypothesized evolutionary significance of grandmothers.     

Sensitivity analysis for informative censoring in parametric survival models

Most statistical methods for censored survival data assume there is no dependence between the lifetime and censoring mechanisms, an assumption which is often doubtful in practice. In this paper we study a parametric model which allows for dependence in terms of a parameter delta and a bias function B(t, theta). We propose a sensitivity analysis on the estimate of the parameter of interest for small values of delta. This parameter measures the dependence between the lifetime and the censoring mechanisms. Its size can be interpreted in terms of a correlation coefficient between the two mechanisms. A medical example suggests that even a small degree of dependence between the failure and censoring processes can have a noticeable effect on the analysis.     

Bifurcation analysis of piecewise smooth ecological models

The aim of this paper is the study of the long-term behavior of population communities described by piecewise smooth models (known as Filippov systems). Models of this kind are often used to describe populations with selective switching between alternative habitats or diets or to mimic the evolution of an exploited resource where harvesting is forbidden when the resource is below a prescribed threshold. The analysis is carried out by performing the bifurcation analysis of the model with respect to two parameters. A relatively simple method, called the puzzle method, is proposed to construct the complete bifurcation diagram step-by-step. The method is illustrated through four examples concerning the exploitation and protection of interacting populations.     

Nectarless flowers: ecological correlates and evolutionary stability

In animal-pollinated flowers, the pollinators cannot detect the presence of nectar before entering flowers, and therefore flowers may cheat by not producing nectar. An earlier model suggested that a mixed strategy of producing nectarful and nectarless flowers would be evolutionarily stable. Here we compare nectarless flowers as a cheating strategy with three competing hypotheses namely "visit-more-flowers", "cross-pollination enhancement" and "better contact". We collected field data on 28 species of plants to test some of the differential predictions of the hypotheses. Nectarless flowers were detected in 24 out of 28 plant species. Correlations of percent nectarless flowers with floral and ecological variables support the cheater flower hypothesis. We further model the cost-benefits of cheating and show that an evolutionary stable ratio of nectarless to nectarful flowers can be reached. The equilibrium ratio is mainly decided by factors associated with pollinator density and pollinator learning.     

Behavioral syndromes: an ecological and evolutionary overview

Recent studies suggest that populations and species often exhibit behavioral syndromes; that is, suites of correlated behaviors across situations. An example is an aggression syndrome where some individuals are more aggressive, whereas others are less aggressive across a range of situations and contexts. The existence of behavioral syndromes focuses the attention of behavioral ecologists on limited (less than optimal) behavioral plasticity and behavioral carryovers across situations, rather than on optimal plasticity in each isolated situation. Behavioral syndromes can explain behaviors that appear strikingly non-adaptive in an isolated context (e.g. inappropriately high activity when predators are present, or excessive sexual cannibalism). Behavioral syndromes can also help to explain the maintenance of individual variation in behavioral types, a phenomenon that is ubiquitous, but often ignored. Recent studies suggest that the behavioral type of an individual, population or species can have important ecological and evolutionary implications, including major effects on species distributions, on the relative tendencies of species to be invasive or to respond well to environmental change, and on speciation rates. Although most studies of behavioral syndromes to date have focused on a few organisms, mainly in the laboratory, further work on other species, particularly in the field, should yield numerous new insights.