The transition between stochastic and deterministic behavior in an excitable gene circuit

We explore the connection between a stochastic simulation model and an ordinary differential equations (ODEs) model of the dynamics of an excitable gene circuit that exhibits noise-induced oscillations. Near a bifurcation point in the ODE model, the stochastic simulation model yields behavior dramatically different from that predicted by the ODE model. We analyze how that behavior depends on the gene copy number and find very slow convergence to the large number limit near the bifurcation point. The implications for understanding the dynamics of gene circuits and other birth-death dynamical systems with small numbers of constituents are discussed.Comment: PLoS ONE: Research Article, published 11 Apr 201

Intra-Individual Variability in Alzheimer's Disease and Cognitive Aging: Definitions, Context, and Effect Sizes

To explore different definitions of intra-individual variability (IIV) to summarize performance on commonly utilized cognitive tests (Mini Mental State Exam; Clock Drawing Test); compare them and their potential to differentiate clinically-defined populations; and to examine their utility in predicting clinical change in individuals from the Alzheimer's Disease Neuroimaging Initiative (ADNI).) were computed for each of these definitions in 500 simulated replicates using scores on the Mini Mental State Exam and Clock Drawing Test. IIV was computed based on test items separately (‘within test’ IIV) and the two tests together (‘across test’ IIV). The best performing definition was then used to compute IIV for a third test, the Alzheimer's Disease Assessment Scale-Cognitive, and the simulations and effect sizes were again computed. All effect size estimates based on simulated data were compared to those computed based on the total scores in the observed data. Association between total score and IIV summaries of the tests and the Clinician's Dementia Rating were estimated to test the utility of IIV in predicting clinically meaningful changes in the cohorts over 12- and 24-month intervals.ES estimates differed substantially depending on the definition of IIV and the test(s) on which IIV was based. IIV (coefficient of variation) summaries of MMSE and Clock-Drawing performed similarly to their total scores, the ADAS total performed better than its IIV summary.IIV can be computed within (items) or across (totals) items on commonly-utilized cognitive tests, and may provide a useful additional summary measure of neuropsychological test performance

Effects of Sample Size on Estimates of Population Growth Rates Calculated with Matrix Models

BACKGROUND: Matrix models are widely used to study the dynamics and demography of populations. An important but overlooked issue is how the number of individuals sampled influences estimates of the population growth rate (lambda) calculated with matrix models. Even unbiased estimates of vital rates do not ensure unbiased estimates of lambda-Jensen's Inequality implies that even when the estimates of the vital rates are accurate, small sample sizes lead to biased estimates of lambda due to increased sampling variance. We investigated if sampling variability and the distribution of sampling effort among size classes lead to biases in estimates of lambda. METHODOLOGY/PRINCIPAL FINDINGS: Using data from a long-term field study of plant demography, we simulated the effects of sampling variance by drawing vital rates and calculating lambda for increasingly larger populations drawn from a total population of 3842 plants. We then compared these estimates of lambda with those based on the entire population and calculated the resulting bias. Finally, we conducted a review of the literature to determine the sample sizes typically used when parameterizing matrix models used to study plant demography. CONCLUSIONS/SIGNIFICANCE: We found significant bias at small sample sizes when survival was low (survival = 0.5), and that sampling with a more-realistic inverse J-shaped population structure exacerbated this bias. However our simulations also demonstrate that these biases rapidly become negligible with increasing sample sizes or as survival increases. For many of the sample sizes used in demographic studies, matrix models are probably robust to the biases resulting from sampling variance of vital rates. However, this conclusion may depend on the structure of populations or the distribution of sampling effort in ways that are unexplored. We suggest more intensive sampling of populations when individual survival is low and greater sampling of stages with high elasticities

Asymmetric reproductive isolation between terminal forms of the salamander ring species Ensatina eschscholtzii revealed by fine-scale genetic analysis of a hybrid zone

<p>Abstract</p> <p>Background</p> <p>Ring species, exemplified by salamanders of the <it>Ensatina eschscholtzii </it>complex, represent a special window into the speciation process because they allow the history of species formation to be traced back in time through the geographically differentiated forms connecting the two terminal forms of the ring. Of particular interest is the nature and extent of reproductive isolation between the geographically terminal forms, in this case <it>E. e. eschscholtzii </it>and <it>E. e. klauberi</it>. Previous studies have documented infrequent hybridization at the end of the ring. Here, we report the first fine-scale genetic analysis of a hybrid zone between the terminal forms in southern California using individual-based Bayesian analyses of multilocus genetic data to estimate levels and direction of hybridization and maximum-likelihood analysis of linkage disequilibrium and cline shape to make inferences about migration and selection in the hybrid zone.</p> <p>Results</p> <p>The center of the hybrid zone has a high proportion of hybrids, about half of which were classified as F1s. Clines are narrow with respect to dispersal, and there are significant deviations from Hardy-Weinberg equilibrium as well as nonrandom associations (linkage disequilibria) between alleles characteristic of each parental type. There is cytonuclear discordance, both in terms of introgression and the geographic position of mitochondrial versus nuclear clines. Genetic disequilibrium is concentrated on the <it>eschscholtzii </it>side of the zone. Nearly all hybrids possess <it>klauberi </it>mtDNA, indicating that most hybrids are formed from female <it>klauberi </it>mating with male <it>eschscholtzii </it>or male hybrids (but not vice versa).</p> <p>Conclusions</p> <p>Our results are consistent with a tension zone trapped at an ecotone, with gene combinations characteristic of <it>klauberi </it>showing up on the <it>eschscholtzii </it>side of the zone due to asymmetric hybridization. We suggest that the observed asymmetry is best explained by increased discriminatory power of <it>eschscholtzii </it>females, or asymmetric postzygotic isolation. The relatively high frequency of hybrids, particularly F1s, contrasts with other contacts between the terminal forms, and with other contacts between other divergent <it>Ensatina </it>lineages, highlighting the diverse outcomes of secondary contact within a single species complex.</p

A road map for designing and implementing a biological monitoring program

Designing and implementing natural resource monitoring is a challenging endeavor undertaken by many agencies, NGOs, and citizen groups worldwide. Yet many monitoring programs fail to deliver useful information for a variety of administrative (staffing, documentation, and funding) or technical (sampling design and data analysis) reasons. Programs risk failure if they lack a clear motivating problem or question, explicit objectives linked to this problem or question, and a comprehensive conceptual model of the system under study. Designers must consider what “success” looks like from a resource management perspective, how desired outcomes translate to appropriate attributes to monitor, and how they will be measured. All such efforts should be filtered through the question “Why is this important?” Failing to address these considerations will produce a program that fails to deliver the desired information. We addressed these issues through creation of a “road map” for designing and implementing a monitoring program, synthesizing multiple aspects of a monitoring program into a single, overarching framework. The road map emphasizes linkages among core decisions to ensure alignment of all components, from problem framing through technical details of data collection and analysis, to program administration. Following this framework will help avoid common pitfalls, keep projects on track and budgets realistic, and aid in program evaluations. The road map has proved useful for monitoring by individuals and teams, those planning new monitoring, and those reviewing existing monitoring and for staff with a wide range of technical and scientific skills

Population Estimation and Trappability of the European Badger (Meles meles): Implications for Tuberculosis Management.

peer-reviewedEstimates of population size and trappability inform vaccine efficacy modelling and are required for adaptive management during prolonged wildlife vaccination campaigns. We present an analysis of mark-recapture data from a badger vaccine (Bacille Calmette–Gue´ rin) study in Ireland. This study is the largest scale (755 km2) mark-recapture study ever undertaken with this species. The study area was divided into three approximately equal–sized zones, each with similar survey and capture effort. A mean badger population size of 671 (SD: 76) was estimated using a closed-subpopulation model (CSpM) based on data from capturing sessions of the entire area and was consistent with a separate multiplicative model. Minimum number alive estimates calculated from the same data were on average 49–51% smaller than the CSpM estimates, but these are considered severely negatively biased when trappability is low. Population densities derived from the CSpM estimates were 0.82–1.06 badgers km22, and broadly consistent with previous reports for an adjacent area. Mean trappability was estimated to be 34–35% per session across the population. By the fifth capture session, 79% of the adult badgers caught had been marked previously. Multivariable modelling suggested significant differences in badger trappability depending on zone, season and age-class. There were more putatively trap-wary badgers identified in the population than trap-happy badgers, but wariness was not related to individual’s sex, zone or season of capture. Live-trapping efficacy can vary significantly amongst sites, seasons, age, or personality, hence monitoring of trappability is recommended as part of an adaptive management regime during large–scale wildlife vaccination programs to counter biases and to improve efficiencies.Department of Agriculture, Food and the MarineTeagasc Walsh Fellowship Programm