Stochastic models of population extinction

Theoretical ecologists have long sought to understand how the persistence of populations depends on biotic and abiotic factors. Classical work showed that demographic stochasticity causes the mean time to extinction to increase exponentially with population size, whereas variation in environmental conditions can lead to a power law scaling. Recent work has focused especially on the influence of the autocorrelation structure ("color") of environmental noise. In theoretical physics, there is a burst of research activity in analyzing large fluctuations in stochastic population dynamics. This research provides powerful tools for determining extinction times and characterizing the pathway to extinction. It yields, therefore, sharp insights into extinction processes and has great potential for further applications in theoretical biology.Comment: A popular review, to appear in "Trends in Ecology & Evolution", 42 pages, 5 figure

The interplay between immigration and local population dynamics in metapopulations

Stochastic models of closed populations predict eventual extinction with certainty. Consequently, their behavior is often characterized by the quasi-stationary state, i.e. the long-term distribution of population sizes conditional on non-extinction. In contrast, models which allow for immigration exhibit a regular stationary state. At the limit of a low immigration rate, a population is expected to alternate between three states: the quasi- stationary state of a closed population, the extinction state, and the transient phase during which a newly arrived immigrant either establishes a new population or fails to do so. We develop this argument into a simple and intuitive framework that can be used to assess the effect of immigration in a general class of population models. We exemplify the framework for models in which immigrants arrive either singly or in groups, for models with an Allee effect, for models with environmental stochasticity, and for models leading to metapopulation dynamics.Peer reviewe

Unbiased probabilistic taxonomic classification for DNA barcoding

Motivation: When targeted to a barcoding region, high-throughput sequencing can be used to identify species or operational taxonomical units from environmental samples, and thus to study the diversity and structure of species communities. Although there are many methods which provide confidence scores for assigning taxonomic affiliations, it is not straightforward to translate these values to unbiased probabilities. We present a probabilistic method for taxonomical classification (PROTAX) of DNA sequences. Given a pre-defined taxonomical tree structure that is partially populated by reference sequences, PROTAX decomposes the probability of one to the set of all possible outcomes. PROTAX accounts for species that are present in the taxonomy but that do not have reference sequences, the possibility of unknown taxonomical units, as well as mislabeled reference sequences. PROTAX is based on a statistical multinomial regression model, and it can utilize any kind of sequence similarity measures or the outputs of other classifiers as predictors. Results: We demonstrate the performance of PROTAX by using as predictors the output from BLAST, the phylogenetic classification software TIPP, and the RDP classifier. We show that PROTAX improves the predictions of the baseline implementations of TIPP and RDP classifiers, and that it is able to combine complementary information provided by BLAST and TIPP, resulting in accurate and unbiased classifications even with very challenging cases such as 50% mislabeling of reference sequences.Peer reviewe

Uncovering hidden spatial structure in species communities with spatially explicit joint species distribution models

1. Modern species distribution models account for spatial autocorrelation in order to obtain unbiased statistical inference on the effects of covariates, to improve the model's predictive ability through spatial interpolation and to gain insight in the spatial processes shaping the data. Somewhat analogously, hierarchical approaches to community-level data have been developed to gain insights into community-level processes and to improve species-level inference by borrowing information from other species that are either ecologically or phylogenetically related to the focal species. 2. We unify spatial and community-level structures by developing spatially explicit joint species distribution models. The models utilize spatially structured latent factors to model missing covariates as well as species-to-species associations in a statistically and computationally effective manner. 3. We illustrate that the inclusion of the spatial latent factors greatly increases the predictive performance of the modelling approach with a case study of 55 species of butterfly recorded on a 10 km × 10 km grid in Great Britain consisting of 2609 grid cells

Mitä teoria sanoo lajien mahdollisuudesta säilyä pirstoutuvassa elinympäristössä?

Matemaatikkojen ja fyysikkojen yhteistyö on kautta tieteen historian ollut niin erottamatonta, että on usein jopa vaikeata erottaa näitä aloja toisistaan. Sen sijaan matemaatikko ekologiassa on edelleenkin jonkinasteinen kummajainen, ainakin suuren yleisön silmissä. Lintujako hän laskee vai kaloja

Exact asymptotic analysis for metapopulation dynamics on correlated dynamic landscapes

We compute the mean patch occupancy for a stochastic, spatially explicit patch-occupancy metapopulation model on a dynamic, correlated landscape, using a mathematically exact perturbation expansion about a mean-field limit that applies when dispersal range is large. Stochasticity in the metapopulation and landscape dynamics gives negative contributions to patch occupancy, the former being more important at high occupancy and the latter at low occupancy. Positive landscape correlations always benefit the metapopulation, but are only significant when the correlation length is comparable to, or smaller than, the dispersal range. Our analytical results allow us to consider the importance of spatial kernels in all generality. We find that the shape of the landscape correlation function is typically unimportant, and that the variance is overwhelmingly the most important property of the colonisation kernel. However, short-range singularities in either the colonisation kernel or landscape correlations can give rise to qualitatively different behaviour

Correlated velocity models as a fundamental unit of animal movement : synthesis and applications

Background: Continuous time movement models resolve many of the problems with scaling, sampling, and interpretation that affect discrete movement models. They can, however, be challenging to estimate, have been presented in inconsistent ways, and are not widely used. Methods: We review the literature on integrated Ornstein-Uhlenbeck velocity models and propose four fundamental correlated velocity movement models (CVM's): random, advective, rotational, and rotational-advective. The models are defined in terms of biologically meaningful speeds and time scales of autocorrelation. We summarize several approaches to estimating the models, and apply these tools for the higher order task of behavioral partitioning via change point analysis. Results: An array of simulation illustrate the precision and accuracy of the estimation tools. An analysis of a swimming track of a bowhead whale (Balaena mysticetus) illustrates their robustness to irregular and sparse sampling and identifies switches between slower and faster, and directed vs. random movements. An analysis of a short flight of a lesser kestrel (Falco naumanni) identifies exact moments when switches occur between loopy, thermal soaring and directed flapping or gliding flights. Conclusions: We provide tools to estimate parameters and perform change point analyses in continuous time movement models as an R package (smoove). These resources, together with the synthesis, should facilitate the wider application and development of correlated velocity models among movement ecologists.Peer reviewe

What can observational data reveal about metacommunity processes?

A key challenge for community ecology is to understand to what extent observational data can be used to infer the underlying community assembly processes. As different processes can lead to similar or even identical patterns, statistical analyses of non-manipulative observational data never yield undisputable causal inference on the underlying processes. Still, most empirical studies in community ecology are based on observational data, and hence understanding under which circumstances such data can shed light on assembly processes is a central concern for community ecologists. We simulated a spatial agent-based model that generates variation in metacommunity dynamics across multiple axes, including the four classic metacommunity paradigms as special cases. We further simulated a virtual ecologist who analysed snapshot data sampled from the simulations using eighteen output metrics derived from beta-diversity and habitat variation indices, variation partitioning and joint species distribution modelling. Our results indicated two main axes of variation in the output metrics. The first axis of variation described whether the landscape has patchy or continuous variation, and thus was essentially independent of the properties of the species community. The second axis of variation related to the level of predictability of the metacommunity. The most predictable communities were niche-based metacommunities inhabiting static landscapes with marked environmental heterogeneity, such as metacommunities following the species sorting paradigm or the mass effects paradigm. The most unpredictable communities were neutral-based metacommunities inhabiting dynamics landscapes with little spatial heterogeneity, such as metacommunities following the neutral or patch sorting paradigms. The output metrics from joint species distribution modelling yielded generally the highest resolution to disentangle among the simulated scenarios. Yet, the different types of statistical approaches utilized in this study carried complementary information, and thus our results suggest that the most comprehensive evaluation of metacommunity structure can be obtained by combining them.Peer reviewe

Quantifying uncertainty of taxonomic placement in DNA barcoding and metabarcoding

A crucial step in the use of DNA markers for biodiversity surveys is the assignment of Linnaean taxonomies (species, genus, etc.) to sequence reads. This allows the use of all the information known based on the taxonomic names. Taxonomic placement of DNA barcoding sequences is inherently probabilistic because DNA sequences contain errors, because there is natural variation among sequences within a species, and because reference data bases are incomplete and can have false annotations. However, most existing bioinformatics methods for taxonomic placement either exclude uncertainty, or quantify it using metrics other than probability. In this paper we evaluate the performance of the recently proposed probabilistic taxonomic placement method PROTAX by applying it to both annotated reference sequence data as well as to unknown environmental data. Our four case studies include contrasting taxonomic groups (fungi, bacteria, mammals and insects), variation in the length and quality of the barcoding sequences (from individually Sanger-sequenced sequences to short Illumina reads), variation in the structures and sizes of the taxonomies (800–130 000 species) and variation in the completeness of the reference data bases (representing 15–100% of known species). Our results demonstrate that PROTAX yields essentially unbiased probabilities of taxonomic placement, which means its quantification of species identification uncertainty is reliable. As expected, the accuracy of taxonomic placement increases with increasing coverage of taxonomic and reference sequence data bases, and with increasing ratio of genetic variation among taxonomic levels over within taxonomic levels. We conclude that reliable species-level identification from environmental samples is still challenging and that neglecting identification uncertainty can lead to spurious inference. A key aim for future research is the completion of taxonomic and reference sequence data bases and making these two types of data compatible