A Compartmental Model for Meningitis: Separating Transmission From Climate Effects on Disease Incidence

The timing and size of many infectious disease outbreaks depend on climatic influences. Meningitis is an example of such a disease. Every year countries in the so-called African meningitis belt are afflicted with meningococcal meningitis disease outbreaks. The timing of these outbreaks coincide with the dry season that starts in February and ends in late May. There are two main hypotheses about this strong seasonal effect. The first hypothesis assumes that during the dry season there is an increase in the risk that an individual will transition from being an asymptomatic carrier to having invasive disease. The second hypothesis states that the incidence of meningitis increases due to higher transmission of the infection during the dry season. These two biological hypotheses suggest dynamics that would necessitate different public health responses: the first would result in broadly correlated outbreak dynamics, and thus a regional vaccination response; the second would result in locally correlated outbreaks, spreading from location to location, for which a localized response may be effective in containing regional spread. In this paper, we develop a statistical model to investigate these hypotheses. Easily interpretable parameters of the model allow us to study and compare differences in the attack rates, rates of transmission and the possible underlying environmental effect during the dry and non-dry seasons. Standard maximum likelihood or Bayesian inference for this model is infeasible as there are potentially tens of thousands of latent variables in the model and each evaluation of the likelihood is expensive. We therefore propose an approximate Bayesian computation (ABC) approach to infer the unknown parameters. Using simulated data examples, we demonstrate that it is possible to learn about some of the important parameters of our model using our methodology. We apply our modeling and inferential approach to data on cases of meningitis for 34 communities in Nigeria from Medecins Sans Frontières (MSF) and World Health Organization (WHO) for 2009. For this particular data set we are able to find weak evidence in favor of the first hypothesis, suggesting a regional vaccination response.     

Inference on Partially Observed Quasi-stationary Markov Chains With Applications to Multistate Population Models

If the full capture histories of captured individuals are available, inferences on multistate open population models may be conducted using the well known Arnason–Schwarz model. However, data of this detail is not always available. It is well known that inference on the transition probabilities of a Markov chain may be conducted using aggregate data and we extend this approach to aggregate data on multistate open population models. We show that for parameters to be identifiable we need to augment the aggregate data and we achieve this by batch marking a cohort of individuals according to their initial state, so that the batch marking augments the aggregate data. Model performance is examined by conducting several simulation studies and the model is applied to a real data set where full capture histories are available so it may be compared with the Arnason–Schwarz estimates. This article has supplementary material online.     

A Threshold Model for Heron Productivity

We demonstrate the potential of conditionally Gaussian state-space models in integrated population modeling, when certain model parameters may be functions of previous observations. The approach is applied to a heron census, and the data are best described by a model with three population-size thresholds which determine the population productivity. The model provides an explanation of how the population rebounds rapidly after major falls in size, which are characteristic of the data. By contrast, a simple logarithmic regression of productivity on population size was not significant. The results are of ecological interest, and suggest hypotheses for further investigation. Supplementary figures are available online.     

A unified capture-recapture framework

This article develops a hierarchical framework for capture-recapture data that separates the capture process from the demographic processes of interest, such as birth and survival. This allows users to parameterize in terms of meaningful demographic parameters. The framework is very flexible with many of the current capture-recapture models included as special cases. The hierarchical nature of the model allows natural expression of relationships, both between parameters and between parameters and the realization of random variables, such as population size. Previously, many of these relationships, such as density dependence have been unable to be explored using capture-recapture data. Density dependence, where survival and birth rates depend on the population size, is an interesting special case. We fit a density-dependent model to male Gonodontis bidentata data and report evidence of negative density dependence in percapita birth rates and weak evidence of negative density dependence in survival.     

Inference and model comparison for species accumulation functions using approximating pure birth processes

Soberon and Llorente proposed using the mean S(t; ϕ) of a pure birth process as a model for species accumulation functions and obtained ordinary least squares point estimates for the vector of parameters ϕ. They provided useful biological interpretations for S(t; ϕ) as well as for the birth rates of the process; they also expressed the strong need for an objective tool to compare different models for a given species accumulation data set. We show that the functions S(t; ϕ) proposed by Soberon and Llorente are generally not means of pure birth processes but that they can be well approximated by the mean of a suitable nonhomogeneous pure birth process B(t). We suggest using S(t; ϕ) and an upper bound for the (unknown) variance of the approximating pure birth process to make statistical inferences about ϕ. A nonlinear regression model with mean S(t; ϕ) and normal errors, possibly correlated, is proposed using a likelihood approach. This model can be compared with other relevant models under consideration by means of their corresponding likelihood ratio, providing a useful, objective, and quantitative tool for comparing different models in the light of the observed data. The suggested approach is exemplified with two species accumulation data sets.     

Relationship between population size and genetic diversity in endangered populations of the European bullhead (Cottus gobio): implications for conservation

This study investigated the relationship between the current size of endangered bullhead (Cottus gobio) populations and microsatellite genetic variability. Additionally, the microsatellite data were used to evaluate whether a genetic test for population bottlenecks was able to provide evidence of recent severe population declines. Finally, our results were used to develop conservation priorities and measures. Population size appears to be a crucial parameter in determining the amount of genetic diversity that can be preserved in bullheads, since a significant positive correlation was observed between both variables. Furthermore, in some populations we were able to detect genetic signatures of the documented decline in population size. We suggest that the most immediate goal for bullhead conservation should be to increase the size and the range of the populations, and in doing so minimise or even reverse further genetic erosion. Potential management actions like habitat quality improvement, reduction of river fragmentation and supplementation programmes (translocation, supportive breeding) are discussed.     

Tropical tree community shifts: Implications for wildlife conservation

In tropical forest systems tree community change after initial succession (approximately 50-100 years) is very difficult to detect because of the very slow pace of transformation. Since the mid 1980s, there has been an accumulation of evidence that many forests traditionally considered old growth or mature forests have been disturbed. Using 18 years of data on forest change in Kibale National Park, Uganda, we tested the following hypotheses. Species that frequently recruit only into areas of large-scale disturbance (e.g., conversion to agriculture) (1) have a more strongly negative annualized rate of population change (i.e., recruitment is less than mortality) than trees recruiting into the understory or canopy treefall gaps and (2) these species are declining in their average cumulative diameter at breast height (DBH). Both hypotheses were verified. We then examined relationships between forest change and diets of the five diurnal primates in Kibale. The emergent patterns suggest that forest change will lead to declines in some species, particularly the black-and-white colobus (Colobus guereza). We concluded that what was considered mature forest in Kibale has actually been disturbed in the recent past, and we discuss how potential sources of disturbance (dry-periods, elephant population fluctuations, and human disturbance) may affect both forest change and animal populations. We assess how such information might be useful in forest management.     

Sexual dimorphism,survival and dispersal in red deer

A detailed and extensive mark-recapture-recovery study of red deer on the island of Rum forms the basis of the modeling of this article. We analyze male and female deer separately, and report results for both in this article, but use the female data to demonstrate our modeling approach. We provide a model-selection procedure that allows us to describe the survival by a combination of age-classes, with common survival within each class, and senility, which is modeled continuously as a parametric function of age. Dispersal out of the study area is modeled separately. Survival and dispersal probabilities are examined for the possible influence of both environmental and individual covariates, including a range of alternative measures of population density. The resulting model is succinct and biologically realistic. We compare and contrast survival rates of male and female deer of different ages and compare the factors that affect their survival. We demonstrate large differences in the rate of senescence between males and females even though their senescence begins at the same age. The differences between the sexes suggest that, in population modeling of sexually size-dimorphic species, it is important to identify sex-specific survival functions.     

Modeling co-occurrence of northern spotted and barred owls: Accounting for detection probability differences

Barred owls (Strix varia) have recently expanded their range and now encompass the entire range of the northern spotted owl (Strix occidentalis caurina). This expansion has led to two important issues of concern for management of northern spotted owls: (1) possible competitive interactions between the two species that could contribute to population declines of northern spotted owls, and (2) possible changes in vocalization behavior and detection probabilities of northern spotted owls induced by presence of barred owls. We used a two-species occupancy model to investigate whether there was evidence of competitive exclusion between the two species at study locations in Oregon, USA. We simultaneously estimated detection probabilities for both species and determined if the presence of one species influenced the detection of the other species. Model selection results and associated parameter estimates provided no evidence that barred owls excluded spotted owls from territories. We found strong evidence that detection probabilities differed for the two species, with higher probabilities for northern spotted owls that are the object of current surveys. Non-detection of barred owls is very common in surveys for northern spotted owls, and detection of both owl species was negatively influenced by the presence of the congeneric species. Our results suggest that analyses directed at hypotheses of barred owl effects on demographic or occupancy vital rates of northern spotted owls need to deal adequately with imperfect and variable detection probabilities for both species.     

Viability of mountain caribou in British Columbia, Canada: Effects of habitat change and population density

Population viability analyses (PVA) are frequently employed to develop recovery plans and inform management of endangered species. Translating results from PVA into meaningful management recommendations often depends on an understanding of how population parameters change with environmental conditions as well as population density. The decline of mountain caribou (Rangifer tarandus caribou) in British Columbia, Canada, is believed to be caused by apparent competition with alternative prey species following changes to the forest age structure from timber harvest and wildfire. In addition, populations have been shown to decline at faster rates at low population density. To evaluate the potential effects of habitat change and population density on population persistence, we used stochastic projection models for 10 distinct populations varying in initial size from <10 to approximately 150 females. In an initial model, we used estimates of vital rates based on information sampled from >350 radiocollared caribou between 1984 and 2004. We then compared the results of the initial model to a set of models that evaluated the effects of habitat conditions and population density via their expected relationships to female adult survival. Assuming that vital rates remain constant over a 200-year time frame, only three populations have high probabilities (>0.95) of extinction. When models incorporate the declines in adult female survival know to occur with increasing proportions of young forest and declining population densities, all 10 populations are predicted to decline to extinction within <200 years. Based on our results, we suggest that PVA models that fail to incorporate the effects of changes in vital rates with habitat and population density may lead to overly optimistic assessments of the probability of population persistence in endangered species.     

Quantifying management-driven changes in organic matter turnover in an agricultural soil: An inverse modeling approach using historical data and a surrogate CENTURY-type model

In order to facilitate inverse modeling of time-series data and/or parameter estimation for process-based models of soil organic carbon (SOC) dynamics, we developed and applied a new surrogate CENTURY SOC model (SCSOC). While SCSOC has mass balance and decomposition kinetics equations for residue and soil organic matter (SOM) pools identical to those of CENTURY, it differs by being: (1) decoupled from models of plant growth, nutrient cycling, and hydrologic processes; (2) capable of employing daily, monthly, or annual timesteps; (3) solvable using widely available non-linear regression software. Here, we describe SCSOC and demonstrate that its numerical solution to the CENTURY SOC equations is highly accurate for both daily and monthly timesteps, provided the monthly physical forcing function inputs are appropriately derived from daily-resolution hydrologic model results.As an example of the proper application of the tool to obtain site-specific parameters and to investigate hypotheses using historical data, we analyzed SOC data from a single subplot of the Morrow Plots (Urbana, Illinois, U.S.A.) that has been cropped continuously in corn since 1876 using management practices that were common for east-central Illinois. The impact of different approaches typically used during calibration were examined by objectively estimating a variety of parameter sets that both govern SOM decomposition kinetics and define the initial mass and fractionation of the SOM. The results suggest that mean SOM turnover times were circa 5-fold longer during the period 1876-1954 relative to 1955-1995, when modern management practices were employed, and significantly different from default CENTURY predictions during both.Modified versions of SCSOC were also constructed in order to (1) show that uncertainty about historical soil erosion does not confound this interpretation of the data and (2) explore alternative assumptions about the structure of the model. One such alternate model showed that unexpectedly rapid decomposition of the corn-derived SOM combined with depletion of slowly-decomposing prairie-derived SOM could explain the post-1955 acceleration in decomposition.     

Modelling the effects of persecution on the population dynamics of golden eagles in Scotland

We used observations of the age structure and breeding productivity of the Scottish population of golden eagles Aquila chrysaetos together with the classic theory of population dynamics to derive current `unmanipulated' estimates of life history parameters. We then used regional differences in age structure associated with differences in persecution intensity to derive estimates of prospective `persecution-free' life history parameters. The different parameter combinations were entered into a population model to simulate their effects on the number of occupied territories over time. Most simulations suggested that with unmanipulated demographic parameters the population should decline. The disparity between these predictions and the observed apparent stability in occupied territories was ascribed to the buffering effect of a lowering in age of breeding in areas where persecution is most intense and that more favourable parameter estimates within the estimated limits may be more realistic. The results indicated, nevertheless, that currently the population is vulnerable to decline as also suggested by the apparent lack of adults to occupy vacant territories. In the absence of the estimated 3-5% annual adult mortality through persecution, modelling suggested the population would increase. Removing estimated effects of persecution on reproductive rate and preadult survival were on their own insufficient to reverse the declines predicted from unmanipulated parameters, although the effect of persecution on preadult survival may be more severe than we estimated. In the absence of persecution we conclude that the population could expand to fill currently vacant but apparently suitable habitat and have a more secure long-term status.     

Mixed-Effects Estimation in Dynamic Models of Plant Growth for the Assessment of Inter-individual Variability

Modeling inter-individual variability in plant populations is a key issue to understand crop heterogeneity and its variations in response to the environment. Being able to describe the interactions among plants and explain the variability observed in the population could provide useful information on how to control it and improve global plant growth. We propose here a method to model plant variability within a field, by extending the so-called GreenLab functional-structural plant model from the individual to the population scale via nonlinear mixed-effects modeling. Parameter estimation of the population model is achieved using the stochastic approximation expectation maximization algorithm, implemented in the platform for plant growth modeling and analysis PyGMAlion. The method is first applied on a set of simulated data and then on a real dataset from a population of 34 winter oilseed rape plants at the rosette stage. Results show that our method allows for a good characterization of the variability in the population with only a limited number of parameters, which is a key point for plant models. Results on simulated data show that parameters associated with a low sensitivity index are inaccurately estimated by the algorithm when considered as random effects, but a good stability of the results can be obtained by considering them as fixed effects. These results open new ways for the analysis of inter-plant variability within a population and the study of plant–plant competition.Supplementary materials accompanying this paper appear online.     

Management recommendations based on matrix projection models: The importance of considering biological limits

Matrix population models are a common tool for evaluating different management strategies. In general, under deterministic analyses, management strategies are recommended that improve those matrix transitions that are most sensitive or elastic with respect to the asymptotic population growth rate, λ. These recommendations usually ignore the biological limit for these transitions. In this paper we use the endangered Serengeti cheetah (Acinonyx jubatus) as a case study to illustrate that ignoring biological limits leads to a recommendation that will not always achieve the desired goal of an asymptotic population growth rate, λ ? 1.We estimate the survivorships of adult cheetahs in captivity using cheetah studbook data, which is a conservative estimate of the biological limit for the adult survivorship of wild cheetahs. Our analysis suggests that adult survival sharply decreases after 8.5 years. In addition, captive cheetahs older than 18 years do not reproduce. We modify a previously published population projection matrix to include the effect of senescence on survival and fecundity. Our model suggests that increasing adult survivorship alone is not sufficient to reverse population decline. However, an additional small increase in newborn survival is likely to result in a viable cheetah population. We show these conclusions hold even in the presence of relatively large parameter perturbations.     

No place to nest or bask: Effects of human disturbance on the nesting and basking habits of yellow-blotched map turtles (Graptemys flavimaculata)

Considerable recent attention has focused on how human disturbance alters the behaviour of imperiled taxa. Data on such impacts are common for waterfowl, marine mammals, and some large game animals. However, little is known about how human disturbances affect reptiles, perhaps because most reptiles are secretive and are not commonly seen by the public. We studied the impact of human disturbances on the nesting and basking behaviour of the yellow-blotched map turtle (Graptemys flavimaculata) on the Pascagoula River in southeastern Mississippi, USA. We found that both nesting and basking behaviour of map turtles were altered by human recreational activities. Turtles attempting to nest commonly abandoned their attempts upon the approach of a boat and, prior to nesting, numerous individuals waited several hours near the beach without emerging. Basking turtles frequently dove into the water upon the approach of a boat and some did not return to bask. Anglers in small boats that remained in the vicinity of basking sites caused the most disturbances, whereas personal water crafts (jet skis) caused fewer disturbances. Our data suggest that interruption of nesting activities may have an especially severe impact on the viability of this population through changes in numbers of clutches females are able to lay and altering the microhabitat females select for their nests.     

Population assessments of gentoo penguins (Pygoscelis papua) breeding at an important Antarctic tourist site, Goudier Island, Port Lockroy, Palmer Archipelago, Antarctica

Goudier Island is located in the Palmer Archipelago, to the west of the Antarctic Peninsula; it is one of the most frequently visited tourist sites in Antarctica. A number of gentoo penguin (Pygoscelis papua) breeding colonies are located on the island and these have been the focus of one of the longest running experiments to examine the impacts of tourist numbers upon penguin breeding performance anywhere in the Antarctic. In this paper we describe the population trends and breeding productivity (chicks per nest) of the 10 colonies on Goudier Island, all of which have now been monitored for 12 consecutive years beginning in the 1996/1997 breeding season. Our results demonstrate that all colonies show considerable inter-annual variability for both the number of breeding pairs and breeding productivity. Of the six visited colonies, two showed an important and significant statistical decline in the number of breeding pairs. One of these declining colonies is used to determine the breeding chronology dates for all other colonies, an important part of the monitoring procedure used to assess breeding success. Our results suggest that in the future, it would be useful to control for this additional disturbance. Our results further suggest that understanding all of the many subtle influences that impact upon gentoo penguin breeding numbers is complex and that some factors may never be completely identified.     

Information needs and priorities for assessing the sensitivity of marine birds to oil spills

Our experience in developing models to predict the potential impacts of oil spills on colonially breeding marine birds has revealed some major gaps in the information available on these systems. We consider the availability of data for a variety of parameters of seabird biology that are required in modelling efforts, and assign provisional priorities to our information needs. In order to develop means of predicting the impacts of oil spills on seabirds, we suggest that colony- or site-specific information on the timing of reproduction and colony occupancy, chick growth rates and body weights, several metabolic parameters, flight speed, and food load size is of relatively low overall priority. Intermediate priority is assigned to the collection of specific data on the dynamics of oil spills, the age and breeding structure of the populations, reproductive success, foraging activity budgets and flight paths, flight costs, and the response of growing chicks to food deprivation. We suggest that studies of seabird biology should give highest priority to obtaining information on population sizes, the probability of adult death upon encountering a spill, age-specific fecundity and survivorship, the time required in foraging trips, the lag time in the response of birds to an oil spill, foraging rate as a function of resource density, and changes in the availability of resources to the birds as a consequence of oil spills.     

Persistence of Gunnison’s prairie dog colonies in Arizona, USA

Although the five species of prairie dogs (Cynomys spp.) are recognized as important components of grassland ecosystems in western North America, they have experienced major population declines due to poisoning, outbreaks of sylvatic plague, recreational shooting, and habitat conversion. From May 2000 to October 2001, we investigated 270 colonies of Gunnison’s prairie dog (Cynomys gunnisoni) in Arizona. Because these colonies were classified as active in previous surveys (1987, 1990-1994, 1998), we were able to examine their persistence. Most (70%) of the colonies became inactive between the initial and recent surveys, with colony extinctions spanning our study area. Colony persistence was positively associated with the persistence of the nearest neighboring colony but was not associated with major vegetation type, distance to nearest neighboring colony, or initial size of the colony. The amount of area occupied by individual colonies varied between surveys, sometimes dramatically. We found little evidence that the reduction in active colonies was due to poisoning, recreational shooting, or habitat conversion. Rather, direct and indirect evidence suggest plague is the primary factor negatively impacting Gunnison’s prairie dog populations in Arizona. Currently, there is no way to control or prevent plague outbreaks in Gunnison’s prairie dog populations. To mitigate the effects of localized plague outbreaks on the overall population of this species, we suggest that Gunnison’s prairie dog be reintroduced to public lands throughout its historical range.     

Chemical,Physical and Biological Criteria for Maturity in Composts for Organic Farming

Properties of organic farming composts were examined during the composting process: pH, electrical conductivity, C/N ratio, total N content, NH₄₊ content, NO_3?content, ash content, and organic matter content. In addition to these properties the respiration rate, microbial population counts, hydrolysis of Fluorescein Diacetate (FDA) and the activity of the enzyme amidase were studied. Composts at several stages of maturity were incubated in soil, and their N mineralization rates were measured. The end of the thermophilic stage was characterized by irreversible decrease in pile temperature to under 55°C, followed by stabilization of the chemical properties. This stage in the composting process is also characterized by decrease in CO₂ evolution rate, changes in microbial populations and specific patterns in FDA hydrolysis and amidase activity. Based on this evidence, we suggest that biological parameters can be considered as indicators for compost maturity.     

A linear functional relationship model for circular data with an application to the assessment of ocean wave measurements

This article suggests a linear functional relationship model for comparing two sets of circular data subject to unobservable errors. Unlike the corresponding and relatively well-studied model for linear data, maximum likelihood estimation for this model is very complicated and no explicit solutions are possible. Using a numerical approximation, we are able to solve the likelihood equations approximately, and to obtain good approximations to the likelihood estimates of the parameters. The quality of our estimates and the feasibility of the estimation method are illustrated via simulation. By establishing a parallel with the model for linear data, we are able to explain the various problems occurring in the process of estimation and to substantiate our numerical results. The interest in the model arose in connection with the study of ocean wave data; an application to such data is also given.