Robust optimal observation of a metapopulation

We consider a two-parameter continuous-time Markovian model for patch occupancy in metapopulation, and address the question of when to observe the population in order to obtain the most accurate and precise estimator of the parameters. Using the likelihood obtained from a diffusion approximation we derive a robust procedure for determining the optimal observation schedule, which is considerably simpler than would otherwise be possible. We investigate the performance of two optimality criteria, ED-optimality and a particular form of maximin-optimality. Both allow one to incorporate prior belief about the parameter values before any data is collected. Kernel density estimates of the maximum likelihood estimator are compared under the various combinations of optimality criteria and prior distributions. Our methods are illustrated with reference to a model for the spread of crown of thorns starfish (Acanthaster planci) among the 55 islands comprising the Ryukyu group in Japan.     

A stochastic forest fire growth model

We consider a stochastic fire growth model, with the aim of predicting the behaviour of large forest fires. Such a model can describe not only average growth, but also the variability of the growth. Implementing such a model in a computing environment allows one to obtain probability contour plots, burn size distributions, and distributions of time to specified events. Such a model also allows the incorporation of a stochastic spotting mechanism.

Application of Markov-chain model for vegetation restoration assessment at landslide areas caused by a catastrophic earthquake in Central Taiwan

The 921 earthquake caused a catastrophic disaster in Central Taiwan. Ten years have passed since the earthquake occurred. Vegetation succession is the basis for establishing a restoration reference which plays an important role in vegetation restoration at landslide sites. Generally, growth conditions for grass are easier and the growth rate is faster than that for trees. Therefore, grass can be considered a pioneer species or an important reference for the early vegetation succession stage. This is the reason why grass is required to be extracted from other land covers. Integrating remote sensing, geographic information system and image classification into vegetation succession models is very important. In this study, the Markov chain model was applied for vegetation restoration assessment and discussion. Chiufenershan and Ninety-nine peaks were selected as the study areas. Five SPOT satellite images are used for land cover mapping and vegetation restoration simulations. Four categories of land covers were extracted, including forest, grass, bare land and water, respectively. From the transitive probability matrix (derived from any two land covers), the results show that vegetation restoration at the Chiufenershan and Ninety-nine peaks landslide areas is ongoing, but that has been disturbed by natural disasters.     

Bayes methods for combining disease and exposure data in assessing environmental justice

Environmental justice reflects the equitable distribution of the burden of environmental hazards across various sociodemographic groups. The issue is important in environmental regulation, siting of hazardous waste repositories and prioritizing remediation of existing sources of exposure. We propose a statistical framework for assessing environmental justice. The framework includes a quantitative assessment of environmental equity based on the cumulative distribution of exposure within population subgroups linked to disease incidence through a dose-response function. This approach avoids arbitrary binary classifications of individuals solely as 'exposed' or 'unexposed'. We present a Bayesian inferential approach, implemented using Markov chain Monte Carlo methods, that accounts for uncertainty in both exposure and response. We illustrate our method using data on leukaemia deaths and exposure to toxic chemical releases in Allegheny County, Pennsylvania.     

Modeling fecundity in birds: Conceptual overview, current models, and considerations for future developments

Fecundity is fundamental to the fitness, population dynamics, conservation, and management of birds. For all the efforts made to measure fecundity or its surrogates over the past century of avian research, it is still mismeasured, misrepresented, and misunderstood. Fundamentally, these problems arise because of partial observability of underlying processes such as renesting, multiple brooding, and temporary emigration. Over the last several decades, various analytical approaches have been developed to estimate fecundity from incomplete and biased data. These, include scalar arithmetic formulae, partial differential equations, individual-based simulations, and Markov chain methodology. In this paper, we: (1) identify component processes of avian reproduction; (2) review existing methods for modeling fecundity; (3) place these diverse models under a common conceptual framework; (4) describe the parameterization, validation, and limitations of such models; and (5) point out future considerations and challenges in the application of fecundity models. We hope this synthesis of existing literature will help direct researchers toward the most appropriate methods to assess avian reproductive success for answering questions in evolutionary ecology, natural history, population dynamics, reproductive toxicology, and management.     

Modelling dispersal with diffusion and habitat selection: Analytical results for highly fragmented landscapes

Quantifying dispersal is crucial both for understanding ecological population dynamics, and for gaining insight into factors that affect the genetic structure of populations. The role of dispersal becomes pronounced in highly fragmented landscapes inhabited by spatially structured populations. We consider a landscape consisting of a set of habitat patches surrounded by unsuitable matrix, and model dispersal by assuming that the individuals follow a random walk with parameters that may be specific to the habitat type. We allow for spatial variation in patch quality, and account for edge-mediated behavior, the latter meaning that the individuals bias their movement towards the patches when close to an edge between a patch and the matrix. We employ a diffusion approximation of the random walk model to derive analytical expressions for various characteristics of the dispersal process. For example, we derive formulae for the time that an individual is expected to spend in its current patch i, and for the time that it will spend in the matrix, both conditional on the individual hitting next a given patch j before hitting any of the other patches or dying. The analytical formulae are based on the assumptions that the landscape is infinitely large, that the patches are circularly shaped, and that the patches are small compared to interpatch distances. We evaluate the effect of these assumptions by comparing the analytical results to numerical results in a real patch network that violates all of the three assumptions. We then consider a landscape that fulfills the assumptions, and show that in this case the analytical results are in a very good agreement with the numerical results. The results obtained here allow the construction of computationally efficient dispersal models that can be used as components of metapopulation models.     

Performance of a Bayesian state-space model of semelparous species for stock-recruitment data subject to measurement error

Measurement errors in spawner abundance create problems for fish stock assessment scientists. To deal with measurement error, we develop a Bayesian state-space model for stock-recruitment data that contain measurement error in spawner abundance, process error in recruitment, and time series bias. Through extensive simulations across numerous scenarios, we compare the statistical performance of the Bayesian state-space model with that of standard regression for a traditional stock-recruitment model that only considers process error. Performance varies depending on the information content in data, as determined by stock productivity, types of harvest situations, and amount of measurement error. Overall, in terms of estimating optimal spawner abundance S_MSY, the Ricker density-dependence parameter β, and optimal harvest rate h_MSY, the Bayesian state-space model works best for informative data from low and variable harvest rate situations for high-productivity salmon stocks. The traditional stock-recruitment model (TSR) may be used for estimating α and h_MSY for low-productivity stocks from variable and high harvest rate situations. However, TSR can severely overestimate S_MSY when spawner abundance is measured with large error in low and variable harvest rate situations. We also found that there is substantial merit in using h_MSY (or benchmarks derived from it) instead of S_MSY as a management target.     

Migration effects in a stochastic multipopulation model for African bee population dynamics

The rate of northern migration of the Africanized honey bee (AHB) in the United States has recently slowed dramatically. This paper investigates the impact of migration on the equilibrium size distributions of a particular stochastic multipopulation model, namely a coupled logistic power law model. The bivariate equilibrium size distribution of the model is derived and illustrated with parameter values used to describe AHB population dynamics. In the model, the difference between the equilibrium sizes of the two populations is a measure of the effect of migration. The distribution of this difference may be approximated by a normal distribution. The mean and variance parameters for the normal are predicted accurately by a second-order regression model based on the migration rate and the maximum size of the first population. The methodology is general, and should be useful in studying the migration effect in many other applications with one-way migration.     

Estimation methods for nonlinear state-space models in ecology

The use of nonlinear state-space models for analyzing ecological systems is increasing. A wide range of estimation methods for such models are available to ecologists, however it is not always clear, which is the appropriate method to choose. To this end, three approaches to estimation in the theta logistic model for population dynamics were benchmarked by Wang (2007). Similarly, we examine and compare the estimation performance of three alternative methods using simulated data. The first approach is to partition the state-space into a finite number of states and formulate the problem as a hidden Markov model (HMM). The second method uses the mixed effects modeling and fast numerical integration framework of the AD Model Builder (ADMB) open-source software. The third alternative is to use the popular Bayesian framework of BUGS. The study showed that state and parameter estimation performance for all three methods was largely identical, however with BUGS providing overall wider credible intervals for parameters than HMM and ADMB confidence intervals.     

On interacting bee/mite populations: a stochastic model with analysis using cumulant truncation

Parasitism by the Varroa mite has had recent drastic impact on both managed and feral bee colonies. This paper proposes a stochastic population dynamics model for interacting African bee colony and Varroa mite populations. Cumulant truncation procedures are used to obtain approximate transient cumulant functions, unconstrained by the usual assumption of bivariate Normality, for an assumed large-scale model. The apparent size of the variance and skewness functions suggest the importance of the proposed truncation procedure which retains some higher-order cumulants, but determining the accuracy of the approximations is problematical. A smaller-scale bee/Varroa mite model is hence proposed and investigated. The accuracy for the means is exceptional, for the second-order cumulants is moderate, and for some third-order cumulants is poor. Notwithstanding the poor accuracy of a skewness approximation, the saddlepoint approximations for the marginal transient population size distributions are excellent. The cumulant truncation methodology is very general, and research is continuing in its application to this new class of host-parasite models.     

A stochastic weather generation model for Alaska

A specific problem encountered in ecosystem-level simulation of Arctic ecosystems is the depth and extent of the driving variable record. Often, climate records are of short duration, gathered at locations different from the area to be simulated, or do not contain all the variables required by a given model. This paper addresses this problem for ecosystem simulation in Alaska with the development of a weather generator. The generator, called WGENAL, is based on the WGEN climate generator developed and validated in the 48 conterminous states. Because of the extreme variability of weather in Alaska that is not accommodated by the statistical metrics in the earlier model, a new climate generator was developed. WGENAL generates daily values of precipitation, maximum temperature, minimum temperature, solar radiation, and wind run. Precipitation is generated using a Markov chain-gamma model. A two-parameter gamma distribution is used to generate wind run. Temperatures and solar radiation are generated using procedures developed in the earlier study. Validation of the generator shows it provides adequate diurnal and seasonal weather records for Fairbanks. Other comparisons of synthetic weather with observed weather for sites north of the Brooks Range in Alaska are also within the error of the original data.     

Establishment of Markov successional model and its application for forest restoration reference in Southern China

Forest succession is the base of establishing restoration reference which plays an important role in forest restoration and restoration estimation. The study presented the establishment of a Markov successional model (MSM) and its application to restoration reference in lower subtropical forest in China. The compositions of successional system in MSM were divided into three species types: pioneering pine trees, heliophytic trees and mesophytic trees. The successional system was divided into three subsystems: early successional stage, mid-successional stage and late-successional stage. Based on the site survey on the changes in the species and their individuals in 25 years, the transition matrices in various subsystems were determined. The predicted results were used to establish the restoration reference of the vegetation restoration in lower subtropical China. According to the ecological restoration reference established in this study, it would take 150 years for the forest to change from pioneer to mature communities in the region. Successional change of tree composition was forecast by the model, and the scenario forecast by the model reflects the actual conditions observed through 52 years of long-term permanent site research. The restoration experience in the region matches the forecast results. The application of a restoration reference model indicates that forest restoration can be accelerated by taking measures which change forest structure. The above results imply that a restoration reference established on the rule of regional forest succession could be very useful not only in directing, but also in assessing and managing regional forest restoration. Previously, one “ideal reference ecosystem” was used as a restoration reference in all correlative studies. In this study, the restoration “process” was used as the restoration reference.     

Nutrient criteria for lakes,ponds, and reservoirs: A Bayesian TREED model approach

We develop regional-scale eutrophication models for lakes, ponds, and reservoirs to investigate the link between nutrients and chlorophyll-a. The Bayesian TREED (BTREED) model approach allows association of multiple environmental stressors with biological responses, and quantification of uncertainty sources in the empirical water quality model. Nutrient data for lakes, ponds, and reservoirs across the United States were obtained from the Environmental Protection Agency (EPA) National Nutrient Criteria Database. The nutrient data consist of measurements for both stressor variables (such as total nitrogen and total phosphorus), and response variables (such as chlorophyll-a), used in the BTREED model. Markov chain Monte Carlo (McMC) posterior exploration guides a stochastic search through a rich suite of candidate trees toward models that better fit the data. The Bayes factor provides a goodness of fit criterion for comparison of resultant models. We randomly split the data into training and test sets; the training data were used in model estimation, and the test data were used to evaluate out-of-sample predictive performance of the model. An average relative efficiency of 1.02 between the training and test data for the four highest log-likelihood models suggests good out-of-sample predictive performance. Reduced model uncertainty relative to over-parameterized alternative models makes the BTREED models useful for nutrient criteria development, providing the link between nutrient stressors and meaningful eutrophication response.     

Space-time modeling for the Missouri Turkey Hunting Survey

The Missouri Turkey Hunting Survey (MTHS) is a postseason mail survey conducted by the Missouri Department of Conservation. The 1996 MTHS provides information concerning the number of turkeys harvested by hunters on each day and the total number of trips made to the counties by these hunters on each day of the hunting season. The success rates are then found from this information. Small sample sizes produce large standard errors for the estimates at the county level. We use a Bayesian hierarchical generalized linear model to estimate daily hunting success rates at the county level. The model includes an autoregressive process for the days of the hunting season and spatially correlated random geographic effects. The computations are performed using Gibbs sampling and adaptive rejection sampling techniques. Results show that there are significant spatial corelations between counties and correlations between days of the hunting season. The estimates are close to the frequency estimates at the state level and much more stable at the county level.     

A density projection approach for non-trivial information dynamics: Adaptive management of stochastic natural resources

We demonstrate a density projection approximation method for solving resource management problems with imperfect state information. The method expands the set of partially-observed Markov decision process (POMDP) problems that can be solved with standard dynamic programming tools by addressing dimensionality problems in the decision maker's belief state. Density projection is suitable for uncertainty over both physical states (e.g. resource stock) and process structure (e.g. biophysical parameters). We apply the method to an adaptive management problem under structural uncertainty in which a fishery manager's harvest policy affects both the stock of fish and the belief state about the process governing reproduction. We solve for the optimal endogenous learning policy—the active adaptive management approach—and compare it to passive learning and non-learning strategies. We demonstrate how learning improves efficiency but typically follows a period of costly short-run investment.     

Climate, canopy conductance and leaf area development controls on evapotranspiration in a boreal coniferous forest over a 10-year period: A united model assessment

The aim of this work was to test a process-based model (hydrological model combined with forest growth model) on the simulation of seasonal variability of evapotranspiration (ET) in an even-aged boreal Scots pine (Pinus sylvestris L.) stand over a 10 year period (1999-2008). The water flux components (including canopy transpiration (E_t) and evaporation from canopy (E_c) and ground surface (E_g) were estimated in order to output the long-term stand water budget considering the interaction between climate variations and stand development. For validation, half-hourly data on eddy water vapor fluxes were measured during the 10 growing seasons (May-September). The model predicted well the seasonal course of ET compared to the measured values, but slightly underestimated the water fluxes both in non-drought and drought (2000, 2003 and 2006) years. The prediction accuracy was, on average, higher in drought years. The simulated ET over the 10 years explained, on average, 58% of the daily variations and 84% of the monthly amount of ET. Water amount from E_t contributed most to the ET, with the fractions of E_t, E_c and E_g being, on average, 67, 11 and 23% over the 10-year period, respectively. Regardless of weather conditions, the daily ET was strongly dependent on air temperature (T_a) and vapor pressure deficit (D_a), but less dependent on soil moisture (W_s). On cloudy and rainy days, there was a non-linear relationship between the ET and solar radiation (R_o). During drought years, the model predicted lower daily canopy stomatal conductance (g_cs) compared with non-drought years, leading to a lower level of E_t. The modeled daily g_cs responded well to D_a and W_s. In the model simulation, the annual LAI increased by 35% between 1999 and 2008. The ratio of E_c: ET correlated strongly with LAI. Furthermore, LAI reduced the proportion of E_g as a result of the increased share of E_c and E_t and radiation interception. Although the increase of LAI affected positively E_t, the contribution of E_t in ET was not significantly correlated with LAI. To conclude, although the model predicted reasonably well the seasonal course of ET, the calculation time steps of different processes in the model should be homogenized in the future to increase the prediction accuracy.     

Using an individual-based model to quantify scale transition in demographic rate functions: Deaths in a coral reef fish

Scientifically informed population management requires quantitatively accurate demographic rate functions that apply at the spatial scale at which populations are actually managed, but practical constraints confine most field measurements of such functions to small study plots. This paper employs an individual-based population growth model to extrapolate the death rate function in a well-studied coral reef fish, the bridled goby Coryphopterus glaucofraenum, from the scale of coral reef “cells” at which it was measured to the larger scale of an entire coral reef. Density dependence in the whole-reef function actually proves stronger than in the local function because high goby density occasionally arises in local patches with few refuges from predators, producing very high mortality there. This IBM-based approach extends the reach of scale transition theory by examining considerably more realistic models than standard analytical methods can presently handle.     

活性污泥总DNA不同提取方法的比较

为了快速、简便和经济地获得活性污泥的总DNA,以用于分子生物学研究,采用5种不同的DNA提取方法提取活性污泥的总DNA,并通过提取的核酸总量、纯度、是否含有聚合酶链反应抑制剂等指标综合分析不同的提取方法对活性污泥总DNA提取效果的影响.结果表明:蛋白酶K-SDS-酚氯仿法和柱提取DNA试剂盒法提取活性污泥总DNA效果最好,提取DNA总量多,纯度高,可不经纯化直接进行PCR扩增反应。     

Coupling a land use model and an ecosystem model for a crop-pasture zone

This paper describes the development of a land use model coupling ecosystem processes. For a given land use pattern in a region, a built-in regional ecosystem model (TESim) simulates leaf physiology of plants, carbon and nitrogen dynamics, and hydrological processes including runoff generation and run-on re-absorption, as well as runoff-induced soil erosion and carbon and nitrogen loss from ecosystems. The simulation results for a certain period from 1976 to 1999 were then used to support land use decisions and to assess the impacts of land use changes on environment. In the coupling model, the land use type for a land unit was determined by optimization of a weighted suitability derived from expert knowledge about the ecosystem state and site conditions. The model was applied to the temperate crop-pasture band in northern China (CCPB) to analyze the interactions between land use and major ecosystem processes and functions and to indicate the added value of the feedbacks by comparing simulations with and without the coupling and feedbacks between land use module and ecosystem processes. The results indicated that the current land use in CCPB is neither economical nor ecologically judicious. The scenario with feedbacks increased NPP by 46.78 g C m⁻² a⁻¹, or 32.23% of the scenario without feedbacks, also decreased soil erosion by 0.65 kg m⁻² a⁻¹, or 23.13%. Without altering the regional land use structure (proportions of each land use type). The system developed in this study potentially benefits both land managers and researchers.     

Modelling the distribution of plant species using the autologistic regression model

For modeling the distribution of plant species in terms of climate covariates, we consider an autologistic regression model for spatial binary data on a regularly spaced lattice. This model belongs to the class of autologistic models introduced by Besag (1974). Three estimation methods, the coding method, maximum pseudolikelihood method and Markov chain Monte Carlo method are studied and comparedvia simulation and real data examples. As examples, we use the proposed methodology to model the distributions of two plant species in the state of Florida.