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

Mathematical model insights into arsenic detoxification

<p>Abstract</p> <p>Background</p> <p>Arsenic in drinking water, a major health hazard to millions of people in South and East Asia and in other parts of the world, is ingested primarily as trivalent inorganic arsenic (iAs), which then undergoes hepatic methylation to methylarsonic acid (MMAs) and a second methylation to dimethylarsinic acid (DMAs). Although MMAs and DMAs are also known to be toxic, DMAs is more easily excreted in the urine and therefore methylation has generally been considered a detoxification pathway. A collaborative modeling project between epidemiologists, biologists, and mathematicians has the purpose of explaining existing data on methylation in human studies in Bangladesh and also testing, by mathematical modeling, effects of nutritional supplements that could increase As methylation.</p> <p>Methods</p> <p>We develop a whole body mathematical model of arsenic metabolism including arsenic absorption, storage, methylation, and excretion. The parameters for arsenic methylation in the liver were taken from the biochemical literature. The transport parameters between compartments are largely unknown, so we adjust them so that the model accurately predicts the urine excretion rates of time for the iAs, MMAs, and DMAs in single dose experiments on human subjects.</p> <p>Results</p> <p>We test the model by showing that, with no changes in parameters, it predicts accurately the time courses of urinary excretion in mutiple dose experiments conducted on human subjects. Our main purpose is to use the model to study and interpret the data on the effects of folate supplementation on arsenic methylation and excretion in clinical trials in Bangladesh. Folate supplementation of folate-deficient individuals resulted in a 14% decrease in arsenicals in the blood. This is confirmed by the model and the model predicts that arsenicals in the liver will decrease by 19% and arsenicals in other body stores by 26% in these same individuals. In addition, the model predicts that arsenic methyltransferase has been upregulated by a factor of two in this population. Finally, we also show that a modification of the model gives excellent fits to the data on arsenic metabolism in human cultured hepatocytes.</p> <p>Conclusions</p> <p>The analysis of the Bangladesh data using the model suggests that folate supplementation may be more effective at reducing whole body arsenic than previously expected. There is almost no data on the upregulation of arsenic methyltransferase in populations chronically exposed to arsenic. Our model predicts upregulation by a factor of two in the Bangladesh population studied. This prediction should be verified since it could have important public health consequences both for treatment strategies and for setting appropriate limits on arsenic in drinking water. Our model has compartments for the binding of arsenicals to proteins inside of cells and we show that these comparments are necessary to obtain good fits to data. Protein-binding of arsenicals should be explored in future biochemical studies.</p

Shifts in Species Composition Constrain Restoration of Overgrazed Grassland Using Nitrogen Fertilization in Inner Mongolian Steppe, China

Long-term livestock over-grazing causes nitrogen outputs to exceed inputs in Inner Mongolia, suggesting that low levels of nitrogen fertilization could help restore grasslands degraded by overgrazing. However, the effectiveness of such an approach depends on the response of production and species composition to the interactive drivers of nitrogen and water availability. We conducted a five-year experiment manipulating precipitation (NP: natural precipitation and SWP: simulated wet year precipitation) and nitrogen (0, 25 and 50 kg N ha-1 yr-1) addition in Inner Mongolia. We hypothesized that nitrogen fertilization would increase forage production when water availability was relatively high. However, the extent to which nitrogen would co-limit production under average or below average rainfall in these grasslands was unknown

Optogenetic Mimicry of the Transient Activation of Dopamine Neurons by Natural Reward Is Sufficient for Operant Reinforcement

Activation of dopamine receptors in forebrain regions, for minutes or longer, is known to be sufficient for positive reinforcement of stimuli and actions. However, the firing rate of dopamine neurons is increased for only about 200 milliseconds following natural reward events that are better than expected, a response which has been described as a “reward prediction error” (RPE). Although RPE drives reinforcement learning (RL) in computational models, it has not been possible to directly test whether the transient dopamine signal actually drives RL. Here we have performed optical stimulation of genetically targeted ventral tegmental area (VTA) dopamine neurons expressing Channelrhodopsin-2 (ChR2) in mice. We mimicked the transient activation of dopamine neurons that occurs in response to natural reward by applying a light pulse of 200 ms in VTA. When a single light pulse followed each self-initiated nose poke, it was sufficient in itself to cause operant reinforcement. Furthermore, when optical stimulation was delivered in separate sessions according to a predetermined pattern, it increased locomotion and contralateral rotations, behaviors that are known to result from activation of dopamine neurons. All three of the optically induced operant and locomotor behaviors were tightly correlated with the number of VTA dopamine neurons that expressed ChR2, providing additional evidence that the behavioral responses were caused by activation of dopamine neurons. These results provide strong evidence that the transient activation of dopamine neurons provides a functional reward signal that drives learning, in support of RL theories of dopamine function

Climate change, phenological shifts, eco-evolutionary responses and population viability: toward a unifying predictive approach

The debate on emission targets of greenhouse gasses designed to limit global climate change has to take into account the ecological consequences. One of the clearest ecological consequences is shifts in phenology. Linking these shifts to changes in population viability under various greenhouse gasses emission scenarios requires a unifying framework. We propose a box-in-a-box modeling approach that couples population models to phenological change. This approach unifies population modeling with both ecological responses to climate change as well as evolutionary processes. We advocate a mechanistic embedded correlative approach, where the link from genes to population is established using a periodic matrix population model. This periodic model has several major advantages: (1) it can include complex seasonal behaviors allowing an easy link with phenological shifts; (2) it provides the structure of the population at each phase, including the distribution of genotypes and phenotypes, allowing a link with evolutionary processes; and (3) it can incorporate the effect of climate at different time periods. We believe that the way climatologists have approached the problem, using atmosphere–ocean coupled circulation models in which components are gradually included and linked to each other, can provide a valuable example to ecologists. We hope that ecologists will take up this challenge and that our preliminary modeling framework will stimulate research toward a unifying predictive model of the ecological consequences of climate change

Spatial and temporal dynamics of fucoid populations (Ascophyllum nodosum and Fucus serratus): A comparison between central and range edge populations

Persistence of populations at range edges relies on local population dynamics and fitness, in the case of geographically isolated populations of species with low dispersal potential. Focusing on spatial variations in demography helps to predict the long-term capability for persistence of populations across the geographical range of species' distribution. The demography of two ecological and phylogenetically close macroalgal species with different life history characteristics was investigated by using stochastic, stage-based matrix models. Populations of Ascophyllum nodosum and Fucus serratus were sampled for up to 4 years at central locations in France and at their southern range limits in Portugal. The stochastic population growth rate (lambda(s)) of A. nodosum was lower and more variable in central than in southern sites whilst for F. serratus this trend was reversed with lambda(s) much lower and more variable in southern than in central populations. Individuals were larger in central than in southern populations for both species, which was reflected in the lower transition probabilities of individuals to larger size classes and higher probability of shrinkage in the southern populations. In both central and southern populations elasticity analysis (proportional sensitivity) of population growth rate showed that fertility elements had a small contribution to lambda(s) that was more sensitive to changes in matrix transitions corresponding to survival. The highest elasticities were found for loop transitions in A. nodosum and for growth to larger size classes in F. serratus. Sensitivity analysis showed high selective pressure on individual growth for both species at both locations. The results of this study highlight the deterministic role of species-specific life-history traits in population demography across the geographical range of species. Additionally, this study demonstrates that individuals' life-transitions differ in vulnerability to environmental variability and shows the importance of vegetative compared to reproductive stages for the long-term persistence of populations.Portuguese Foundation for Science and Technology (FCT) [SFRH/BPD/75843/2011]; European Regional Development Fund (ERDF) through the COMPETE - Operational Competitiveness Programme; FCT [Pest-CIMAR LA 0015/2013, EXCL/AAG-GLO/0661/2012

Effects of Increased Nitrogen Deposition and Precipitation on Seed and Seedling Production of Potentilla tanacetifolia in a Temperate Steppe Ecosystem

The responses of plant seeds and seedlings to changing atmospheric nitrogen (N) deposition and precipitation regimes determine plant population dynamics and community composition under global change.In a temperate steppe in northern China, seeds of P. tanacetifolia were collected from a field-based experiment with N addition and increased precipitation to measure changes in their traits (production, mass, germination). Seedlings germinated from those seeds were grown in a greenhouse to examine the effects of improved N and water availability in maternal and offspring environments on seedling growth. Maternal N-addition stimulated seed production, but it suppressed seed mass, germination rate and seedling biomass of P. tanacetifolia. Maternal N-addition also enhanced responses of seedlings to N and water addition in the offspring environment. Maternal increased-precipitation stimulated seed production, but it had no effect on seed mass and germination rate. Maternal increased-precipitation enhanced seedling growth when grown under similar conditions, whereas seedling responses to offspring N- and water-addition were suppressed by maternal increased-precipitation. Both offspring N-addition and increased-precipitation stimulated growth of seedlings germinated from seeds collected from the maternal control environment without either N or water addition. Our observations indicate that both maternal and offspring environments can influence seedling growth of P. tanacetifolia with consequent impacts on the future population dynamics of this species in the study area.The findings highlight the importance of the maternal effects on seed and seedling production as well as responses of offspring to changing environmental drivers in mechanistic understanding and projecting of plant population dynamics under global change

Empirical Models of Transitions between Coral Reef States: Effects of Region, Protection, and Environmental Change

There has been substantial recent change in coral reef communities. To date, most analyses have focussed on static patterns or changes in single variables such as coral cover. However, little is known about how community-level changes occur at large spatial scales. Here, we develop Markov models of annual changes in coral and macroalgal cover in the Caribbean and Great Barrier Reef (GBR) regions

Projected changes of rainfall seasonality and dry spells in a high greenhouse gas emissions scenario

In this diagnostic study we analyze changes of rainfall seasonality and dry spells by the end of the twenty-first century under the most extreme IPCC5 emission scenario (RCP8.5) as projected by twenty-four coupled climate models contributing to Coupled Model Intercomparison Project 5 (CMIP5). We use estimates of the centroid of the monthly rainfall distribution as an index of the rainfall timing and a threshold-independent, information theory-based quantity such as relative entropy (RE) to quantify the concentration of annual rainfall and the number of dry months and to build a monsoon dimensionless seasonality index (DSI). The RE is projected to increase, with high inter-model agreement over Mediterranean-type regions---southern Europe, northern Africa and southern Australia---and areas of South and Central America, implying an increase in the number of dry days up to 1Â month by the end of the twenty-first century. Positive RE changes are also projected over the monsoon regions of southern Africa and North America, South America. These trends are consistent with a shortening of the wet season associated with a more prolonged pre-monsoonal dry period. The extent of the global monsoon region, characterized by large DSI, is projected to remain substantially unaltered. Centroid analysis shows that most of CMIP5 projections suggest that the monsoonal annual rainfall distribution is expected to change from early to late in the course of the hydrological year by the end of the twenty-first century and particularly after year 2050. This trend is particularly evident over northern Africa, southern Africa and western Mexico, where more than 90% of the models project a delay of the rainfall centroid from a few days up to 2Â weeks. Over the remaining monsoonal regions, there is little inter-model agreement in terms of centroid changes