Fitting complex population models by combining particle filters with Markov chain Monte Carlo

We show how a recent framework combining Markov chain Monte Carlo (MCMC) with particle filters (PFMCMC) may be used to estimate population state-space models. With the purpose of utilizing the strengths of each method, PFMCMC explores hidden states by particle filters, while process and observation parameters are estimated using an MCMC algorithm. PFMCMC is exemplified by analyzing time series data on a red kangaroo (Macropus rufus) population in New South Wales, Australia, using MCMC over model parameters based on an adaptive Metropolis-Hastings algorithm. We fit three population models to these data; a density-dependent logistic diffusion model with environmental variance, an unregulated stochastic exponential growth model, and a random-walk model. Bayes factors and posterior model probabilities show that there is little support for density dependence and that the random-walk model is the most parsimonious model. The particle filter Metropolis-Hastings algorithm is a brute-force method that may be used to fit a range of complex population models. Implementation is straightforward and less involved than standard MCMC for many models, and marginal densities for model selection can be obtained with little additional effort. The cost is mainly computational, resulting in long running times that may be improved by parallelizing the algorithm.     

The use of well-defined biomarkers (such as blood lead) in risk assessment

Biomarkers have a number of different uses in risk assessment, including (1) a variety of applications as dosimeters, (2) as an aid in quantifying inter-individual variability in susceptibility; and (3) as intermediate effect parameters that can help the analyst predict outcomes that are difficult to measure directly. This paper focuses primarily on applications of the first and second types, which are most frequently found in assessing risks from inorganic compounds.     

Testing the effectiveness of capture mark recapture population estimation techniques using a computer simulation with known population size

Estimation of small mammal population sizes is important for monitoring ecosystem condition and for conservation. Here, we test the accuracy of standard methods of population size estimation using Capture-Mark-Recapture (CMR) on a simulated population of agents. The use of a computer simulation allows complete control of population sizes and behaviors, thereby avoiding assumptions that may be violated in real populations. We find that the recommended protocol for CMR sampling, using uniformly distributed traps, consistently overestimates population sizes by as much as 100% when studies are conducted over only two trapping periods. More than 20 trapping periods are required before this method, or that of placing traps randomly, gives an accurate estimation of population size (i.e., within a 95% confidence limit of the actual value). Non-random sampling, by placing traps on runways used by small mammals, produces the most accurate, and least variable, estimates of population. However, we show that around 10 trapping periods are still required to produce an accurate population estimate using this method. Given that most real populations do not comply with the ‘ideal’ assumptions made by CMR, we suggest that population estimates based on CMR may be fundamentally flawed, and recommend that protocols for CMR population estimation methods may need revising.     

Low levels of lead and glutathione markers of redox status in human blood

Exposure to lead (Pb) is implicated in a plethora of health threats in both adults and children. Increased exposure levels are associated with oxidative stress in the blood of workers exposed at occupational levels. However, it is not known whether lower Pb exposure levels are related to a shift toward a more oxidized state. To assess the association between blood lead level (BLL) and glutathione (GSH) redox biomarkers in a population of healthy adults, BLL and four GSH markers (GSH, GSSG, GSH/GSSG ratio and redox potential E _h ) were measured in the blood of a cross-sectional cohort of 282 avid seafood-eating healthy adults living on Long Island (NY). Additionally, blood levels of two other metals known to affect GSH redox status, selenium (Se) and mercury (Hg), and omega-3 index were tested for effect modification. Regression models were further adjusted for demographic and smoking status. Increasing exposure to Pb, measured in blood, was not associated with GSSG, but was associated with lower levels of GSH/GSSG ratio and more positive GSH redox potential E _h , driven by its association with GSH. No effect modification was observed in analyses stratified by Hg, Se, omega-3 index, sex, age, or smoking. Blood Pb is associated with lower levels of GSH and the GSH/GSSG ratio in this cross-sectional study of healthy adults.     

Using citizen science butterfly counts to predict species population trends

Citizen scientists are increasingly engaged in gathering biodiversity information, but trade‐offs are often required between public engagement goals and reliable data collection. We compared population estimates for 18 widespread butterfly species derived from the first 4 years (2011–2014) of a short‐duration citizen science project (Big Butterfly Count [BBC]) with those from long‐running, standardized monitoring data collected by experienced observers (U.K. Butterfly Monitoring Scheme [UKBMS]). BBC data are gathered during an annual 3‐week period, whereas UKBMS sampling takes place over 6 months each year. An initial comparison with UKBMS data restricted to the 3‐week BBC period revealed that species population changes were significantly correlated between the 2 sources. The short‐duration sampling season rendered BBC counts susceptible to bias caused by interannual phenological variation in the timing of species’ flight periods. The BBC counts were positively related to butterfly phenology and sampling effort. Annual estimates of species abundance and population trends predicted from models including BBC data and weather covariates as a proxy for phenology correlated significantly with those derived from UKBMS data. Overall, citizen science data obtained using a simple sampling protocol produced comparable estimates of butterfly species abundance to data collected through standardized monitoring methods. Although caution is urged in extrapolating from this U.K. study of a small number of common, conspicuous insects, we found that mass‐participation citizen science can simultaneously contribute to public engagement and biodiversity monitoring. Mass‐participation citizen science is not an adequate replacement for standardized biodiversity monitoring but may extend and complement it (e.g., through sampling different land‐use types), as well as serving to reconnect an increasingly urban human population with nature.     

Seasonal variation in paediatric blood lead levels in Syracuse,NY, USA

Venous blood lead values for 2,633 children aged 0–4 years in Syracuse, New York, collected between 1 April 1992 and 31 March 1993 were summarised by census tract for study of geographic variability. A demographic exposure model is presented showing housing stock and SES (socioeconomic status) parameters as the most significant predictor variables. A seasonal trend in blood lead levels was observed with late summer values about 40% higher than late winter values for census tracts with the highest geometric mean PbB levels. Seasonal variation is compared with a biokinetic uptake model to examine hypotheses about temporal variations in soil and dust lead exposure patterns.     

Use of the ouput of a lead risk assessment model to establish soil lead cleanup levels

Three general methods to calculate soil contaminant cleanup levels are assessed: the truncated lognormal approach, Monte Carlo analysis, and the house-by-house approach. When these methods are used together with a lead risk assessment model, they yield estimated soil lead cleanup levels that may be required in an attempt to achieve specified target blood lead levels for a community. The truncated lognormal approach is exemplified by the Society for Environmental Geochemistry and Health (SEGH) model, Monte Carlo analysis is exemplified by the US EPA's LEAD Model, and the house-by-house approach is used with a structural equation model to calculate site-specific soil lead cleanup levels. The various cleanup methods can each be used with any type of lead risk assessment model. Although all examples given here are for lead, the cleanup methods can, in principle, be used as well with risk assessment models for other chemical contaminants to derive contaminant-specific soil cleanup levels.     

Evidence of a fall in cord blood lead levels in South Wales 1984–85

A monitoring scheme for blood lead was based on cord blood samples and maternal blood samples taken in Swansea, South Wales. A fall of around 20% during 1984–85 is described. During this period there was virtually no change in petrol sales in the area and no overall change in air lead levels. Air lead showed large seasonal changes but these were not reflected in blood lead. Water lead levels gave no evidence of changes of any importance during the period of monitoring. These results suggest that petrol lead was at most a minor contributor to blood lead.     

An Integrated Monte Carlo Methodology for the calibration of water quality models

This paper proposes an Integrated Monte Carlo Methodology (IMCM) to solve the parameter estimation problem in water quality models. The methodology is based on Bayesian approach and Markov Chain Monte Carlo techniques and it operates by means of four modules: Markov Chain Monte Carlo (MCMC), Moving Feasible Ranges (MFR), Statistical Analysis of the Joint Posterior Distribution (SAD) and Uncertainty Propagation Analysis (UPA). The main innovation of the new proposal lies in the combination of MCMC and MFR modules which provides the joint posterior distribution of the calibrated parameters following the classical Bayesian approach. While MCMC module, based on Shuffled Complex Evolution Metropolis (SCEM-UA) algorithm, is specially designed to sample complex joint posterior shapes within certain parameter ranges, the MFR readjusts these ranges until the coverage of the feasible parameter space is guaranteed. Once the joint posterior distribution is properly defined, the SAD provides the parameter statistics and the UPA performs an analysis of the uncertainty propagation through the model. The possibilities of the new proposal have been tested on the basis of a simple model featuring different activated sludge batch experiments. IMCM has been implemented in Matlab and it is prepared to be easily connected to any software package.     

Changes in blood lead and water lead in Edinburgh. An eight year follow-up to the Edinburgh lead study

This study aimed to measure changes in household water lead and blood lead in young people living in Edinburgh over a period of 8 years. Two hundred and twenty-three families were eligible and 207 (93%) agreed to participate. A half-hour stagnation sample of kitchen cold water was taken from each household, and 171 young people (aged 14–17 years) provided a blood sample for lead analysis. Information on plumbing changes, exposure to other sources of lead and factors which might influence blood lead was collected by questionnaire. Edinburgh is supplied with water treated in one of two treatment plants. There was a different programme of water treatment in each plant. In one (A) lime and orthophosphate was introduced in the interval between the original and follow-up studies. In the other (F) lime treatment began before the original study and orthophosphate was introduced subsequently. In water from treatment plant A, mean water lead levels fell from 34 to 4.3 gL-1 (87%). In water supplied from treatment plant F the corresponding values were 9.3 to 3.6 gL-1 (61%). These reductions were due to both water treatment and removal of lead plumbing. Houses with no lead plumbing have water lead levels 89% lower than houses with lead tanks, and 47% lower than houses with lead pipes. About one-third of households with lead tanks are predicted to have water lead levels above the current EC limit of 50 gL- 1, though only 3% or less of the remaining households would exceed this limit. If the proposed 10 gL-1 limit were introduced, 34% of households supplied from plant A and 25% from plant F would breach the limit. Blood lead levels fell from an average of 11.0 gdL-1 to 4.0 gdL-1. Males had higher values than females and the main factors influencing levels were water lead and age of house. Our results show substantial reductions in household water lead and blood lead in our sample over a period of 8 years and represent an important achievement in public health. However, more progress will be required if the proposed new limit of 10 gL-1 for water lead is to be met. There is a need for the continuing surveillance of household water lead and blood lead levels in representative samples of the population.     

The relationship between surface dust lead loadings on carpets and the blood lead of young children

The final clean-up of residential lead abatement projects in federally-supported housing, as well as in other housing in a number of states, must meet surface dust lead clearance levels expressed as g of lead per square foot. These clearance levels were established because hand-to-mouth ingestion of lead-contaminated dust is recognised as a major pathway through which many children are exposed. A dilemma exists because many floors in housing undergoing abatement are carpeted and the established clearance levels are generally not recommended for use on carpets. These clearance levels are also used as 'action levels' to determine whether exposure reduction activities are needed. The US Environmental Protection Agency is currently in the process of issuing standards for hazardous levels of lead in interior dust and bare soil under Title X of the Housing and Community Development Act of 1992, The Residential Lead-Based Paint Hazard Reduction Act of 1992. An effort to develop a potential surface dust lead clearance level for carpets was made using an existing vacuum dust collection method that has previously been shown to be a reliable indicator of childhood lead exposure. This method was designed for use on carpeted and non-carpeted surfaces. Using data from the Cincinnati Soil Lead Abatement Demonstration Project, the suggested floor-dust lead level where an estimated 95% of the population of children would be expected to have blood lead values below the national goal of 10 g dL^–1, was more than an order of magnitude lower than the current floor-dust lead clearance level of 1080 g m^–2 (100 g ft^–2). Further comparisons of blood lead and carpet lead levels in other parts of the country should be performed before a risk-based lead loading clearance level is established.     

The scent of dominance: female field crickets use odour to predict the outcome of male competition

Pheromones may convey information about mate quality and social status. In the field cricket Gryllus integer, females mount the males for copulation, such that males cannot coerce females to mate. We examined whether virgin G. integer females preferred the scent of potentially dominant males to that of subordinate males. First, we collected pheromones by confining males on filter paper. Next, we offered filter paper from each of two size-matched males and control paper to females that had never been exposed to males, and measured the time spent by the female on each kind of paper. Finally, dominance status of the males in each size-matched pair was determined by pitting the two males against one another in agonistic contests. When offered filter paper from subsequently dominant versus subsequently subordinate males, females spent more time on the paper from the dominant male than the subordinate male, and much less time on control paper. Thus, pheromones may inform female G. integer about a male's potential to achieve dominant social status. Male pheromones were also associated with the female's tendency to mount a male. In contrast to cockroaches, where females prefer the scent of subordinate males (presumably to avoid risk of injury), female crickets prefer the scent of potentially dominant males and are more likely than males to wound their mating partners.     

Modelling with uncertainty: Introducing a probabilistic framework to predict animal population dynamics

Predictive population models designed to assist managers and policy makers require an explicit treatment of inherent uncertainty and variability. These are particular concerns when modelling non-native and reintroduced species, when data have been collected within one geographical or ecological context but predictions are required for another, or when extending models to predict the consequences of environmental change (e.g., climate or land-use). We present an aspatial, probabilistic framework of hierarchical process models for predicting population growth even when data are sparse or of poor quality. Insight into the factors affecting population dynamics in real landscapes can be provided and Kullback–Leibler distances are used to compare the relative output of models. This flexible yet robust framework gives easily interpretable results, allowing managers as well as modellers to invalidate anomalous models and apply others to real-life scenarios.We illustrate the framework’s power with a meta-analysis of European wild boar (Sus scrofa) data. We test hypotheses about the effect of geographic region, hunting and mast years on wild boar population growth, to build models of wild boar dynamics for the UK. The framework quantifies the importance of hunting pressure as a driver of population growth, and confirms that reproductive success is greatly decreased in poor mast years, suggesting that the key to predicting wild boar dynamics is to ascertain local hunting pressure and to better understand changing food availability. Geography had no significant effect, indicating that it is not a good proxy for modelling the impact of change in climate or land-use on wild boar populations at the European scale. We use the framework to predict population abundance 9 years after an isolated population of wild boar established in the UK; in a comparison with the only field data and two independent modelling exercises, our framework provides the most robust and informative results.     

Social network analysis and valid Markov chain Monte Carlo tests of null models

Analyses of animal social networks derived from group-based associations often rely on randomisation methods developed in ecology (Manly, Ecology 76:1109–1115, 1995) and made available to the animal behaviour community through implementation of a pair-wise swapping algorithm by Bejder et al. (Anim Behav 56:719–725, 1998). We report a correctable flaw in this method and point the reader to a wider literature on the subject of null models in the ecology literature. We illustrate the importance of correcting the method using a toy network and use it to make a preliminary analysis of a network of associations among eagle rays.

Using simulation to explore the functional relationships of terrestrial carnivore population indices

Population indices based on visits to detection stations commonly are used to monitor wildlife populations. Inferences about populations are based on 1 of 2 measures: (1) change in the proportion of stations visited at least once or (2) change in the cumulative number of visits by unique individuals. The functional relationships between index responses and population density is poorly understood and can lead to misinterpretation of index data when an incorrect functional relationship (e.g. linear) is assumed. We created a flexible simulation environment to study the response of detection-based population indices under a wide variety of conditions meant to reflect species life history and study design. Proportional indices exhibited non-linear saturating responses to changes in population density while cumulative indices responded linearly. Shapes of responses were functions of home range sizes, individual detection probabilities, and spatial arrangement of animals and sampling stations. Non-linear relationships of proportional indices lead to under-estimation of mean population density when data are aggregated from multiple detection stations deployed in a heterogeneous landscape. Cumulative indices have significant statistical advantages over proportional indices including smaller sample sizes required to detect density change, linearity, consistent index responses across a wide range of densities, and ability to aggregate data to meet minimum sample size requirements. Our simulation provides a flexible tool for the interpretation of station-based population indices.     

Organochlorine levels in human blood from residents in areas of limited pesticide use in Sudan

Ninety-nine human blood samples were collected from the riverine region of northern Sudan and the traditional and mechanized rain-fed areas of western and eastern Sudan, representing areas of limited pesticide use in Sudan. Blood samples were analyzed for organochlorine pesticides by gas liquid chromatography (GLC) followed by electron-capture detection (ECD). p,p′-DDE (a metabolite of DDT), heptachlor epoxide, β-hexachlorocyclohexane (β-HCH), and dieldrin were detected in all locations surveyed. The level of total organochlorine burden was highest in the traditional rain-fed area, followed by the mechanized rain-fed area, and the riverine area. A highly significant correlation was observed between total organochlorine blood burden and the age of the donors (r = 0.608**).     

Development of a probabilistic blood lead prediction model

A partially probabilistic blood lead prediction model has been developed, based on the US Environmental Protection Agency integrated exposure-uptake-biokinetic blood lead model (IEUBK model). This study translated the IEUBK model into a spreadsheet format. The uptake submodel incorporates uncertainty distributions for exposure and bioavailability parameters. The biokinetic submodel is duplicated with a table incorporating partitioning and decay of lead levels in the body. As a case study, the probabilistic model is applied to a lead exposure scenario involving a former smelter site in Sandy, Utah. The probabilistic model produces less biased estimates of means and standard deviations than the deterministic model. Parameter uncertainty is propagated in the model by the use of Monte Carlo simulation. Thus, sensitivity analysis is possible, and driving variables can be determined.     

Blood lead determinants of a population living in a former lead mining area in Southern Scotland

The impact of high environmental lead levels on public health is currently under much debate. Such a situation exists in two former lead mining villages set in the Southern Uplands of Scotland, where the environment is heavily contaminated through past mining activity. A survey was conducted based on representative samples of male and female adults and of all children living in the area, to examine the distribution of blood lead levels and to compare this with the distribution in residents in a control area. Possible routes of exposure including the determination of lead in domestic water, in house dust, in airborne dust, on food preparation surfaces, on hands, in garden soils and through home grown vegetable consumption were investigated. The results indicate that there is a general increase in lead exposure in environmental variables in the contaminated area, while blood lead levels show an excess of between 45 and 70 percent compared with the control. The determinants of blood lead are discussed through correlation and multiple regression analysis.     

The use of simulation modeling to evaluate the mechanisms responsible for the nutritional benefits of food-for-protection mutualisms

In some mutualisms, a plant or insect provides a food resource in exchange for protection from herbivores, competitors or predators. This food resource can benefit the consumer, but the relative importance of different mechanisms responsible for this benefit is unclear. We used a colony-level simulation model to test the relative importance of increased larval production, increased worker foraging and increased worker survival for colony growth of fire ants, Solenopsis invicta, that consume plant-based foods. Increased food for larvae had the largest effect on colony growth of S. invicta followed by decreased worker mortality. Increased foraging rate had a small effect in the simulation model but data from a small laboratory experiment and another published study suggest that plant-based foods have little or no effect on foraging rates of S. invicta. Colony growth steadily increased the longer plant-based food was available and colonies were most responsive to plant-based food in the early summer (i.e., June). Our results demonstrate that population level simulation modeling can be a useful tool for examining the ecology of mutualistic interactions and the mechanisms through which species interact.     

Current uses of the EPA lead model to assess health risk and action levels for soil

The EPA lead model predicts mean blood lead levels and risk of elevated blood lead levels in children based on lead uptake from multiple sources. In the latest model versions, environmental data from individual homes within a community can be used to predict the overall blood lead distribution and percent risk of exceeding a specific blood lead level (i.e. 10 g dl^–1). Recent criteria used by the EPA to evaluate this information include no more than 5% of houses with a greater than 5% lead risk, and a community weighted-average risk below 5%. Environmental (primarily soil) and blood lead data from a residential community near a smelter were used to illustrate recent uses of the model. Scheduled remediation in the community will remove soil for approximately 60% of the houses (i.e. those with lead levels > 1000 mg kg^–1). After remediation, the model results indicate a relatively low community risk (0.5–1.9%), although the percentage of houses with lead risks above 5% ranged from 3 to as high as 13%, depending on the variation in blood lead and assuming the model's 7 g dl^–1 increase in blood lead with each 1000 mg kg^–1 increase in soil lead level. A comparison of the limited blood lead data with soil lead levels below 1000 mg kg^–1, however, indicated no apparent relationship. Given these uncertainties, less invasive actions than additional soil removal (e.g. exposure intervention, monitoring conditions, and follow-up as necessary) may be appropriate under the new EPA guidance for lead in soil.