Metapopulation dynamics of a perennial plant, Succisa pratensis, in an agricultural landscape

Most metapopulation models neglect the local dynamics, and systems characterized by slow population turnover, time lags and non-equilibrium, are only rarely examined within a metapopulation context. In this study we used a realistic, spatially explicit, dynamic metapopulation model of a long-lived grassland plant, Succisa pratensis, to examine the relative importance of local population dynamics, and short and long-distance dispersal of seeds.     

The Application of Neutral Landscape Models in Conservation Biology

Neutral landscape models, derived from percolation theory in the field of landscape ecology, are grid-based maps in which complex habitat distributions are generated by random or fractal algorithms. This grid-based representation of landscape structure is compatible with the raster-based format of geographical information systems (GIS), which facilitates comparisons between theoretical and real landscapes. Neutral landscape models permit the identification of critical thresholds in connectivity, which can be used to predict when landscapes will become fragmented. The coupling of neutral landscape models with generalized population models, such as metapopulation theory, provides a null model for generating predictions about population dynamics in fragmented landscapes. Neutral landscape models can contribute to the following applications in conservation: (1) incorporation of complex spatial patterns in (meta)population models; (2) identification of species' perceptions of landscape structure; (3) determination of landscape connectivity; (4) evaluation of the consequences of habitat fragmentation for population subdivision; (5) identification of the domain of metapopulation dynamics; (6) prediction of the occurrence of extinction thresholds; ( 7) determination of the genetic consequences of habitat fragmentation; and (8) reserve design and ecosystem management. This generalized, spatially explicit framework bridges the gap between spatially implicit, patch-based models and spatially realistic GIS applications which are usually parameterized for a single species in a specific landscape. Development of a generalized, spatially explicit framework is essential in conservation biology because we will not be able to develop individual models for every species of management concern.     

Unveiling human-assisted dispersal mechanisms in invasive alien insects: Integration of spatial stochastic simulation and phenology models

Capturing the spread of biological invasions in heterogeneous landscapes is a complex modelling task where information on both dispersal and population dynamics needs to be integrated. Spatial stochastic simulation and phenology models have rarely been combined to assist in the study of human-assisted long-distance dispersal events.Here we develop a process-based spatially explicit landscape-extent simulation model that considers the spread and detection of invasive insects. Natural and human-assisted dispersal mechanisms are modelled with an individual-based approach using negative exponential and negative power law dispersal kernels and gravity models. The model incorporates a phenology sub-model that uses daily temperature grids for the prediction and timing of the population dynamics in each habitat patch. The model was applied to the study of the invasion by the important maize pest western corn rootworm (WCR) Diabrotica virgifera ssp. virgifera in Europe. We parameterized and validated the model using maximum likelihood and simulation methods from the historical invasion of WCR in Austria.WCR was found to follow stratified dispersal where international transport networks in the Danube basin played a key role in the occurrence of long-distance dispersal events. Detection measures were found to be effective and altitude had a significant effect on limiting the spread of WCR. Spatial stochastic simulation combined with phenology models, maximum likelihood methods and predicted versus observed regression showed a high degree of flexibility that captured the salient features of WCR spread in Austria. This modelling approach is useful because it allows to fully exploit and the often limited and heterogeneous information available regarding the population dynamics and dispersal of alien invasive insects.     

Recruitment and attrition of associated plants under a shading crop canopy: Model selection and calibration

Associated plant and animal diversity provides ecosystem services within crop production systems. The importance of the maintenance or restoration of diversity is therefore increasingly acknowledged. Here we study the population dynamics of associated annual plants (‘weeds’) during the growth of a crop in a season and introduce a minimal model to characterize the recruitment and attrition of the associated plants under the influence of shading by the crop. A mechanistically based, logistic, light interception model was parameterized with light interception measurements in two single crops (barley and rye) and in mixtures of these cereals with peas. Population dynamics data were collected for the annuals Papaver rhoeas, Centaurea cyanus, Chrysanthemum segetum, and Misopates orontium. A minimal population dynamics model was identified for each annual plant species, using system identification techniques as model selection and calibration.     

Field-scale roles of density, temperature, nitrogen, and predation on aphid population dynamics

Robust analyses of noisy, stage-structured, irregularly spaced, field-scale data incorporating multiple sources of variability and nonlinear dynamics remain very limited, hindering understanding of how small-scale studies relate to large-scale population dynamics. We used a novel, complementary Bayesian and frequentist state-space model analysis to ask how density, temperature, plant nitrogen, and predators affect cotton aphid (Aphis gossypii) population dynamics in weekly data from 18 field-years and whether estimated effects are consistent with small-scale studies. We found clear roles of density and temperature but not of plant nitrogen or predators, for which Bayesian and frequentist evidence differed. However, overall predictability of field-scale dynamics remained low. This study demonstrates stage-structured state-space model analysis incorporating bottom-up, top-down, and density-dependent effects for within-season (nearly continuous time), nonlinear population dynamics. The analysis combines Bayesian posterior evidence with maximum-likelihood estimation and frequentist hypothesis testing using average one-step-ahead residuals.     

Structure of the social network and its influence on transmission dynamics in a honeybee colony

Infectious processes in a social group are driven by a network of contacts that is generally structured by the organization arising from behavioral and spatial heterogeneities within the group. Although theoretical models of transmission dynamics have placed an overwhelming emphasis on the importance of understanding the network structure in a social group, empirical data regarding such contact structures are rare. In this paper, I analyze the network structure and the correlated transmission dynamics within a honeybee colony as determined by food transfer interactions and the changes produced in it by an experimental manipulation. The study demonstrates that widespread transmission in the colony is correlated to a lower clustering coefficient and higher robustness of the social network. I also show that the social network in the colony is determined by the spatial distribution of various age classes, and the resulting organizational structure provides some amount of immunity to the young individuals. The results of this study demonstrates how, using the honeybee colony as a model system, concepts in network theory can be combined with those in behavioral ecology to gain a better understanding of social transmission processes, especially those related to disease dynamics.     

Nonlinear relationships between vital rates and state variables in demographic models

To accurately estimate population dynamics and viability, structured population models account for among-individual differences in demographic parameters that are related to individual state. In the widely used matrix models, such differences are incorporated in terms of discrete state categories, whereas integral projection models (IPMs) use continuous state variables to avoid artificial classes. In IPMs, and sometimes also in matrix models, parameterization is based on regressions that do not always model nonlinear relationships between demographic parameters and state variables. We stress the importance of testing for nonlinearity and propose using restricted cubic splines in order to allow for a wide variety of relationships in regressions and demographic models. For the plant Borderea pyrenaica, we found that vital rate relationships with size and age were nonlinear and that the parameterization method had large effects on predicted population growth rates, X (linear IPM, 0.95; nonlinear IPMs, 1.00; matrix model, 0.96). Our results suggest that restricted cubic spline models are more reliable than linear or polynomial models. Because even weak nonlinearity in relationships between vital rates and state variables can have large effects on model predictions, we suggest that restricted cubic regression splines should be considered for parameterizing models of population dynamics whenever linearity cannot be assumed.     

A spatial-temporal optimization approach to watershed management: Acid mine drainage treatment in the Cheat River watershed, WV, USA

Most water management studies concentrate on the inter-temporal allocation problem or, more recently, spatial dynamics - but not both. While early spatial-temporal studies focused on the allocation of water quantity, this paper presents an approach to water quality analysis that incorporates both spatial and temporal dynamics in a watershed framework. The acid mine drainage (AMD) problem in the Cheat River watershed of West Virginia, USA, serves as a case study and provides an opportunity to test the modeling approach developed. The empirical models are written in General Algebraic Modeling System (GAMS) and solved using the CPLEX mixed integer programming package. The results suggest that available investments should be concentrated in heavily impaired stream segments. The model can be used to assess the economic implications of alternative watershed Total Maximum Daily Load (TMDL) implementation or other management strategies.     

Potentials and limitations of using large-scale forest inventory data for evaluating forest succession models

Forest gap models have been applied widely to examine forest development under natural conditions and to investigate the effect of climate change on forest succession. Due to the complexity and parameter requirements of such models a rigorous evaluation is required to build confidence in the simulation results. However, appropriate data for model assessment are scarce at the large spatial and temporal scales of successional dynamics. In this study, we explore a data source for the evaluation of forest gap models that has been used only little in the past, i.e., large-scale National Forest Inventory data. The key objectives of this study were (a) to examine the potentials and limitations of using large-scale forest inventory data for evaluating the performance of forest gap models and (b) to test two particular models as case studies to derive recommendations for their future improvement.     

A Bayesian state-space formulation of dynamic occupancy models

Species occurrence and its dynamic components, extinction and colonization probabilities, are focal quantities in biogeography and metapopulation biology, and for species conservation assessments. It has been increasingly appreciated that these parameters must be estimated separately from detection probability to avoid the biases induced by non-detection error. Hence, there is now considerable theoretical and practical interest in dynamic occupancy models that contain explicit representations of metapopulation dynamics such as extinction, colonization, and turnover as well as growth rates. We describe a hierarchical parameterization of these models that is analogous to the state-space formulation of models in time series, where the model is represented by two components, one for the partially observable occupancy process and another for the observations conditional on that process. This parameterization naturally allows estimation of all parameters of the conventional approach to occupancy models, but in addition, yields great flexibility and extensibility, e.g., to modeling heterogeneity or latent structure in model parameters. We also highlight the important distinction between population and finite sample inference; the latter yields much more precise estimates for the particular sample at hand. Finite sample estimates can easily be obtained using the state-space representation of the model but are difficult to obtain under the conventional approach of likelihood-based estimation. We use R and WinBUGS to apply the model to two examples. In a standard analysis for the European Crossbill in a large Swiss monitoring program, we fit a model with year-specific parameters. Estimates of the dynamic parameters varied greatly among years, highlighting the irruptive population dynamics of that species. In the second example, we analyze route occupancy of Cerulean Warblers in the North American Breeding Bird Survey (BBS) using a model allowing for site-specific heterogeneity in model parameters. The results indicate relatively low turnover and a stable distribution of Cerulean Warblers which is in contrast to analyses of counts of individuals from the same survey that indicate important declines. This discrepancy illustrates the inertia in occupancy relative to actual abundance. Furthermore, the model reveals a declining patch survival probability, and increasing turnover, toward the edge of the range of the species, which is consistent with metapopulation perspectives on the genesis of range edges. Given detection/non-detection data, dynamic occupancy models as described here have considerable potential for the study of distributions and range dynamics.     

Spatial and temporal hydrodynamic and water quality modeling analysis of a large reservoir on the South Carolina (USA) coastal plain

Two-dimensional, 31-segment, 61-channel hydrodynamic and water quality models of Lake Marion (surface area 330.7 km²; volume 1548.3×10⁶ m³) were developed using the WASP5 modeling system. Field data from 1985 to 1990 were used to parameterize the models. Phytoplankton kinetic rates and constants were obtained from a related in situ study; others from modeling literature. The hydrodynamic model was calibrated to estimates of daily lake volume; the water quality model was calibrated for ammonia, nitrate, ortho-phosphate, dissolved oxygen, chlorophyll-a, biochemical oxygen demand, organic nitrogen, and organic phosphorus. Water quality calibration suggested the model characterized phytoplankton and nutrient dynamics quite well. The model was validated (Kolmogorov–Smirnov two-sample goodness-of-fit test at P<0.05) by reparameterizing the nutrient loading functions using an independent set of field data. The models identified several factors that may contribute to the spatial variability previously reported from other research in the reservoir, despite the superficial absence of complex structure. Sensitivity analysis of the phytoplankton kinetic rates suggest that study site-specific estimates were important for obtaining model fit to field data. Sediment sources of ammonia (10–60 mg m⁻² day⁻¹) and phosphate (1–6 mg m⁻² day⁻¹) were important to achieve model calibration, especially during periods of high temperatures and low dissolved oxygen. This sediment flux accounted for 78% (nitrogen) and 50% (phosphorus) of the annual load. Spatial and temporal variability in the lake, reflected in the calibrated and validated models, suggest that ecological factors that influence phytoplankton productivity and nutrient dynamics are different in various parts of the lake. The WASP5 model as implemented here does not fully accommodate the ecological variability in Lake Marion due to model constraints on the specification of rate constants. This level of spatial detail may not be appropriate for an operational reservoir model, but as a research tool the models are both versatile and useful.     

Within-tree life process models of the southern pine beetle, dendroctonus frontalis

This paper develops models of gallery construction, emergence and re-emergence for use in a general population dynamics model of the southern pine beetle, Dendroctonuc frontalis Zimmermann. Models of these processes were originally developed from laboratory data, and are extended here to account for fluctuating temperatures and variable attack densities under field conditions. The resulting models were tested using data from three natural populations (infestations) from east Texas. These tests reveal that the laboratory-derived models closely predict the timing and length of gallery, and the timing of emergence and re-emergence in the field.     

Parameterizing,evaluating and comparing metapopulation models with data from individual-based simulations

Due to the lack of sufficient data and appropriate ecological information parameterizing predictive population dynamical models usually is a difficult task. The approach proposed in this study is meant to overcome this problem by using detailed individual-based simulations to generate artificial data. With short-term data samples, the models to be investigated can be parameterized and their predictions be compared. The flexibility of individual-based simulations as experimental tools also facilitates the evaluation and comparison of different (aggregated) model types. The presented approach is a step towards unifying models of different complexity. As an example we applied it to two metapopulation models of insect species in a highly fragmented landscape: the well-known incidence function model with a patch-based representation of space and a grid-based analogue. The models are tested with respect to their data requirement and recommendations for a better data sampling are derived.     

Static modeling of dynamic recreation behavior: Implications for prediction and welfare estimation

This paper examines the consequences of using a static model of recreation trip-taking behavior when the underlying decision problem is dynamic. Specifically we examine the implications for trip forecasting and welfare estimation using a panel dataset of Lake Michigan salmon anglers for the 1996 and 1997 fishing seasons. We derive and estimate both a structural dynamic model using Bellman's equation, and a reduced-form static model with trip probability expressions mimicking those of the dynamic model. We illustrate an inherent identification problem in the reduced-form model that creates biased welfare estimates, and we discuss the general implications of this for the interpretation of preference parameters in static models. We then use both models to simulate trip taking behavior and show that although their in-sample trip forecasts are similar, their welfare estimates and out-of-sample forecasts are quite different.     

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.     

Linking species- and ecosystem-level impacts of climate change in lakes with a complex and a minimal model

To study the interaction between species- and ecosystem-level impacts of climate change, we focus on the question of how climate-induced shifts in key species affect the positive feedback loops that lock shallow lakes either in a transparent, macrophyte-dominated state or, alternatively, in a turbid, phytoplankton-dominated state. We hypothesize that climate warming will weaken the resilience of the macrophyte-dominated clear state. For the turbid state, we hypothesize that climate warming and climate-induced eutrophication will increase the dominance of cyanobacteria. Climate change will also affect shallow lakes through a changing hydrology and through climate change-induced eutrophication. We study these phenomena using two models, the full ecosystem model PCLake and a minimal dynamic model of lake phosphorus dynamics. Quantitative predictions with the complex model show that changes in nutrient loading, hydraulic loading and climate warming can all lead to shifts in ecosystem state. The minimal model helped in interpreting the non-linear behaviour of the complex model. The main output parameters of interest for water quality managers are the critical nutrient loading at which the system will switch from clear to turbid and the much lower critical nutrient loading – due to hysteresis – at which the system switches back. Another important output parameter is the chlorophyll-a level in the turbid state. For each of these three output parameters we performed a sensitivity analysis to further understand the dynamics of the complex model PCLake. This analysis showed that our model results are most sensitive to changes in temperature-dependence of cyanobacteria, planktivorous fish and zooplankton. We argue that by combining models at various levels of complexity and looking at multiple aspects of climate changes simultaneously we can develop an integrated view of the potential impact of climate change on freshwater ecosystems.