Removal process estimation of population size for a population with a known sex ratio

A removal model for estimating population size which uses the known population sex ratio is studied. A maximum likelihood estimate and an optimal martingale estimate of the population size are proposed. Their standard errors and large sample properties are obtained. Simulation studies are reported, and the performance of the proposed estimators are compared with the standard maximum likelihood estimator which ignores the sex ratio information. An example on a capture study of deer mice is given.     

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.     

On the use of correlated beta random variables with animal population modelling

We give reasons why demographic parameters such as survival and reproduction rates are often modelled well in stochastic population simulation using beta distributions. In practice, it is frequently expected that these parameters will be correlated, for example with survival rates for all age classes tending to be high or low in the same year. We therefore discuss a method for producing correlated beta random variables by transforming correlated normal random variables, and show how it can be applied in practice by means of a simple example. We also note how the same approach can be used to produce correlated uniform, triangular, and exponential random variables.     

Complex dynamics of the population with a simple age structure

The effects of the following modes of density-dependent control of population growth: density-dependent birth rate, adult survival rate, juvenile survival rate are compared based on the mathematical model of population dynamics. It is shown that the most efficient mechanisms limiting population size are decreasing with the growth of the adult population birth rate and/or the decreasing survival rate of the offspring with the increase in their number. However, these same mechanisms are responsible for oscillations of the population size and its chaotic change. The density-dependence of the adult survival rate is not efficient in constraining the population growth, but it can substantially limit the magnitude of oscillations of the population size.     

Estimating the population size with a behavioral response in capture-recapture experiment

A new estimating procedure is suggested to estimate the population size in a capture-recapture experiment. The capture intensities for first-capture and recapture are allowed to be different and time dependent but they are assumed to be proportional. It is shown that the information on the proportionality constant is crucial to the estimation of the population size. Sensitivity analysis with a misspecification of the proportionality constant is conducted. The method has also been extended to the case with an unknown proportionality. A real example is given.     

Modeling effects of toxin exposure in fish on long-term population size, with an application to selenium toxicity in bluegill (Lepomis macrochirus)

A primary goal in ecotoxicology is the prediction of population-level effects of contaminant exposure based on individual-level response. Assessment of toxicity at the population level has predominately focused on the population growth rate (PGR), but the PGR may not be a relevant toxicological endpoint for populations at equilibrium. Equilibrium population size may be a more meaningful endpoint than the PGR because a population with smaller equilibrium size is more susceptible to the negative effects of environmental variability. We address the individual-to-population extrapolation problem with modeling utilizing classical mathematical theory. We developed and analyzed a general model applicable to many freshwater fish species, that includes density-dependent juvenile survival and additional juvenile mortality due to toxicity exposure, and we quantified effect on equilibrium population size as a means of assessing toxicity. Individual-level effects are typically greater than population-level effects until the individual effect is large, due to compensatory density-dependent relationships. These effects are sensitive to the recruitment potential of a population, in particular the low-density first-year survival rate S_b. Assuming high S_b could result in underestimating effects of population-level toxicity. The equilibrium size depends directly on S_b, the reproductive potential, the toxin concentration at which mean mortality is 50% (LC₅₀), and the rate at which individual mortality increases with increasing toxin concentration. More experimental data are needed to decrease the uncertainty in estimating these parameters. We then used existing data for selenium toxicity in bluegill sunfish to parameterize a simulation version of the model as an example to assess the effects of environmental stochasticity on toxicity response. Effects of environmental variability resulted in simulated extinctions at much lower toxin concentrations than predicted deterministically.     

On the latent state estimation of nonlinear population dynamics using Bayesian and non-Bayesian state-space models

Nonlinear state-space models have been increasingly applied to study population dynamics and data assimilation in environmental sciences. State-space models can account for process error and measurement error simultaneously to correct for the bias in the estimates of system state and model parameters. However, few studies have compared the performance of different nonlinear state-space models for reconstructing the state of population dynamics from noisy time series. This study compared the performance of the extended Kalman filter (EKF), unscented Kalman filter (UKF) and Bayesian nonlinear state-space models (BNSSM) through simulations. Synthetic population time series were generated using the theta logistic model with known parameters, and normally distributed process and measurement errors were introduced using the Monte Carlo simulations. At higher levels of nonlinearity, the UKF and BNSSM had lower root mean square error (RMSE) than the EKF. The BNSSM performed reliably across all levels of nonlinearity, whereas increased levels of nonlinearity resulted in higher RMSE of the EKF. The Metropolis–Hastings algorithm within the Gibbs algorithm was used to fit the theta logistic model to synthetic time series to estimate model parameters. The estimated posterior distribution of the parameter θ indicated that the 95% credible intervals included the true values of θ (=0.5 and 1.5), but did not include 1.0 and 0.0. Future studies need to incorporate the adaptive Metropolis algorithm to estimate unknown model parameters for broad applications of Bayesian nonlinear state-space models in ecological studies.     

Modeling the brown bear population in Slovenia: A tool in the conservation management of a threatened species

In this paper, we address three aspects of the brown bear population in Slovenia: its size (and its evolution over time), its spatial expansion out of the core area, and its potential habitat based on natural habitat suitability. Data collected through measurement/observation of the bear population and from the literature are used. A model is developed for each aspect. The results are estimates of population size, a picture of the spatial expansion of the population and maps of its optimal and maximal potential habitat (based on natural suitability). Overall, the brown bear population has been increasing since the establishment of a core protective area and has been expanding outside this area. The habitat suitability maps show that there is room for further expansion. Based on habitat suitability and bear population density, as well as human activity and current damage reports, we recommend that the Alps should be temporarily kept free of the bears, until the necessary mitigation measures regarding human–bear conflicts are carried out. On the other hand it is of crucial importance to adapt human activities and improve bear management in the optimal habitat, with which the goals of successful conservation of the species might be achieved.     

Zooplankton population model coupled to a biogeochemical model of the North Western Mediterranean Sea ecosystem

A stage structured population (SSP) model based on Fennel's [Fennel, W., 2001. Modelling copepods with links to circulation models. Journal of Plankton Research, 23, 1217–1232] equations is applied to Centropages typicus (Kröyer), a dominant copepod species of the North Western Mediterranean Sea (NWMS) and a prey of small pelagic fish. The model considers five groups of stages and development rates are represented by a mechanistic formulation depending on individual specific growth in each stage. Individual growth is calculated from the individual energy budget depending on food availability and temperature.     

Modeling population effects of the Deepwater Horizon oil spill on a long-lived species

The 2010 Deepwater Horizon (DWH) oil spill exposed common bottlenose dolphins (Tursiops truncatus) in Barataria Bay, Louisiana to heavy oiling that caused increased mortality and chronic disease and impaired reproduction in surviving dolphins. We conducted photographic surveys and veterinary assessments in the decade following the spill. We assigned a prognostic score (good, fair, guarded, poor, or grave) for each dolphin to provide a single integrated indicator of overall health, and we examined temporal trends in prognostic scores. We used expert elicitation to quantify the implications of trends for the proportion of the dolphins that would recover within their lifetime. We integrated expert elicitation, along with other new information, in a population dynamics model to predict the effects of observed health trends on demography. We compared the resulting population trajectory with that predicted under baseline (no spill) conditions. Disease conditions persisted and have recently worsened in dolphins that were presumably exposed to DWH oil: 78% of those assessed in 2018 had a guarded, poor, or grave prognosis. Dolphins born after the spill were in better health. We estimated that the population declined by 45% (95% CI 14–74) relative to baseline and will take 35 years (95% CI 18–67) to recover to 95% of baseline numbers. The sum of annual differences between baseline and injured population sizes (i.e., the lost cetacean years) was 30,993 (95% CI 6607–94,148). The population is currently at a minimum point in its recovery trajectory and is vulnerable to emerging threats, including planned ecosystem restoration efforts that are likely to be detrimental to the dolphins’ survival. Our modeling framework demonstrates an approach for integrating different sources and types of data, highlights the utility of expert elicitation for indeterminable input parameters, and emphasizes the importance of considering and monitoring long-term health of long-lived species subject to environmental disasters. Article impact statement: Oil spills can have long-term consequences for the health of long-lived species; thus, effective restoration and monitoring are needed.     

A simulation framework for water allocation to meet the environmental requirements of urban rivers: model development and a case study for the Liming River in Daqing City,China

In this paper, we describe the development of a simulation framework for allocating water from different sources to meet the environmental flows of an urban river. The model permits the development of a rational balance in the utilization of storm water, reclaimed water from wastewater treatment plants, and freshwater from reservoirs with consideration of the limited capacities of different water resources. It is designed to permit the full utilization of unconventional water sources for the restoration of river water quality by increasing river flow and improving water quality. To demonstrate practical use of the model, a case study is presented in which the model was used to simulate the environmental water allocation for the Liming River in Daqing City, China, based on the three water sources mentioned above. The results demonstrate that the model provides an effective approach for helping managers allocate water to satisfy the river’s environmental water requirements.     

Modeling the population dynamics of cotton bollworm Helicoverpa armigera (Hübner) (Lepidoptera: Noctuidae) over a wide area in northern China

The cotton bollworm Helicoverpa armigera (Lepidoptera: Noctuidae) is one of the most serious crop pests in northern China, calling for accurate prediction of pest outbreaks and strategies for pest control. A computer model is developed to simulate the population dynamics of H. armigera over a wide area in northern China. The area considered covers 12 provinces where serious outbreaks of H. armigera have been observed. In this model, pest development is driven by local ambient temperature, and adults migrate long distances between regions and select preferred hosts for oviposition within a region. Six types of host including cotton, wheat, corn, peanut, soybean and a single category composed of all other minor hosts are considered in this model. Survival rates of eggs and larvae are based on life-table data, and simulated as a function of host type, host phenology and temperature. The incidence of diapause depends on temperature and photoperiod experienced during the larval stage. Survival rate of non-diapause pupae is a nonlinear function of rainfall, and overwinter survival rate is a nonlinear function of temperature. Insecticide is applied when population density exceeds the economic threshold on a host crop within a region. Comparisons of model output with light-trap data indicate that our model reflects the pest population dynamics over a wide area, and could potentially be used for testing novel pest control strategies in northern China.     

Evaluation of the performance of rural wastewater treatment plants using chemical measurements in combination with statistical techniques: a case study

The performance of a wastewater treatment plant was assessed statistically using multivariate cluster and principle component analysis. This was after measuring some physico-chemical properties in the influent, effluent, downstream, and upstream waters over a 4-month period. The cluster analysis grouped the sampling sites into three clusters: relatively non-polluted (upstream), medium polluted (downstream), and polluted (influent and effluent). The polluted water was further subdivided into very highly (influent) and highly (effluent) polluted. The grouping of influent and effluent into one cluster was due to some water quality parameters such as amount of copper, lead, and phosphates that are not efficiently removed by the plant. Using principal component analysis, samples from the same site taken over a period of 4 months were scattered, indicating inconsistencies in the performance of the plant. This was more pronounced during the rainy season, suggesting that increased water volumes from open sewers make the already poorly performing plant worse. The major loading factors found by principle component analysis were phosphate, lead, iron, zinc, copper, pH, and conductivity. Generally, the wastewater treatment system was found to be efficient in removing heavy metals and these were found in the sludge, but not anions. The mean percentage metal removal could be arranged in the following decreasing order: iron (85%)?>?zinc (57%)?>?copper (40%) and lead (38%) following the concentrations (mg?kg^?1) found in the sludge: iron (11,300)?>?zinc (820)?>?copper (180)?>?lead (20)?>?cadmium (3). Phosphate and iron concentrations in the effluent were found to be above the South African Bureau of Standards (SABS) recommendations. The major cause of poor performance is the high volume of the wastewater, exceeding the capacity of the plant 10 times.     

Examining the colonization process of exotic species varying in competitive abilities using a cellular automaton model

Current threats of invasive species have significant implications for ecological systems. Given their potential impacts, invasive species have been the subject of extensive empirical and theoretical studies. However, these studies have tended to focus on species that produce highly visible ecological and economic impacts. In our study, we take a step back from focusing on these high-impact invasive species, and examine the general colonization (invasion) process of exotic species that have various “competitive abilities” against the native species. Using a two-species cellular automaton model, we demonstrate that: (1) a threshold level of competitive ability is required for the exotic species to successfully establish in a new landscape and (2) an exotic species with superior competitive ability does not necessarily become dominant in a landscape (alternatively, a species that has inferior competitive ability may successfully colonize a new system). Our findings have significant implications for the study of species invasions and also provide clues to how species assemble in ecological communities.     

Application of a spatial meta-population model with stochastic parameters to the management of the invasive grass Nassella trichotoma in North Canterbury, New Zealand

Optimising the management of invasive plants requires the identification of the population size outcomes for alternative management strategies. Mathematical models can be useful tools for making such management strategy comparisons. In this paper we develop a generic landscape meta-population model and apply it to the weedy grass, Nassella trichotoma, an invasive species occupying approximately 800 land parcels, predominantly pastoral farms, in the Hurunui district, North Canterbury, New Zealand. Empirical evidence reveals that this meta-population is currently stable (at a median density of 6 plants ha⁻¹) under a community strategy requiring manual removal (termed ‘grubbing’) of plants annually from all land parcels. Reduction in population size requires an alternative management strategy. Field data, collected over a 12 year period, were used to provide stochastic parameter values for land parcel size, carrying capacity, rates of local population growth and grubbing.The model reveals that at steady state, the most significant contribution to population growth on a land parcel comes from within the land parcel itself; the expected annual per capita growth on an individual land parcel is 4 orders of magnitude greater than the expected annual contribution from plants arising from other land parcels. This result implies that many of the farms currently supporting N. trichotoma may pose little or no threat to, nor are threatened themselves by, other farms infested by the weed. However, the steady state distribution (of the weed's population density) was sensitive to the spread rate, revealing a need for data on this process. It was also sensitive to how any increase in the grubbing rate is distributed; increasing it via a uniform distribution U(0, 1) where all rates between 0 and 100% year⁻¹ are equally probable did not affect the steady state, whereas increasing the rates via the uniform distribution U(0.25, 0.75) resulted in fewer farms with high population densities. In general the model provides a basis for exploring the effects of a wide range of alternative grubbing strategies on population growth in N. trichotoma.     

Using a fisheries ecosystem model with a water quality model to explore trophic and habitat impacts on a fisheries stock: A case study of the blue crab population in the Chesapeake Bay

Recent calls for the development of ecosystem-based fisheries management compel the development of resource management tools and linkages between existing fisheries management tools and other resource tools to enable assessment and management of multiple impacts on fisheries resources. In this paper, we describe the use of the Chesapeake Bay Fisheries Ecosystem Model (CBFEM), developed using the Ecopath with Ecosim (EwE) software, and the Chesapeake Bay Water Quality Model (WQM) to demonstrate how linkages between available modeling tools can be used to inform ecosystem-based natural resource management. The CBFEM was developed to provide strategic ecosystem information in support of fisheries management. The WQM was developed to assess impacts on water quality. The CBFEM was indirectly coupled with the WQM to assess the effects of water quality and submerged aquatic vegetation (SAV) on blue crabs. The output from two WQM scenarios (1985-1994), a baseline scenario representing actual nutrient inputs and another with reduced inputs based on a tributary management strategy, was incorporated into the CBFEM. The results suggested that blue crab biomass could be enhanced under management strategies (reduced nutrient input) when the effective search rate of blue crab young-of-the-year's (YOY's) predators or the vulnerability of blue crab YOY to its predators was adjusted by SAV. Such model linkages are important for incorporating physical and biological components of ecosystems in order to explore ecosystem-based fisheries management options.     

Approaching the upper boundary of driver-response relationships: identifying factors using a novel framework integrating quantile regression with interpretable machine learning

● A novel framework integrating quantile regression with machine learning is proposed. ● It aims to identify factors driving observations to upper boundary of relationship. ● Increasing N:P and TN concentration help fulfill the effect of TP on CHL. ● Wetter and warmer decrease potential and increase eutrophication control difficulty. ● The framework advances applications of quantile regression and machine learning. The identification of factors that may be forcing ecological observations to approach the upper boundary provides insight into potential mechanisms affecting driver-response relationships, and can help inform ecosystem management, but has rarely been explored. In this study, we propose a novel framework integrating quantile regression with interpretable machine learning. In the first stage of the framework, we estimate the upper boundary of a driver-response relationship using quantile regression. Next, we calculate “potentials” of the response variable depending on the driver, which are defined as vertical distances from the estimated upper boundary of the relationship to observations in the driver-response variable scatter plot. Finally, we identify key factors impacting the potential using a machine learning model. We illustrate the necessary steps to implement the framework using the total phosphorus (TP)-Chlorophyll a (CHL) relationship in lakes across the continental US. We found that the nitrogen to phosphorus ratio (N׃P), annual average precipitation, total nitrogen (TN), and summer average air temperature were key factors impacting the potential of CHL depending on TP. We further revealed important implications of our findings for lake eutrophication management. The important role of N׃P and TN on the potential highlights the co-limitation of phosphorus and nitrogen and indicates the need for dual nutrient criteria. Future wetter and/or warmer climate scenarios can decrease the potential which may reduce the efficacy of lake eutrophication management. The novel framework advances the application of quantile regression to identify factors driving observations to approach the upper boundary of driver-response relationships.