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.     

Model selection criteria for overdispersed data and their application to the characterization of a host-parasite relationship

In the statistical modeling of a biological or ecological phenomenon, selecting an optimal model among a collection of candidates is a critical issue. To identify an optimal candidate model, a number of model selection criteria have been developed and investigated based on estimating Kullback’s (Information theory and statistics. Dover, Mineola, 1968) directed or symmetric divergence. Criteria that target the directed divergence include the Akaike (2nd international symposium on information theory. Akadémia Kiadó, Budapest, Hungary, pp 267–281, 1973, IEEE Trans Autom Control AC 19:716–723, 1974) information criterion, AIC, and the “corrected” Akaike information criterion (Hurvich and Tsai in Biometrika 76:297–307, 1989), AICc; criteria that target the symmetric divergence include the Kullback information criterion, KIC, and the “corrected” Kullback information criterion, KICc (Cavanaugh in Stat Probab Lett 42:333–343, 1999; Aust N Z J Stat 46:257–274, 2004). For overdispersed count data, simple modifications of AIC and AICc have been increasingly utilized: specifically, the quasi Akaike information criterion, QAIC, and its corrected version, QAICc (Lebreton et al. in Ecol Monogr 62(1):67–118 1992). In this paper, we propose analogues of QAIC and QAICc based on estimating the symmetric as opposed to the directed divergence: QKIC and QKICc. We evaluate the selection performance of AIC, AICc, QAIC, QAICc, KIC, KICc, QKIC, and QKICc in a simulation study, and illustrate their practical utility in an ecological application. In our application, we use the criteria to formulate statistical models of the tick (Dermacentor variabilis) load on a white-footed mouse (Peromyscus leucopus) in northern Missouri.     

Design of a Domain Specific Language for modelling processes in landscapes

The modelling of processes that occur in landscapes is often confronted to issues related to the representation of space and the difficulty of properly handling time and multiple scales. In order to investigate these issues, a flexible modelling environment is required. We propose to develop such a tool based on a Domain Specific Language (DSL) that capitalises on the service-oriented architecture (SOA) paradigm. The modelling framework around the DSL is composed of a model building environment, a code generator and compiler, and a program execution platform. The DSL introduces five language elements (entity, service, relation, scenario and datafacer) that can be combined to offer a wide range of possibilities for modelling in space and time at different scales. When developing a model, model parts are either built using the DSL or taken from libraries of previously built ones, and adapted to the specific model. The practical usage of the DSL is illustrated first with the Lotka–Volterra model, and then with a landscape modelling experiment on the spread of a mosquito-borne disease in the Sahelian region of West Africa. An interesting characteristic of this approach is the possibility of adding new elements into an existing model, and replacing others with more appropriate ones, thus allowing potentially complex models to be built from simpler parts.     

A new hypothesis concerning the nature of small pelagic fish clusters: An individual-based modelling study of Sardinella aurita dynamics off West Africa

Coastal populations of small pelagic fish display nested aggregation levels. Above the level of the school structure, clusters are observed the nature of which has not been definitively determined. We hypothesized that these clusters corresponded to a materialisation of the microcohorts originating from successive spawnings of fish populations in their vital domain.A candidate individual-based model was developed to investigate this hypothesis. This model is based on pattern-oriented modelling of a concrete documented case: the dynamics of the round sardinella (Sardinella aurita) population living off the West African coasts and subject to environmental fluctuations caused by seasonal upwelling. The simulated agents were round sardinella microcohorts situated and moving in a discretised physical environment. The combined effects of environmental forcing (temperature, wind, retention) and inner biological dynamics (reproduction, growth and mortality, competition) condition the dynamics of this population.The modelled behaviour generated realistic dynamic patterns (population distribution, spawning zones, periods and plasticity, biomass fluctuations), which were obtained simultaneously and successfully compared with observations. The steady-state number of microcohorts obtained after simulation convergence was similar to the number of clusters observed in situ in this area for this population.The realism and diversity of the patterns simultaneously simulated suggested the cluster-microcohort equivalence hypothesis as a candidate framework accounting for the origin of the clusters observed in situ. Within this preliminary exploration, we discuss the consistency of the hypothesis and the accuracy of the model. If the correspondence between clusters and microcohorts proves to be real, it may be transient and progressively modified by other environmental factors. If stable over time, as simulated in the model, the number of observed clusters should be related to the number of spawning events in the species’ lifetime.     

Application of an evolutionary algorithm to the inverse parameter estimation of an individual-based model

Inverse parameter estimation of individual-based models (IBMs) is a research area which is still in its infancy, in a context where conventional statistical methods are not well suited to confront this type of models with data. In this paper, we propose an original evolutionary algorithm which is designed for the calibration of complex IBMs, i.e. characterized by high stochasticity, parameter uncertainty and numerous non-linear interactions between parameters and model output. Our algorithm corresponds to a variant of the population-based incremental learning (PBIL) genetic algorithm, with a specific “optimal individual” operator. The method is presented in detail and applied to the individual-based model OSMOSE. The performance of the algorithm is evaluated and estimated parameters are compared with an independent manual calibration. The results show that automated and convergent methods for inverse parameter estimation are a significant improvement to existing ad hoc methods for the calibration of IBMs.     

Allowing macroalgae growth forms to emerge: Use of an agent-based model to understand the growth and spread of macroalgae in Florida coral reefs,with emphasis on Halimeda tuna

The growth patterns of macroalgae in three-dimensional space can provide important information regarding the environments in which they live, and insights into changes that may occur when those environments change due to anthropogenic and/or natural causes. To decipher these patterns and their attendant mechanisms and influencing factors, a spatially explicit model has been developed. The model SPREAD (SPatially-explicit Reef Algae Dynamics), which incorporates the key morphogenetic characteristics of clonality and morphological plasticity, is used to investigate the influences of light, temperature, nutrients and disturbance on the growth and spatial occupancy of dominant macroalgae in the Florida Reef Tract. The model species, Halimeda and Dictyota spp., are modular organisms, with an “individual” being made up of repeating structures. These species can also propagate asexually through clonal fragmentation. These traits lead to potentially indefinite growth and plastic morphology that can respond to environmental conditions in various ways. The growth of an individual is modeled as the iteration of discrete macroalgal modules whose dynamics are affected by the light, temperature, and nutrient regimes. Fragmentation is included as a source of asexual reproduction and/or mortality. Model outputs are the same metrics that are obtained in the field, thus allowing for easy comparison. The performance of SPREAD was tested through sensitivity analysis and comparison with independent field data from four study sites in the Florida Reef Tract. Halimeda tuna was selected for initial model comparisons because the relatively untangled growth form permits detailed characterization in the field. Differences in the growth patterns of H. tuna were observed among these reefs. SPREAD was able to closely reproduce these variations, and indicate the potential importance of light and nutrient variations in producing these patterns.     

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.     

A model of deforestation by human population interactions

A differential equation was employed in modelling deforestation by human population interactions to yield an explicit mathematical model. The theoretical relation and many possible models were applied to the grid cell data in Hiroshima Prefecture, and relative appropriateness of each model was evaluated by Akaike's information criterion (AIC) using raw data. Intensive further verification was executed bythe bootstrap method. It was demonstrated that the theoretical relation was in the best agreement among many other models in comparison.     

A capture-recapture model with heterogeneity and behavioural response

We develop the non-parametric maximum likelihood estimator (MLE) of the full M_bh capture-recapture model which utilizes both initial capture and recapture data and permits both heterogeneity (h) between animals and behavioural (b) response to capture. Our MLE procedure utilizes non-parametric maximum likelihood estimation of mixture distributions (Lindsay, 1983; Lindsay and Roeder, 1992) and the EM algorithm (Dempsteret al., 1977). Our MLE estimate provides the first non-parametric estimate of the bivariate capture-recapture distribution.Since non-parametric maximum likelihood estimation exists for submodels M_h (allowing heterogeneity only), Mb (allowing behavioural response only) and M₀ (allowing no changes), we develop maximum likelihood-based model selection, specifically the Akaike information criterion (AIC) (Akaike, 1973). The AIC procedure does well in detecting behavioural response but has difficulty in detecting heterogeneity.     

A brief guide to model selection,multimodel inference and model averaging in behavioural ecology using Akaike’s information criterion

Akaike’s information criterion (AIC) is increasingly being used in analyses in the field of ecology. This measure allows one to compare and rank multiple competing models and to estimate which of them best approximates the “true” process underlying the biological phenomenon under study. Behavioural ecologists have been slow to adopt this statistical tool, perhaps because of unfounded fears regarding the complexity of the technique. Here, we provide, using recent examples from the behavioural ecology literature, a simple introductory guide to AIC: what it is, how and when to apply it and what it achieves. We discuss multimodel inference using AIC—a procedure which should be used where no one model is strongly supported. Finally, we highlight a few of the pitfalls and problems that can be encountered by novice practitioners.     

Establishment patterns in a secondary tree line ecotone

On semi-open pre-alpine fen pastures Alder encroachment creates a dynamic mosaic of grassland and woodland, which is rich in ecotones from fen to Carr. The structural diversity in colonisation patterns of Alder on fens suggests a dependency on multiple environmental drivers. Unidirectional progressive ecotone development provides an opportunity to address a current deficit in understanding successional patterns, i.e. process-pattern relationships in a multiple factor regime.We developed an individual-based model of Alder establishment on fen grassland to investigate the dependency of encroachment patterns upon seed production, dispersal distances and safe site availability. The purpose of the model is to provide a causal understanding of establishment patterns of Alder. In the model, all life processes of Alder individuals were parameterised with field data. This allowed us to strictly perform bottom-up simulations and successfully check plausibility by comparing simulated establishment patterns of cohorts with observed ecotone structures.Simulation results show that establishment patterns strongly depend on environmental drivers. Spatial progression of Alder encroachment and width of ecotones, respectively, mainly depend on wind speed during seed dispersal. Dense establishment of Alder leading to community change from fen grassland to Carr, requires windows of opportunity, which are defined by the rare coincidence of widespread dispersal, high seed production and favorable establishment conditions. Life-history traits of Alder (mast year cycle, high seed weight, weak establishment in fen) spatially and temporarily constrain the encroachment process. The structural diversity of long-term encroachment patterns is explained by the event-driven character of encroachment.Modelling individual establishment pathways of seedlings starting from germination revealed an endogenous stochasticity in establishment patterns emerging from low seed densities in the tail of the dispersal function. We conclude an inherent stochastic structure of dispersal-limited tree line ecotones, which limits reconstruction of processes from patterns.In order to describe long-term successional patterns of Alder encroachment at landscape scale, we propose the combination of two concepts: deterministic “patch-movement” of Alder woodland driven by continuous ecotone migration together with rare and stochastic “infiltration” of single Alder trees into open fen grasslands. Conservation management can control predictable “patch-movement” by cutting off maturing saplings around existing Alder woods. But the preservation of the actual large proportion of open grassland in fen pastures from infiltrating Alder seedlings and from the subsequent shift of the pasture to a densely wooded state would require mowing additionally to extensive grazing.     

Model weights and the foundations of multimodel inference

Statistical thinking in wildlife biology and ecology has been profoundly influenced by the introduction of AIC (Akaike's information criterion) as a tool for model selection and as a basis for model averaging. In this paper, we advocate the Bayesian paradigm as a broader framework for multimodel inference, one in which model averaging and model selection are naturally linked, and in which the performance of AIC-based tools is naturally evaluated. Prior model weights implicitly associated with the use of AIC are seen to highly favor complex models: in some cases, all but the most highly parameterized models in the model set are virtually ignored a priori. We suggest the usefulness of the weighted BIC (Bayesian information criterion) as a computationally simple alternative to AIC, based on explicit selection of prior model probabilities rather than acceptance of default priors associated with AIC. We note, however, that both procedures are only approximate to the use of exact Bayes factors. We discuss and illustrate technical difficulties associated with Bayes factors, and suggest approaches to avoiding these difficulties in the context of model selection for a logistic regression. Our example highlights the predisposition of AIC weighting to favor complex models and suggests a need for caution in using the BIC for computing approximate posterior model weights.     

Diameter growth models for mixed-species stands of Coastal British Columbia including thinning and fertilization effects

In this study, diameter growth models for three species growing in mixed-stands of Coastal British Columbia (BC), Canada, under a variety of silvicultural treatments were developed. The three species were: Douglas-fir (Pseudotsuga menziesii var. menziesii (Mirb.) Franco), western hemlock (Tsuga heterophylla (Raf.) Sarg.), and western redcedar (Thuja plicata Donn). A Box and Lucas model (1959) was initially fitted to the diameter growth series for each tree, as this model is very flexible and was based on processes reflective of the metabolic processes governing tree growth. Next, a random coefficients modelling approach (i.e., parameter prediction approach) was used to modify the estimated parameters for each species using functions of tree size and stage of development, site productivity, and inter-tree competition variables, while accounting for temporal correlation within trees. Impacts of fertilization on diameter growth were estimated by including the time since fertilization as an additional variable. Since state variables that are changed as a result of thinning were already in the model, accurate results post-thinning were obtained with no changes to the model. For the combined effects of thinning and fertilization, a two-step additive approach was used, where the state variables were changed following thinning and the diameter increment was modified for fertilization using the time since fertilization variable. Results indicated that multiple treatments sustain a change in growth for a longer time period following treatment than thinning or fertilization alone.     

Predicting occurrence of juvenile shark habitat to improve conservation planning

Fishing and habitat degradation have increased the extinction risk of sharks, and conservation strategies recognize that survival of juveniles is critical for the effective management of shark populations. Despite the rapid expansion of marine protected areas (MPAs) globally, the paucity of shark‐monitoring data on large scales (100s–1000s km) means that the effectiveness of MPAs in halting shark declines remains unclear. Using data collected by baited remote underwater video systems (BRUVS) in northwestern Australia, we developed generalized linear models to elucidate the ecological drivers of habitat suitability for juvenile sharks. We assessed occurrence patterns at the order and species levels. We included all juvenile sharks sampled and the 3 most abundant species sampled separately (grey reef [Carcharhinus amblyrhynchos], sandbar [Carcharhinus plumbeus], and whitetip reef sharks [Triaenodon obesus]). We predicted the occurrence of juvenile sharks across 490,515 km² of coastal waters and quantified the representation of highly suitable habitats within MPAs. Our species‐level models had higher accuracy (? ≥ 0.69) and deviance explained (≥48%) than our order‐level model (? = 0.36 and deviance explained of 10%). Maps of predicted occurrence revealed different species‐specific patterns of highly suitable habitat. These differences likely reflect different physiological or resource requirements between individual species and validate concerns over the utility of conservation targets based on aggregate species groups as opposed to a species‐focused approach. Highly suitable habitats were poorly represented in MPAs with the most restrictions on extractive activities. This spatial mismatch possibly indicates a lack of explicit conservation targets and information on species distribution during the planning process. Non‐extractive BRUVS provided a useful platform for building the suitability models across large scales to assist conservation planning across multiple maritime jurisdictions, and our approach provides a simple for method for testing the effectiveness of MPAs.     

Pattern-oriented modeling of bird foraging and pest control in coffee farms

We develop a model of how land use and habitat diversity affect migratory bird populations and their ability to suppress an insect pest on Jamaican coffee farms. Bird foraging—choosing which habitat patch and prey to use as prey abundance changes over space and time—is the key process driving this system. Following the “pattern-oriented” modeling strategy, we identified nine observed patterns that characterize the real system's dynamics. The model was designed so that these patterns could potentially emerge from it. The resulting model is individual-based, has fine spatial and temporal resolutions, represents very simply the supply of the pest insect and other arthropod food in six habitat types, and includes foraging habitat selection as the only adaptive behavior of birds. Although there is an extensive heritage of bird foraging theory in ecology, most of it addresses only the individual level and is too simple for our context. We used pattern-oriented modeling to develop and test foraging theory for this across-scale problem: rules for individual bird foraging that cause the model to reproduce a variety of patterns observed at the system level. Four alternative foraging theories were contrasted by how well they caused the model to reproduce the nine characteristic patterns. Four of these patterns were clearly reproduced with the “null” theory that birds select habitat randomly. A version of classical theory in which birds stay in a patch until food is depleted to some threshold caused the model to reproduce five patterns; this theory caused lower, not higher, use of habitat experiencing an outbreak of prey insects. Assuming that birds select the nearby patch providing highest intake rate caused the model to reproduce all but one pattern, whereas assuming birds select the highest-intake patch over a large radius produced an unrealistic distribution of movement distances. The pattern reproduced under none of the theories, a negative relation between bird density and distance to trees, appears to result from a process not in the model: birds return to trees at night to roost. We conclude that a foraging model for small insectivorous birds in diverse habitat should assume birds can sense higher food supply but over short, not long, distances.     

Estimating marine biogeochemical rates of the carbonate pH system—A Kalman filter tested

Oxygen (O₂), nitrate (NO₃), dissolved inorganic carbon (DIC) or pCO₂, and pH or total alkalinity (TA), are useful indices of marine chemical, physical and biological processes operating on varying time-scales. Although these properties are increasingly being monitored at high frequency, they have not been extensively used for studying ecosystem dynamics. We test whether we can estimate time-evolving biogeochemical rates (e.g. primary production, respiration, calcification and carbonate dissolution, and nitrification) from synthetic high frequency time-series of O₂, NO₃, DIC, pCO₂, TA or pH. More specifically, a Kalman filter has been implemented in a very simplified biogeochemical model describing the dynamics of O₂, NO₃, DIC and TA and linking the concentration data to biogeochemical fluxes. Different sets of concentration data are assimilated and biogeochemical rates are estimated. The frequency of assimilation required to get acceptable results is investigated and is compared with the frequency of sampling in the field or in controlled experimental settings.Smoothing of the data to remove data noise before assimilation improves the estimation of the biogeochemical rates. The best estimated rates are obtained when assimilating O₂, NO₃ and TA although the assimilation of DIC instead of TA also gives satisfactory results. In case pH or pCO₂ is assimilated rather than DIC or TA, the linearization of the (now nonlinear) observation equation introduces perturbations and the Kalman filter behaves suboptimal. We conclude that, given the resolution of data required, the tool has potential to estimate biogeochemical rates of the carbonate system under controlled settings.     

Comparison and ranking of different modelling techniques for prediction of site index in Mediterranean mountain forests

Forestry science has a long tradition of studying the relationship between stand productivity and abiotic and biotic site characteristics, such as climate, topography, soil and vegetation. Many of the early site quality modelling studies related site index to environmental variables using basic statistical methods such as linear regression. Because most ecological variables show a typical non-linear course and a non-constant variance distribution, a large fraction of the variation remained unexplained by these linear models. More recently, the development of more advanced non-parametric and machine learning methods provided opportunities to overcome these limitations. Nevertheless, these methods also have drawbacks. Due to their increasing complexity they are not only more difficult to implement and interpret, but also more vulnerable to overfitting. Especially in a context of regionalisation, this may prove to be problematic. Although many non-parametric and machine learning methods are increasingly used in applications related to forest site quality assessment, their predictive performance has only been assessed for a limited number of methods and ecosystems.In this study, five different modelling techniques are compared and evaluated, i.e. multiple linear regression (MLR), classification and regression trees (CART), boosted regression trees (BRT), generalized additive models (GAM), and artificial neural networks (ANN). Each method is used to model site index of homogeneous stands of three important tree species of the Taurus Mountains (Turkey): Pinus brutia, Pinus nigra and Cedrus libani. Site index is related to soil, vegetation and topographical variables, which are available for 167 sample plots covering all important environmental gradients in the research area. The five techniques are compared in a multi-criteria decision analysis in which different model performance measures, ecological interpretability and user-friendliness are considered as criteria.When combining these criteria, in most cases GAM is found to outperform all other techniques for modelling site index for the three species. BRT is a good alternative in case the ecological interpretability of the technique is of higher importance. When user-friendliness is more important MLR and CART are the preferred alternatives. Despite its good predictive performance, ANN is penalized for its complex, non-transparent models and big training effort.     

Mating effort and space use of an alpine ungulate during the rut

In ungulates, the rut generally leads to increased intra and interpopulation movements for males. Because movements induce energetic costs and missed feeding opportunities, they could be an indication of male mating effort. We studied space use of 44 male mountain goats (Oreamnos americanus) from three neighboring subpopulations in southeast Alaska, during the rut from 2005 to 2008. Using mixed models and an information theoretic approach with AIC, we analyzed the relationships between individual traits of males and their space use. We found no indication of breeding migration between subpopulations. Distances between individual seasonal ranges were not related to any individual trait. Daily movements, home range sizes, and total distance traveled during the rut did not vary with mass or age of individuals. As such, effects of individual traits on male space use during the rut appear weak and observed space use patterns do not support any of the main mating effort hypotheses.