Pattern-oriented Modeling Approach Research Articles

A simulation model of functional habitat connectivity demonstrates the importance of species establishment in older forests

Fragmented natural habitats, such as old-growth forests, have been often considered island-like systems. However, whereas the isolation of real islands is mostly a function of their spatial arrangement, the biodiversity of old-growth forest patches is also affected by how well the surrounding suboptimal habitats, such as younger forests, can support the functional connectivity between the old-forest fragments. The latter topic remains largely unclear due to the lack of mechanistic knowledge about the processes behind species’ affinity for old forest. Although in animal ecology, functional connectivity has often been investigated with mechanistic agent-based models, these have rarely been applied for passively dispersing organism groups. We used a pattern-oriented modeling approach by combining a spatially explicit agent-based model and an empirical biodiversity dataset of Estonian old-growth nemoral forest sites, to study how forests of different ages between the old-forest fragments are exploited by different passively or slowly dispersing functional groups. We found that the establishment of ground layer vegetation, epiphytes, ectomycorrhizal and pathogenic fungi is significantly restricted in the younger forests, whereas no clear difference between forest-age classes emerged for survival. Our results thus suggest that establishment, not survival, is the main process behind the species’ affinity for old forest, concurring with studies that have demonstrated the importance of suitable microhabitat availability in older forests. We conclude that young secondary forests do not support the connectivity – and consequently, biodiversity – of many old-forest specific groups.

Spatial Validation of Agent-Based Models

This paper adapts an existing techno–social agent-based model (ABM) in order to develop a new framework for spatially validating ABMs. The ABM simulates citizen opposition to locally unwanted land uses, using historical data from an energy infrastructure siting process in Southern California. Spatial theory, as well as the model’s design, suggest that adequate validation requires multiple tests rather than relying solely on a single test-statistic. A pattern-oriented modeling approach was employed that first mapped real and simulated citizen comments across the US Census tract. The suite of spatial tests included Global Moran’s I, complemented with bivariate correlations, as well as the local indicators of spatial association (LISA) test. The global tests showed the model explained up to 65% of the variation in the historical data for US Census tract-level citizen comments on a locally unwanted land use. These global tests were also found helpful to inform the model’s calibration for the current application. The LISA results were even stronger, showing that the model predicted citizen comment clustering correctly in five of six Census tracts. It slightly over predicted comments further away from the land use. The LISA results and pattern-oriented modeling validation techniques identified theoretical factors to improve the modeling specification in future applications. The combined suite of validation techniques helped improve confidence in the model’s predictions.

Temporal plasticity in habitat selection criteria explains patterns of animal dispersal.

Patterns of dispersal behavior are often driven by the composition and configuration of suitable habitat in a matrix of unsuitable habitat. Interactions between animal behavior and landscapes can therefore influence population dynamics, population and species distributions, population genetic structure, and the evolution of behavior. Spatially explicit individual-based models (IBMs) are ideal tools for exploring the effects of landscape structure on dispersal. We developed an empirically parameterized IBM in the modeling framework SEARCH to simulate dispersal of translocated American martens in Wisconsin. We tested the hypothesis that a time-limited disperser should be willing to settle in lower quality habitat over time. To evaluate model performance, we used a pattern-oriented modeling approach. Our best model matched all empirical dispersal patterns (e.g., dispersal distance) except time to settlement. This model incorporated a required search phase as well as the mechanism for declining habitat selectivity over time, which represents the first demonstration of this hypothesis for a vertebrate species. We suggest that temporal plasticity in habitat selectivity allows individuals to maximize fitness by making a tradeoff between habitat quality and risk of mortality. Our IBM is pragmatic in that it addresses a management need for a species of conservation concern. However, our model is also paradigmatic in that we explicitly tested a theory of dispersal behavior. Linking these 2 approaches to ecological modeling can further the utility of individual-based modeling and provide direction for future theoretical and empirical work on animal behavior.

A neutral model for the simulation of linear networks in territories

A landscape matrix is the support of biotic and abiotic flows, and in that sense, requires increased interest from ecological modellers. This matrix is partly composed of linear elements, such as roads and field borders, that delimit land uses and are the result of socio-economic drivers. The geometrical properties of these elements could affect flows of water bodies, fauna, and flora. A large amount of research on landscape matrix simulation has been conducted using neutral models, but the efforts have been limited to 1km2 and have been principally devoted to field borders. However, simulating largest territories in neutral models requires consideration of supplementary elements, such as road networks. Furthermore, the sinuosities of the linear elements in territories have rarely been considered per se. We proposed a hierarchical model based on successive imbrication of deformed networks, with the deformation being realized on the basis of a reverse Douglas–Peucker algorithm. We first isolated the hierarchical levels of the landscape and analyzed their relative deformations. Then we constructed the hierarchical model and we tested it on a real territory in the Mediterranean zone. Its structural realism was tested against other common neutral models using the pattern-oriented modelling approach. The hierarchical model was the only neutral model able to represent simultaneously the variabilities of three patterns having implications in ecological processes: polyline lengths, sinuosities and polygon areas. Possible improvements of the model to address non-stationary processes and its potential for implementing geoprospective scenarios are discussed.

Modelling food web structure using an end-to-end approach in the coastal ecosystem of the Gulf of Gabes (Tunisia)

Given the ecological importance and high socio-economic value of the fishery of the Gulf of Gabes, an end-to-end model was applied to its continental shelf ecosystem to characterize the structure of the food web in the 2000s. This approach consisted in forcing a high trophic level model (OSMOSE) with an existing biogeochemical model (Eco3M-MED) representing the seasonal dynamics of the low trophic levels. The two models were linked through trophic interactions to represent the ecosystem dynamics from primary producers to top predators. In this study, we developed the multispecies, individual-based model OSMOSE in the Gulf of Gabes (OSMOSE-GoG). This model aims to capture the main processes that influence species life cycle and simulate the functioning of the ecosystem according to opportunistic predation process based on size selection and spatio-temporal co-occurrence between a predator and its prey. The spatial distribution of the eleven modelled species was derived from a Multi-Scale Species Distribution Modelling approach. We calibrated OSMOSE-GoG model with available data of biomass and fishing yield, using an optimization method based on evolutionary algorithms which is suitable for complex and stochastic models. Finally, OSMOSE-GoG was validated against independent data sets at different hierarchical levels: the individual (diet composition), population (mean size of commercial catch) and community levels (mean trophic level) following the Pattern-Oriented Modelling approach. The model outputs were overall consistent with the diet compositions and mean trophic levels derived from the ECOPATH model of the Gulf of Gabes (ECOPATH-GoG) and the observations of mean size of catches. The OSMOSE-GoG can be considered as a baseline model to investigate ecosystem responses to environmental changes and fishing management measures in the Gulf of Gabes.

Machine learning meets individual-based modelling: Self-organising feature maps for the analysis of below-ground competition among plants

Individual-based models (IBM) simulate populations and communities whose dynamics are shaped by the properties, interactions and behaviour of the constituent organisms as well as the corresponding abiotic boundary conditions. Structurally realistic IBM can provide insights into the functioning of such systems and predict the effects of variable scenarios. We suggest complementing IBM with machine learning (ML) methods in order (i) to visualise correlation patterns between model inputs and model outputs, (ii) to provide simulation-based decision tools for non-modellers, and (iii) to derive information about factors difficult to obtain in the field on the basis of data that are more readily measurable. On top of this, ML methods can complement the established pattern-oriented modelling approach used to analyse the behaviour of IBM and to detect model uncertainties. As an example to demonstrate the strength of an IBM-ML connection, we combined the individual-based Plant Interaction Model (Pi model) with self-organising feature maps (SOM) – a special type of ML. Based on simulation experiments with complete knowledge of the simulated system, the SOM was trained and used to visualise the nonlinear relationship between two IBM inputs (namely the mode of below-ground competition and below-ground resource limitation) and two model outputs (the mortality rate and the Clark Evans Index of the spatial distribution of plants). Our study also highlights an application of the SOM to infer the modes of below-ground competition (either symmetric or asymmetric) from the remaining measurable variables (resource limitation, mortality rate and Clark Evans Index). This procedure was successful in 92% of cases, revealing its great potential as a means to assess parameters difficult to measure in nature. This example shows that SOM are powerful tools to revert the hierarchy of variables and to generalise dependencies of parameters in individual based modelling.

An end-to-end coupled model ROMS-N2P2Z2D2-OSMOSE of the southern Benguela foodweb: parameterisation, calibration and pattern-oriented validation

In order to better understand ecosystem functioning under simultaneous pressures (e.g. both climate change and fishing pressures), integrated modelling approaches are advocated. We developed an end-to-end model of the southern Benguela ecosystem by coupling the high trophic level model OSMOSE with a biophysical model (ROMS-N2P2Z2D2). OSMOSE is a spatial, multispecies, individual-based model simulating the whole life cycle of fish with fish schools interacting through opportunistic and size-based predation. It is linked to the biogeochemical model through the predation process; plankton groups are food for fish and fish apply a predation mortality on plankton. Here we describe the two-way coupling between the models and follow a pattern-oriented modelling approach to validate the simulations. At the individual level, model outputs are consistent with observed diets for several species from small pelagic fish to top predatory fish, although biases emerge from underestimation of macrozooplankton and lack of vertical structure. At the population level, the seasonality of the size structure is similar between the model and data. At the community level, the modelled trophic structure is consistent with the knowledge available for this ecosystem. The structure of the foodweb is an emergent property of the model, showing trophic links between species, their strength and the strong connectivity observed. We also highlight the capacity of this model for tracking indicators at various hierarchical levels.

Incorporating behavioral–ecological strategies in pattern-oriented modeling of caribou habitat use in a highly industrialized landscape

Woodland caribou (Rangifer tarandus) are classified as threatened in Canada, and the Little Smoky herd in west-central Alberta is at immediate risk of extirpation due in part, to anthropogenic activities such as oil, gas, and forestry that have altered the ecosystem dynamics. Winter season represents an especially challenging time of year for this Holarctic species as it is characterized by a shortage of basic resources and is when most industrial development occurs, to which caribou can perceive as increased predation risk. To investigate the impact of industrial features on caribou, we developed a spatially explicit, agent-based model (ABM) to simulate the underlying behavioral mechanisms caribou are most likely to employ when navigating their landscape in winter. The ABM model is composed of cognitive caribou agents possessing memory and decision-making heuristics that act to optimize tradeoffs between energy acquisition and predator/disturbance avoidance. A set of environmental data layers was used to develop a virtual grid representing the landscape in terms of forage availability, energy content, and predation-risk. The model was calibrated with caribou bio-energetic values from literature sources, and validated using GPS data from thirteen caribou radio-collars deployed over 6 months from 2004 to 2005. Simulations were conducted on alternative caribou habitat-selection strategies by assigning different fitness-maximizing goals to agents. The model outcomes were evaluated using a pattern-oriented modeling approach with actual caribou data. The scenario in which the caribou agent must trade off the mutually competing goals of obtaining its daily energy requirement, conserving reproductive energy, and minimizing predation risk, was found to be the best-fit scenario. Not recognizing industrial features as risk causes simulated caribou to unrealistically reduce their daily and landscape movements; equally, having risk take precedence results in unrealistic energetic deficits and large-scale movement patterns, unlike those observed in actual caribou. These results elucidate the most likely behavioral strategies caribou use to select their winter habitat, the relative extent to which they perceive industry features as potential predation, and the differential energetic costs associated with each strategy. They can assist future studies of how caribou may respond to continued industrial development and/or mitigation measures.

Prediction of specific leaf area distribution in plant communities along a soil resource gradient using trait trade-offs in a pattern-oriented modelling approach

The functional-trait approach to communities focuses on the distribution of traits and on their variations in communities along environmental gradients. We devised a pattern-oriented demarche to predict specific leaf area (SLA) distribution in three plant communities located along an environmental gradient governed by soil fertility and nutrient stress in subalpine gypsic dolines. An individual-based model incorporating physiological mechanisms simulated the growth of thirty functional groups varying in leaf traits (SLA and correlated leaf life-span) and nitrogen (N) stress tolerance which competed with their neighbours for access to light and nitrogen. The SLAs of these groups encompassed the range of SLAs measured in the sites. Leaf traits governed the daily temperature-dependent processes involved in capturing resources (N and light), biomass synthesis and loss, and the value of the parameter Nc governed the decrease in growth rate of organisms according to a decline in N supply. Biomass drove the comp...

Mechanisms of coexistence between native bull trout (Salvelinus confluentus) and non-native lake trout (Salvelinus namaycush): inferences from pattern-oriented modeling

Determining the ecological mechanisms that control population abundances is an important issue for the conservation of endangered and threatened species. We examined whether a threatened bull trout ( Salvelinus confluentus ) population could coexist at observed levels with the ecologically similar introduced species, lake trout ( Salvelinus namaycush ), using a pattern-oriented analysis of population dynamics models. We used a large suite of stage- and age-structured models to examine how both competitive and predatory interactions, combined with differing life-history strategies and species vital rates, drove salmonid coexistence patterns. In our models, an ontogenetic shift in juvenile bull trout resource use was the most important factor contributing to the two species coexistence; however, this coexistence occurred with reduced abundances in bull trout that increase the chances of extirpation for the native species. Observed levels of competition were found to have stronger effects than predation on population abundances. We used a pattern-oriented modeling approach to inference; this approach assumes process models that can generate patterns similar to the observed patterns are better supported than those that cannot. This methodology may find wide use on a number of data-limited fishery management and conservation problems.

Modelling the timing and duration of dormancy in populations of Calanus finmarchicus from the Northwest Atlantic shelf

Calanus finmarchicus relies on dormancy to thrive in the seasonal environment of the boreal Atlantic. The lipid accumulation window (LAW) hypothesis proposes that a seasonal window of environmental conditions allows developing individuals to store enough lipids for dormancy to be safely initiated. Successful dormancy requires a sufficient amount of lipids to fulfil the reduced metabolic demand of the dormant individual and to sustain the final maturation process. We used a pattern-oriented modelling approach that implements the LAW hypothesis and employs a genetic algorithm for parameter estimation, in order to reproduce the observed phenology and demography of C. finmarchicus populations from the two contrasting regions, the Gulf of St. Lawrence (GSL) and the Gulf of Maine (GoM) in the northwest Atlantic shelf. In the GSL, the model reproduced the timing of dormancy, the abundance and individual condition of late copepodid stages. In the GoM, the model produced a semi-annual dormancy pattern, as no locally produced individual could last the 6–8 months of dormancy inferred from the available observations. Further testing requires extending demographic time series, including lipid condition of late copepodid stages in the GoM, and the implementation of a 3-D modelling framework that would explicitly address the complex interactions between circulation and population dynamics of C. finmarchicus over the entire northwest Atlantic shelf.

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.

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.

Dynamics and impact of the coral disease white plague: insights from a simulation model

Coral disease is playing a significant role in structuring today's coral reef communities. While monitoring programs document declines associated with coral disease, there is a lack of tools that can test hypotheses of disease incidence and control. Here, we describe a modeling tool developed to test hypotheses about the spread and impact of white plague disease in diverse coral populations distributed across heterogeneous reef landscapes. The model Simulation of Infected Corals (SICO) was based on the dynamics of white plague over the course of 6 yr of monitoring on the fore-reefs of Little Cayman (Cayman Islands, British West Indies). A pattern-oriented modeling approach using a genetic algorithm was used to calibrate model parameters that describe disease introduction, transmissibility, and host susceptibility. Simulation patterns most accurately reflected patterns observed at study sites when disease was introduced at regular intervals and was transmissible within a limited area. Projecting forward in time, coral cover tended to drop precipitously until colonies were so sparse that disease transmission among colonies was rare. A sensitivity analysis of disease parameters indicated that the effect of changing disease parameters depended on the type of coral community, but that in communities dominated by susceptible species, local preventative measures were generally more effective than treatment measures in limiting disease impact.

Modelling Mediterranean landscape succession-disturbance dynamics: A landscape fire-succession model

We present a spatially explicit Landscape Fire-Succession Model (LFSM) developed to represent Mediterranean Basin landscapes and capable of integrating modules and functions that explicitly represent human activity. Plant-functional types are used to represent spatial and temporal competition for resources (water and light) in a rule-based modelling framework. Vegetation dynamics are represented using a rule-based community-level modelling approach that considers multiple succession pathways and vegetation climax states. Wildfire behaviour is represented using a cellular-automata model of fire spread that accounts for land-cover flammability, slope, wind and vegetation moisture. Results show that wildfire spread parameters have the greatest influence on two aspects of the model: land-cover change and the wildfire regime. This sensitivity highlights the importance of accurately parameterising this type of grid-based model for representing landscape-level processes. We use a pattern-oriented modelling approach in conjunction with wildfire power-law frequency-area scaling exponent β to calibrate the model. Parameters describing the role of soil moisture on vegetation dynamics are also found to significantly influence land-cover change. Recent improvements in understanding the role of soil moisture and wildfire fuel loads at the landscape-level will drive advances in Mediterranean LFSMs.

The role of size inequality in self-thinning: A pattern-oriented simulation model for arid savannas

The self-thinning line is a very robust pattern, which can be obtained in modeling studies by a variety of different mechanistic assumptions. Our opinion is that we can only advance in our understanding of mechanisms leading to the self-thinning relationship if we demand that the model also reproduces several other characteristic features (patterns) of the self-thinning process such as the degree of size inequality and the average size. We use a pattern-oriented modeling approach to develop a model of self-thinning under size inequality in overcrowded, even-aged stands, which reproduces these three patterns simultaneously. Our approach is to first develop an initial model based on our current ecological knowledge and then to refine the model by modifying the initial model to derive the model that reproduces all patterns of interest. The initial model is as simple as possible while avoiding incidental, ecologically unjustified, assumptions. It is a further development of zone of influence-simulation models: each plant is described by two circles, one describing a minimum-domain-area and one describing the zone of influence. In the initial model, mortality is “death-by-contact” of minimum-domain-areas and growth is a function of inter-tree competition, i.e. overlapping zones of influence. Model parameterization is based on field data on Acacia reficiens in southern Africa. Simulations follow patches of initially small trees through time for up to 1000 years with five parameters, three describing growth and two describing inter-tree competition. A sensitivity analysis shows that all parameters of the initial model contribute significantly to the number and size of plants through time. The two competition parameters, which describe competitive asymmetry and the size of the zone of influence relative to canopy size, are both important for generating size inequality. Thus, both competitive asymmetry and spatial pattern contribute to size inequality, and their relative importance may vary greatly. The sensitivity analysis suggests that all processes included in the initial model are essential to the evolution of size inequality. However, size inequality under the initial model is below field values, meaning that additional, as yet unconsidered processes, contribute to size inequality. Our best-fit model additionally contains details on growth stochasticity. This study establishes the often-proposed direct link between mortality driven by local competition and self-thinning and highlights the importance of stochasticity in ecological processes.