A pattern-oriented modelling approach to simulating populations of grey partridge

A number of wildlife species including the grey partridge (Perdix perdix) have shown dramatic post-war population declines. Multiple drivers have been proposed as reasons for the declines, for example agrochemical use and intensification of agricultural practices, climate, predation, and changes in landscape structure. These drivers may interact in non-linear ways and are inherently spatio-temporal in nature. Therefore models used to investigate mechanisms should be spatio-temporal, of proper scale, and have a high degree of biological realism. Here we describe the development and testing of an agent-based model (ABM) of grey partridge using a well documented pre-decline historical data set in conjunction with a pattern-oriented modelling (POM) approach. Model development was an iterative process of defining performance criteria, testing model behaviour, and reformulating as necessary to emulate system properties whilst ensuring that internal mechanisms were biologically realistic. The model was documented using ODdox, a new protocol for describing large agent-based models. Parameter fitting in the model was achieved to within ±2% accuracy for 15 out of 17 field data patterns used, and within 5% for the remaining two. Tests of interactions between input parameters showed that 62% of parameter pairs tested had significant interactions underlining the complex nature of the model structure. Sensitivity analysis identified chick mortality as being the most sensitive factor, followed by adult losses to hunting and adult overwinter mortality, agreeing in general with previous partridge models. However, the ABM used here could separate individual drivers, providing a better understanding of the underlying mechanisms behind population regulation, and allowing factors to be compared directly. The ABM used is rich in output signals allowing detailed testing and refinement of the model. This approach is particularly suited to systems such as the partridge system where data for comparison to model outputs is readily available. Despite the accurate fit between historical data and model output, making use of the predictive power of the approach the model requires further calibration and testing under modern field conditions.     

Strategic directions for agent-based modeling: avoiding the YAAWN syndrome

In this short communication, we examine how agent-based modeling has become common in land change science and is increasingly used to develop case studies for particular times and places. There is a danger that the research community is missing a prime opportunity to learn broader lessons from the use of agent-based modeling (ABM), or at the very least not sharing these lessons more widely. How do we find an appropriate balance between empirically rich, realistic models and simpler theoretically grounded models? What are appropriate and effective approaches to model evaluation in light of uncertainties not only in model parameters but also in model structure? How can we best explore hybrid model structures that enable us to better understand the dynamics of the systems under study, recognizing that no single approach is best suited to this task? Under what circumstances – in terms of model complexity, model evaluation, and model structure – can ABMs be used most effectively to lead to new insight for stakeholders? We explore these questions in the hope of helping the growing community of land change scientists using models in their research to move from ‘yet another model’ to doing better science with models.     

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.     

Proposing an information criterion for individual-based models developed in a pattern-oriented modelling framework

Individual-based models (IBMs) have been improved in quality and reliability in recent years with an approach called pattern-oriented modelling (POM). POM proposes guidelines to develop models reproducing multiple patterns observed on the field and to test systematically how well the IBMs reproduce them. POM studies used generally traditional methods of goodness of fit such as the sum of squares evaluation or ad hoc comparisons of fitting errors and variations. Model selection, however, can be a rigorous statistical approach based on information theory and information criteria such as the Akaike's information criterion (AIC) or the deviance information criterion (DIC). So far, it has not been tried to link POM to these rigorous techniques. The main problems to achieve that are: (a) the difficulty to have likelihood functions for IBMs’ parameters and (b) the possibility to obtain posterior distributions of IBMs’ parameters given the patterns to reproduce. In a first part, this paper answers problem (a) by proposing and explaining how to calculate a deviance measure (POMDEV) for models developed in a context of POM. And while answering the second problem, a second part of the paper proposes an information criterion for model selection in a POM context (the pattern-oriented modelling information criterion: POMIC). This criterion does not yet have the same theoretical foundation as, e.g., AIC, but uses formal analogies to the DIC. In a third part POMIC is tested with a modelling exercise. This exercise shows the potential of POMIC to use multiple patterns for selecting among multiple potential submodels and eventually select the most parsimonious and well fitting model version. We conclude that POMIC, although being a heuristically derived approach, can greatly improve the POM framework.     

The Sensitivity of Population Viability Analysis to Uncertainty about Habitat Requirements: Implications for the Management of the Endangered Southern Brown Bandicoot

Abstract:  Whenever population viability analysis (PVA) models are built to help guide decisions about the management of rare and threatened species, an important component of model building is the specification of a habitat model describing how a species is related to landscape or bioclimatic variables. Model-selection uncertainty may arise because there is often a great deal of ambiguity about which habitat model structure best approximates the true underlying biological processes. The standard approach to incorporate habitat models into PVA is to assume the best habitat model is correct, ignoring habitat-model uncertainty and alternative model structures that may lead to quantitatively different conclusions and management recommendations. Here we provide the first detailed examination of the influence of habitat-model uncertainty on the ranking of management scenarios from a PVA model. We evaluated and ranked 6 management scenarios for the endangered southern brown bandicoot ( Isoodon obesulus ) with PVA models, each derived from plausible competing habitat models developed with logistic regression. The ranking of management scenarios was sensitive to the choice of the habitat model used in PVA predictions. Our results demonstrate the need to incorporate methods into PVA that better account for model uncertainty and highlight the sensitivity of PVA to decisions made during model building. We recommend that researchers search for and consider a range of habitat models when undertaking model-based decision making and suggest that routine sensitivity analyses should be expanded to include an analysis of the impact of habitat-model uncertainty and assumptions.     

Stochastic growth reduces population fluctuations in Daphnia-algal systems

Deterministic, size-structured models are widely used to describe consumer-resource interactions. Such models typically ignore potentially large random variability in juvenile development rates. We present simple representations of this variability and show five approaches to calculating the model parameters for Daphnia pulex interacting with its algal food. Using our parameterized models of growth variability, we investigate the robustness of a recently proposed stabilizing mechanism for Daphnia populations. Growth rate variability increases the range of enrichments over which small-amplitude cycles or quasi-cycles occur, thus increasing the plausibility that the underlying mechanism contributes to the prevalence of small-amplitude cycles in the field and in experiments. More generally, our approach allows us to relate commonly available information on variance of development times to population stability.     

A Behaviorally Explicit Demographic Model Integrating Habitat Selection and Population Dynamics in California Sea Lions

Abstract: Although there has been a call for the integration of behavioral ecology and conservation biology, there are few tools currently available to achieve this integration. Explicitly including information about behavioral strategies in population viability analyses may enhance the ability of conservation biologists to understand and estimate patterns of extinction risk. Nevertheless, most behavioral‐based PVA approaches require detailed individual‐based data that are rarely available for imperiled species. We present a mechanistic approach that incorporates spatial and demographic consequences of behavioral strategies into population models used for conservation. We developed a stage‐structured matrix model that includes the costs and benefits of movement associated with 2 habitat‐selection strategies (philopatry and direct assessment). Using a life table for California sea lions (Zalophus californianus), we explored the sensitivity of model predictions to the inclusion of these behavioral parameters. Including behavioral information dramatically changed predicted population sizes, model dynamics, and the expected distribution of individuals among sites. Estimated population sizes projected in 100 years diverged up to 1 order of magnitude among scenarios that assumed different movement behavior. Scenarios also exhibited different model dynamics that ranged from stable equilibria to cycles or extinction. These results suggest that inclusion of behavioral data in viability models may improve estimates of extinction risk for imperiled species. Our approach provides a simple method for incorporating spatial and demographic consequences of behavioral strategies into population models and may be easily extended to other species and behaviors to understand the mechanisms of population dynamics for imperiled populations.     

Aphid population response to agricultural landscape change: A spatially explicit,individual-based model

A spatially explicit individual-based simulation model has been developed to represent aphid population dynamics in agricultural landscapes. The application of the model to Rhopalosiphum padi (L.) population dynamics is detailed, including an outline of the construction of the model, its parameterisation and validation. Over time, the aphids interact with the landscape and with one another. The landscape is modified by varying a simple pesticide regime, and the multi-scale spatial and temporal implications for a population of aphids is analysed. The results show that a spatial modelling approach that considers the effects on the individual of landscape properties and factors such as wind speed and wind direction provides novel insight into aphid population dynamics both spatially and temporally. This forms the basis for the development of further simulation models that can be used to analyse how changes in landscape structure impact upon important species distributions and population dynamics.     

Eliciting cognitive processes underlying patterns of human-wildlife interactions for agent-based modelling

Integrating humans in our perception of ecosystems is of critical importance to adequately protect natural resources. This poses the challenge of understanding human decision making in the context of decisions potentially threatening nature's integrity. We developed a spatially explicit agent-based model that simulates commercial whale-watching vessel movements based on a representation of the captains’ decision making process when observing marine mammals in and around the Saguenay-St. Lawrence Marine Park in Québec, Canada. We focus here on the human part of the global model, the submodel of whale movements having been developed and validated independently (Lamontagne, 2009). The objective of this study is to select and validate a model of whale-watching captains’ decision making using the pattern-oriented modelling approach (POM): three models of cognitive heuristics (satisficing, tallying and Take The Best) along with a null model (random choice) were tested. These concurrent decision making models were built upon knowledge extracted from data collected during field investigations, including interviews with whale-watching captains and park wardens, onboard and shore-based observations, and analyses of a multi-year dataset of sampled whale-watching excursions. Model selection is performed by statistically comparing simulated and real patterns of boat trajectories (excursion length), spatial hotspots (kernel home range 50%), and excursion content (species observed, time allocated to different activities). The selection process revealed that the Take The Best heuristic was the best performing model. We used the distribution of the number of whale-watching boats in the vicinity (2000 m) of each vessel as a secondary pattern to validate the ability of each decision making model to reproduce real observations. Given the prevalence of the species attribute in the choice of which whale to observe, the Take The Best heuristic's ability to deal with non-compensatory information partly explains its overall best performance. Moreover, implementation of communication abilities between modelled captains led to the emergence of persistent observation sites in the park, which is a well-known collective spatiotemporal characteristic of the whale-watching industry; thus validating the fundamental assumption that cooperation is an important mechanism behind the pattern of whale-watching boat dynamics. The relatively good performance of the satisficing and tallying heuristics supports both field evidence and literature on bounded rationality in that humans likely use collections of heuristics (adaptive toolbox) to solve decision problems in different contexts. The POM strategy appears suitable to build up an informative ABM regarding the management of human activities in a natural environment so that further developments will be assessed following the same approach.     

Simulation and analysis of outbreaks of bark beetle infestations and their management at the stand level

Outbreaks of bark beetles in forests can result in substantial economic losses. Understanding the factors that influence the development and spread of bark beetle outbreaks is crucial for forest management and for predicting outbreak risks, especially with the expected global warming. Although much research has been done on the ecology and phenology of bark beetles, the complex interplay between beetles, host trees, beetle antagonists and forest management makes predicting beetle population development especially difficult. Using the recent infestations of the European Spruce Bark Beetle (Ips typographus L. Col. Scol.) in the Bavarian Forest National Park (Germany) as a case study, we developed a spatially explicit agent-based simulation model (SAMBIA) that takes into account individual trees and beetles. This model primarily provides a tool for analysing and understanding the spatial and temporal aspects of bark beetles outbreaks at the stand scale. Furthermore, the model should allow an estimation of the effectiveness of concurrent impacts of both antagonists and management to confine outbreak dynamics in practice. We also used the model to predict outbreak probabilities in various settings. The simulation results indicated a distinct threshold behaviour of the system in response to pressure by antagonists or management of the bark beetle population. Despite the different scenarios considered, we were able to extract from the simulations a simple rule of thumb for the successful control of an outbreak: if roughly 80% of individual beetles are killed by antagonists or foresters, outbreaks will rarely take place. Our model allows the core dynamics of this complex system to be reduced to this inherent common denominator.     

Parallel agent-based modeling of spatial opinion diffusion accelerated using graphics processing units

In this article, we describe a parallel agent-based model of spatial opinion diffusion that is driven by graphics processing units (GPUs). Modeling opinion exchange and diffusion across landscapes often involves the simulation of large numbers of geographically located individual decision-makers and a massive number of individual-level interactions. This simulation requires substantial computational power. GPU-enabled computing resources provide a massively parallel processing platform based on a fine-grained shared memory paradigm. This massively parallel processing platform holds considerable promise for meeting the computing requirement of agent-based models of spatial problems. In this article, we focus on the parallelization of an agent-based spatial opinion model using GPU technologies. We discussed key algorithms designed for parallel agent-based opinion modeling: including domain decomposition and mutual exclusion. Experiments conducted to examine computing performance show that GPUs provide a computationally efficient alternative to traditional parallel computing architectures and substantially accelerate agent-based models of large-scale opinion exchange among individual decision makers.     

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.     

Modelling llama population development under environmental and market constraints in the Bolivian highlands

Changes in the size of animal populations over time are mainly determined by demographic and environmental factors. Livestock population dynamics are additionally influenced by harvesting decisions taken by herders. In Bolivia, not much is known about current llama husbandry and the main influencing factors determining population sizes. We collected data on demography, environmental factors and market values affecting the current and future llama population in three different regions in Bolivia. We generated a population model and assessed the future development of the llama population including environmental factors (rangeland carrying capacity, disturbance phenomena), herd structure and dynamics, and economic market demands. We calibrated and validated the llama model on the basis of 20-year data sets of the regions of Oruro, Potosi and La Paz, respectively. Model calibration by means of the Gauss-Marquardt-Levenberg algorithm yielded a model efficiency of 0.94. For model validation, however, the simulation slightly overestimated the observed llama population yielding model efficiencies of 0.91 and 0.87 for Potosi and La Paz, respectively. Model outcomes were most sensitive to death and birth rates of juveniles and death rate of females compared to environmental or other demographic factors. Population trajectories approached an overall carrying capacity for Oruro, Potosi and La Paz of 8.8 × 10⁵, 9.1 × 10⁵, and 9.0 × 10⁵ llama individuals after 100 years of simulation. Hence, detailed monitoring of demographic, environmental, and economic factors can improve predictions of llama population development over time. Further management should focus on improving birth rates and lowering female mortality through providing supplemental food and shelters against the harsh environmental conditions of the Andean highlands.     

A case study of bats and white‐nose syndrome demonstrating how to model population viability with evolutionary effects

Ecological factors generally affect population viability on rapid time scales. Traditional population viability analyses (PVA) therefore focus on alleviating ecological pressures, discounting potential evolutionary impacts on individual phenotypes. Recent studies of evolutionary rescue (ER) focus on cases in which severe, environmentally induced population bottlenecks trigger a rapid evolutionary response that can potentially reverse demographic threats. ER models have focused on shifting genetics and resulting population recovery, but no one has explored how to incorporate those findings into PVA. We integrated ER into PVA to identify the critical decision interval for evolutionary rescue (DIER) under which targeted conservation action should be applied to buffer populations undergoing ER against extinction from stochastic events and to determine the most appropriate vital rate to target to promote population recovery. We applied this model to little brown bats (Myotis lucifugus) affected by white‐nose syndrome (WNS), a fungal disease causing massive declines in several North American bat populations. Under the ER scenario, the model predicted that the DIER period for little brown bats was within 11 years of initial WNS emergence, after which they stabilized at a positive growth rate (λ = 1.05). By comparing our model results with population trajectories of multiple infected hibernacula across the WNS range, we concluded that ER is a potential explanation of observed little brown bat population trajectories across multiple hibernacula within the affected range. Our approach provides a tool that can be used by all managers to provide testable hypotheses regarding the occurrence of ER in declining populations, suggest empirical studies to better parameterize the population genetics and conservation‐relevant vital rates, and identify the DIER period during which management strategies will be most effective for species conservation.     

Evaluating mortality rates with a novel integrated framework for nonmonogamous species

The conservation of wildlife requires management based on quantitative evidence, and especially for large carnivores, unraveling cause‐specific mortalities and understanding their impact on population dynamics is crucial. Acquiring this knowledge is challenging because it is difficult to obtain robust long‐term data sets on endangered populations and, usually, data are collected through diverse sampling strategies. Integrated population models (IPMs) offer a way to integrate data generated through different processes. However, IPMs are female‐based models that cannot account for mate availability, and this feature limits their applicability to monogamous species only. We extended classical IPMs to a two‐sex framework that allows investigation of population dynamics and quantification of cause‐specific mortality rates in nonmonogamous species. We illustrated our approach by simultaneously modeling different types of data from a reintroduced, unhunted brown bear (Ursus arctos) population living in an area with a dense human population. In a population mainly driven by adult survival, we estimated that on average 11% of cubs and 61% of adults died from human‐related causes. Although the population is currently not at risk, adult survival and thus population dynamics are driven by anthropogenic mortality. Given the recent increase of human‐bear conflicts in the area, removal of individuals for management purposes and through poaching may increase, reversing the positive population growth rate. Our approach can be generalized to other species affected by cause‐specific mortality and will be useful to inform conservation decisions for other nonmonogamous species, such as most large carnivores, for which data are scarce and diverse and thus data integration is highly desirable.     

Projecting population trends of endangered amphibian species in the face of uncertainty: A pattern-oriented approach

Amphibian populations have been declining worldwide for the last three decades. Determining the risk of extinction is one of the major goals of amphibian conservation, yet few quantitative models have been developed for amphibian populations. Like most rare or threatened populations, there is a paucity of life history data available for most amphibian populations. Data on the critical juvenile life stage are particularly lacking. Pattern oriented modeling (POM) has been used successfully to estimate life history parameters indirectly when critical data lacking, but has not been applied to amphibian populations. We describe a spatially explicit, individual-based, stochastic simulation model developed to project population dynamics of pond-breeding amphibian populations. We parameterized the model with life history and habitat data collected for the endangered Houston toad (Bufohoustonensis), a species for which there is a high degree of uncertainty for juvenile and adult male survival. During model evaluation, we focused on explicitly reducing this uncertainty, evaluating 16 different versions of the model that represented the range of parametric uncertainty for juvenile and adult male survival. Following POM protocol, we compared simulation results to four population-level patterns observed in the field: population size, adult sex ratio, proportion of toads returning to their natal pond, and mean maximum distance moved. Based on these comparisons, we rejected 11 of the 16 model versions. Results of the remaining versions confirmed that population persistence depends heavily on juvenile survival, and further suggested that probability of juvenile survival is likely between 0.0075 and 0.015 (previous estimates ranged from 0.003 to 0.02), and that annual male survival is near 0.15 (previous estimates ranged up to 0.43).     

Enchytraeid population dynamics: Resource limitation and size-dependent mortality

Enchytraeids are regarded as keystone soil organisms in forest ecosystems. Their abundance and biomass fluctuate widely. Predicting the consequences of anthropogenic disturbances requires an understanding of the mechanisms underlying enchytraeid population dynamics. Here I develop a simple model, which predicts that the type of dynamics is controlled by resource input rate. If fungal resource input is a discrete event once a year, an exponential growth phase is followed by starvation and sharp decline of enchytraeid abundance. Model simulations with three different forcing functions were compared to field data. Initial parameter values were obtained from various independent sources, and parameters were estimated by minimizing the residual sum of squares. The best fitting model with resource addition once a year explained 39% of the variation in enchytraeid biomass over an 8-year study period. Further, variation in rainfall explained 59% of the variation in R² of the exponential phase models, which is also an index of the stability of population size-structure. The results emphasize the importance of resource limitation for enchytraeid population dynamics and support the hypothesis that the mortality during the decline phase is size-dependent.     

Impact of minimum winter temperatures on the population dynamics of Dendroctonus frontalis.

Predicting population dynamics is a fundamental problem in applied ecology. Temperature is a potential driver of short-term population dynamics, and temperature data are widely available, but we generally lack validated models to predict dynamics based upon temperatures. A generalized approach involves estimating the temperatures experienced by a population, characterizing the demographic consequences of physiological responses to temperature, and testing for predicted effects on abundance. We employed this approach to test whether minimum winter temperatures are a meaningful driver of pestilence from Dendroctonus frontalis (the southern pine beetle) across the southeastern United States. A distance-weighted interpolation model provided good, spatially explicit, predictions of minimum winter air temperatures (a putative driver of beetle survival). A Newtonian heat transfer model with empirical cooling constants indicated that beetles within host trees are buffered from the lowest air temperatures by approximately 1-4 degrees C (depending on tree diameter and duration of cold bout). The life stage structure of beetles in the most northerly outbreak in recent times (New Jersey) were dominated by prepupae, which were more cold tolerant (by >3 degrees C) than other life stages. Analyses of beetle abundance data from 1987 to 2005 showed that minimum winter air temperature only explained 1.5% of the variance in interannual growth rates of beetle populations, indicating that it is but a weak driver of population dynamics in the southeastern United States as a whole. However, average population growth rate matched theoretical predictions of a process-based model of winter mortality from low temperatures; apparently our knowledge of population effects from winter temperatures is satisfactory, and may help to predict dynamics of northern populations, even while adding little to population predictions in southern forests. Recent episodes of D. frontalis outbreaks in northern forests may have been allowed by a warming trend from 1960 to 2004 of 3.3 degrees C in minimum winter air temperatures in the southeastern United States. Studies that combine climatic analyses, physiological experiments, and spatially replicated time series of population abundance can improve population predictions, contribute to a synthesis of population and physiological ecology, and aid in assessing the ecological consequences of climatic trends.