A comparison of two methods for generating artificial multi-assemblage ecological datasets

Simulated ecological datasets have been widely used to assess the ability of ordination techniques to portray patterns in ecological assemblage data. Such datasets typically contain a single assemblage sampled over an environmental gradient or set of gradients. Little has been done on the generation of artificial datasets that contain a number of different species assemblages, to aid in the evaluation of multivariate techniques that test for differences between assemblages of species. This paper describes and compares two simulation methods that generate ecologically realistic artificial multi-assemblage datasets. Both methods provide multivariate data (e.g. species abundances) for replicate sites within discretely different assemblages. The first technique is a coenocline model based on species' responses to variation modeled by a five-parameter β-function, where variation in species abundances both within and between assemblages is governed by differences in the positions of sites and assemblages along environmental gradients. The second technique, the resampling method, involves bootstrap resampling of real assemblage datasets, with the addition of selected types of controlled differences between assemblages. Here we use it to generate turnover in species composition. We calibrate both simulation methods based on a field assemblage of bird species. The two different simulation methods portray different levels and types of between-assemblage variation. The resampling method allows greater control over some aspects of assemblage difference (e.g. independently varying differences in species richness and compositional turnover) than the coenocline method. Both can generate usable replicated simulated datasets for assessing the ability of multivariate tests to detect ecological variation among assemblages.     

Variability in cell wall preparations: quantification and comparison of common methods

Cell wall materials were prepared from apple tissue by seven different procedures, some of which are methods in current use in laboratories. The yield, the composition and the fractionation patterns of the pectin content, following sequential extraction in water, chelating agent (CDTA) and a pectin lyase treatment, was compared for each CWM. Variability of the yields and compositions of the CWM were small and few differences were statistically significant. There were differences in the partitioning pattern of the pectin during fractionation but also a high standard deviation of the yields between repetitions.     

Quiescence, excitability, and heterogeneity in ecological models

Introducing quiescent phases into dynamical systems and ecological models tends to stabilize equilibria against the onset of oscillations and also to lower the amplitudes of existing periodic orbits. However, these effects occur when all interacting species go quiescent with the same rates and return to activity with the same rates. On the other hand, if the species differ with respect to these rates, then an equilibrium may even be destabilized. At least in the case of two interacting species this bifurcation phenomenon is closely related to the well-known Turing instability. In particular, for two species it is true that an equilibrium can be destabilized by quiescent phases if and only if it is excitable in the Turing sense. These effects are thoroughly studied and exhibited at the example of classical ecological models and epidemic models. Similar effects occur in delay equations and reaction-diffusion equations. The effect of stabilization against oscillations by quiescent phases can be shown as a special realization of a general principle saying that spatial heterogeneity stabilizes. The results on local stability of stationary points can be extended to periodic orbits. In particular, a geometric argument on the flow along a periodic orbit explains why convex periodic orbits, as observed in numerical simulations, tend to shrink when quiescent phases are introduced.     

Comparative phylogeography: Molecular methods, ecological interpretation

Phylogeohraphy is a new field of study concerned with the principles and processes governing the geographic distribution of genealogical lineages, mainly within and among closely related species. This brief review emphasizes the importance of the ecological approach to the understanding of molecular genetic data. Comparative phylogeohraphy is a promising line of investigation, which provides an opportunity to touch the ground of microevolutionary processes by comparing phylogeohraphical patterns and ecological traits of representatives of individual ecosystems, regional faunas, systematically close species, host-parasite complexes, etc.     

Two-locus models of disease: comparison of likelihood and nonparametric linkage methods.

The power to detect linkage for likelihood and nonparametric (Haseman-Elston, affected-sib-pair, and affected-pedigree-member) methods is compared for the case of a common, dichotomous trait resulting from the segregation of two loci. Pedigree data for several two-locus epistatic and heterogeneity models have been simulated, with one of the loci linked to a marker locus. Replicate samples of 20 three-generation pedigrees (16 individuals/pedigree) were simulated and then ascertained for having at least 6 affected individuals. The power of linkage detection calculated under the correct two-locus model is only slightly higher than that under a single locus model with reduced penetrance. As expected, the nonparametric linkage methods have somewhat lower power than does the lod-score method, the difference depending on the mode of transmission of the linked locus. Thus, for many pedigree linkage studies, the lod-score method will have the best power. However, this conclusion depends on how many times the lod score will be calculated for a given marker. The Haseman-Elston method would likely be preferable to calculating lod scores under a large number of genetic models (i.e., varying both the mode of transmission and the penetrances), since such an analysis requires an increase in the critical value of the lod criterion. The power of the affected-pedigree-member method is lower than the other methods, which can be shown to be largely due to the fact that marker genotypes for unaffected individuals are not used.     

Zooplankton-phytoplankton interactions: the case for refining methods, measurements and models

Many of the classic experiments on the interactions between animals and their food supply were performed using laboratory cultures of Daphnia but comparable predator-prey cycles have seldom been recorded in the field. In this paper, we report the results of a field experiment designed to examine the effect of seasonal variations in the supply of edible algae on the population dynamics of Daphnia hyalina var lacustris. The experiment was performed in a large (45 m diameter) enclosure that was fertilised at regular intervals to sustain phytoplankton production. The results demonstrate that predator prey interactions of the kind recorded in culture can be detected in the field if large numbers of samples are collected and the results analysed using appropriate methods. Analyses using the numbers of Daphnia collected at a single station and chlorophyll a as a measure of food availability produced inconclusive results. Similarly, Daphnia birth rates calculated using the total number of individuals provided a poor measure of the animals reproductive response to changes in the supply of food. The clearest evidence of systematic plant-herbivore interactions was obtained when improved estimates of Daphnia numbers and adult birth rates were combined with estimates of edible rather than total algal biomass. Daphnia birth rates were then positively correlated with the estimated amount of ingestible carbon (r = 0.77) and the proportion of gravid adults decreased dramatically when the concentration of food fell below 0.10 mg C l^-1. Measurements and models of phytoplankton loss rates were then used to assess the impact of Daphnia grazing on the growth and decline of three species of edible algae. The results demonstrated that most species were able to sustain positive growth rates despite short-term increases in the population filtration rate. For much of the summer, the Daphnia appeared to behave as non-interactive grazers and had very little effect on the growth rate of their main phytoplankton food. Their grazing activity did, however, arrest the growth of a late summer population of Chlorella when the Daphnia were estimated to be filtering all the water contained in the enclosure in less than a day.     

Structural identifiability of systems biology models: a critical comparison of methods

Analysing the properties of a biological system through in silico experimentation requires a satisfactory mathematical representation of the system including accurate values of the model parameters. Fortunately, modern experimental techniques allow obtaining time-series data of appropriate quality which may then be used to estimate unknown parameters. However, in many cases, a subset of those parameters may not be uniquely estimated, independently of the experimental data available or the numerical techniques used for estimation. This lack of identifiability is related to the structure of the model, i.e. the system dynamics plus the observation function. Despite the interest in knowing a priori whether there is any chance of uniquely estimating all model unknown parameters, the structural identifiability analysis for general non-linear dynamic models is still an open question. There is no method amenable to every model, thus at some point we have to face the selection of one of the possibilities. This work presents a critical comparison of the currently available techniques. To this end, we perform the structural identifiability analysis of a collection of biological models. The results reveal that the generating series approach, in combination with identifiability tableaus, offers the most advantageous compromise among range of applicability, computational complexity and information provided.     

Detecting behaviours in ecological models

Given an ecological model, I address the question of how to identify the different dynamical behaviours it can exhibit. This requires three steps: the discrimination of different behaviours, the detection of novel behaviours in the model space given current knowledge on model behaviour and the display of the results for visual inspection. I propose simple heuristic algorithms to carry out these steps in the case of models generating time series. I test the method on three models of increasing complexity, analysing both local and global structures in the time series and demonstrating the flexibility of the approach.     

Bayesian methods for comparing species physiological and ecological response curves

Many ecological questions require information on species' optimal conditions or critical limits along environmental gradients. These attributes can be compared to answer questions on niche partitioning, species coexistence and niche conservatism. However, these comparisons are unconvincing when existing methods do not quantify the uncertainty in the attributes or rely on assumptions about the shape of species' responses to the environmental gradient. The aim of this study was to develop a model to quantify the uncertainty in the attributes of species response curves and allow them to be tested for substantive differences without making assumptions about the shape of the responses. We developed a model that used Bayesian penalised splines to produce and compare response curves for any two given species. These splines allow the data to determine the shape of the response curves rather than making a priori assumptions. The models were implemented using the R2OpenBUGS package for R, which uses Markov Chain Monte Carlo simulation to repetitively fit alternative response curves to the data. As each iteration produces a different curve that varies in optima, niche breadth and limits, the model estimates the uncertainty in each of these attributes and the probability that the two curves are different. The models were tested using two datasets of mosses from Antarctica. Both datasets had a high degree of scatter, which is typical of ecological research. This noise resulted in considerable uncertainty in the optima and limits of species response curves, but substantive differences were found. Schistidium antarctici was found to inhabit wetter habitats than Ceratodon purpureus, and Polytrichastrum alpinum had a lower optimal temperature for photosynthesis than Chorisodontium aciphyllum under high light conditions. Our study highlights the importance of considering uncertainty in physiological optima and other attributes of species response curves. We found that apparent differences in optima of 7.5 °C were not necessarily substantive when dealing with noisy ecological data, and it is necessary to consider the uncertainty in attributes when comparing the curves for different species. The model introduced here could increase the robustness of research on niche partitioning, species coexistence and niche conservatism.     

Variability for host preference in insect populations: Mechanistic and evolutionary models

Two models that explain variation in behaviour associated with locating and accepting different habitats (host plants) are described and analyzed. One model describes the dynamics of search-mode ontogeny in Battus philenor butterflies. This model predicts that the proportion of females using either of two search modes at any given time reflects an equilibrium between the rate at which females switch from using a narrow-leaf search mode to using a broad-leaf search mode and the rate at which the opposite switch is made. Preliminary data suggest that the model predicts reasonably well the observed seasonal change in predominant search mode in the field. The second model, really a set of related models, describes the dynamics of genes that influence searching behaviour. Several predictions of these models are: (1) gentic variation for proportional allocation of offspring to different habitats should be more common under soft-selection regimes than under hard-selection regimes. (2) Polyphagy should be more common under soft selection than under hard selection. (3) Whether changes in the relative abundances or relative quality of different habitats lead to evolutionary change in apportionment of offspring to habitats depends in a complex way on mode of population regulation, method of search, type of limitation of fecundity and genetic properties of loci affecting preference. Although the two types of models superficially appear to address different types of behavioural variation, they may be used in a complementary fashion to understand the evolution of habitat selection behaviour.     

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.     

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.     

Persistence and extinction for stochastic ecological models with internal and external variables

Journal of Mathematical Biology - The dynamics of species’ densities depend both on internal and external variables. Internal variables include frequencies of individuals exhibiting different...