Selecting parameters for calibration via sensitivity analysis: An individual-based model of mosquitofish population dynamics

A stochastic individual-based model (IBM) of mosquitofish population dynamics in experimental ponds was constructed in order to increase, virtually, the number of replicates of control populations in an ecotoxicology trial, and thus to increase the statistical power of the experiments. In this context, great importance had to be paid to model calibration as this conditions the use of the model as a reference for statistical comparisons. Accordingly, model calibration required that both mean behaviour and variability behaviour of the model were in accordance with real data. Currently, identifying parameter values from observed data is still an open issue for IBMs, especially when the parameter space is large. Our model included 41 parameters: 30 driving the model expectancy and 11 driving the model variability. Under these conditions, the use of “Latin hypercube” sampling would most probably have “missed” some important combinations of parameter values. Therefore, complete factorial design was preferred. Unfortunately, due to the constraints of the computational capacity, cost-acceptable “complete designs” were limited to no more than nine parameters, the calibration question becoming a parameter selection question. In this study, successive “complete designs” were conducted with different sets of parameters and different parameter values, in order to progressively narrow the parameter space. For each “complete design”, the selection of a maximum of nine parameters and their respective n values was carefully guided by sensitivity analysis. Sensitivity analysis was decisive in selecting parameters that were both influential and likely to have strong interactions. According to this strategy, the model of mosquitofish population dynamics was calibrated on real data from two different years of experiments, and validated on real data from another independent year. This model includes two categories of agents; fish and their living environment. Fish agents have four main processes: growth, survival, puberty and reproduction. The outputs of the model are the length frequency distribution of the population and the 16 scalar variables describing the fish populations. In this study, the length frequency distribution was parameterized by 10 scalars in order to be able to perform calibration. The recently suggested notion of “probabilistic distribution of the distributions” was also applied to our case study, and was shown to be very promising for comparing length frequency distributions (as such).     

MORPH—An individual-based model to predict the effect of environmental change on foraging animal populations

This paper describes an individual-based model, MORPH, that has been designed to predict the effect of environmental change on foraging animal populations. The key assumptions of MORPH are that individuals within populations behave in order to maximise their perceived fitness, but that perceived fitness may not always be positively related to the actual chances of survival and reproduction. MORPH has been parameterised for coastal birds on several European sites and predicted the effect of environmental change, caused by factors such as habitat loss, disturbance from humans and sea-level rise, on the survival and body condition of these species. However, MORPH contains a basic framework to describe animal physiology and foraging behaviour, and the distribution and abundance of the resources required by these animals. Therefore, MORPH is not restricted to coastal birds, and is potentially applicable to a wider range of systems. To be applied to a forager system, MORPH requires parameters describing (i) the distribution of the food supply and how food quality and abundance changes through time; (ii) the rate at which foragers consume food given the abundance of food and competitors; (iii) the amount of food the forager must consume each day to survive; (iv) the distribution and seasonal changes in other factors which influence the foraging behaviour and survival of foragers. The purpose of this paper is to (i) describe MORPH, (ii) give examples of its application, (iii) describe the types of systems to which MORPH can be applied, and (iv) publish its source code and a user guide.     

Exploring community assembly through an individual-based model for trophic interactions

Traditionally, the dynamics of community assembly has been analyzed by means of deterministic models of differential equations. Despite the theoretical advances provided by such models, they are restricted to questions about community-wide features. The individual-based modeling offers an opportunity to link bionomic features to patterns at the community scale, allowing us to understand how trait-based assembly rules can arise by dynamical processes. The present paper introduces an individual-based model of community assembly, and discusses some of the major advantages and drawbacks of this approach. The model was framed to deal with predation among size-structured populations, incorporating allometric constraints to energetic requirements, movement, life-history features and interaction relationships among individuals. A protocol of assembly procedure is proposed, in which a period of intense species introductions is followed by a period without introductions. The resultant communities did not present any pattern of trait over-dispersion, meaning that the multivariate distances of bionomic features among co-occurring species were neither larger nor more regular than expected in a random collection of species. It suggests a weak influence of interspecific interactions in the model environment and individualistic rules of coexistence, driven mainly by the spatial structure. This highlights that trait over-dispersion and resource partitioning should not be considered a necessary condition for coexistence, even in communities entirely structured by internal processes like predation and competition.     

Behavioral games involving a clever prey avoiding a clever predator: An individual-based model of dusky dolphins and killer whales

Faced with an intermittent but potent threat, animals exhibit behavior that allows them to balance foraging needs and avoid predators and over time, these behaviors can become hard-wired adaptations with both species trying to maximize their own fitness. In systems where both predator and prey share similar sensory modalities and cognitive abilities, such as with marine mammals, the dynamic nature of predator-prey interactions is poorly understood. The costs and benefits of these anti-predator adaptations need to be evaluated and quantified based on the dynamic engagement of predator and prey. Many theoretic models have addressed the complexity of predator-prey relationships, but few have translated into testable mechanistic models. In this study, we developed a spatially-explicit, geo-referenced, individual-based model of a prototypical adult dusky dolphin off Kaikoura, New Zealand facing a more powerful, yet infrequent predator, the killer whale. We were interested in two primary objectives, (1) to capture the varying behavioral game between a clever prey and clever predator based on our current understanding of the Kaikoura system, (2) to compare evolutionary costs vs. benefits (foraging time and number of predator encounters) for an adult non-maternal dusky dolphin at various levels of killer whale-avoidance behaviors and no avoidance rules. We conducted Monte Carlo simulations to address model performance and parametric uncertainty. Mantel tests revealed an 88% correlation (426 × 426 distance matrix, km²) between observed field sightings of dusky dolphins with model generated sightings for non-maternal adult dusky dolphin groups. Simulation results indicated that dusky dolphins incur a 2.7% loss in feeding time by evolving the anti-predator behavior of moving to and from the feeding grounds. Further, each evolutionary strategy we explored resulted in dolphins incurring an additional loss of foraging time. At low killer whale densities (appearing less than once every 3 days), each evolutionary strategy simulated converged towards the evolutionary cost of foraging, that is, the loss in foraging time approached the 2.7% loss experienced by evolving near shore-offshore movement behavior. However, the highest level of killer whale presence resulted in 38% decreases in foraging time. The biological significance of these losses potentially incurred by a dusky dolphin is dependent on various factors from dolphin group foraging behavior and individual energy needs to dolphin prey availability and behavior.     

Pattern formation and individual-based models: The importance of understanding individual-based movement

This paper demonstrates that while pattern formation can stabilize individual-based models of predator–prey systems, the same individual-based models also allow for stabilization by alternate mechanisms, particularly localized consumption or diffusion limitation. The movement rules of the simulation are the critical feature which determines which of these mechanisms stabilizes any particular predator–prey individual-based model. In particular, systems from well-connected subpopulations, in each of which a predator can attack any prey, generally exhibit stabilization by pattern formation. In contrast, when restricted movement within a (sub-)population limits the ability of predators to consume prey, localized consumption or diffusion limitation can stabilize the system. Thus while the conclusions from differential equations on the role of pattern formation for stability may apply to discrete and noisy systems, it will take a detailed understanding of movement and scales of interaction to examine the role of pattern formation in real systems. Additionally, it will be important to link an understanding of both foraging and inter-patch movement, since by analogy to the models, both would be critical for understanding how real systems are stabilized by being discrete and spatial.     

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.     

Large scale parameter study of an individual-based model of clonal plant with volunteer computing

Understanding clonal strategies (i.e. the ability of plants to reproduce vegetatively) is particularly important to explain species persistence. A clonal individual may be considered as a network of interconnected ramets that colonizes space. Resources in this network can be shared and/or stored. We developed an individual-based model (IBM) to simulate the growth of an individual clonal plant. Typically a realistic IBM requires a large set of parameters to adequately represent the complexity of the clonal plant growth. Simulations in the literature are often limited to small subsets of the parameter space and are guided by the a priori knowledge and with heuristic aims of the researcher. The aim of this paper was to demonstrate the benefit of volunteer computing in computational ecology to systematically browse the parameter space and analyze the simulation results in order to draw rigorous conclusions. To be specific, we simulated clonal plant growth using nine growth rules related to the metabolic process, plant architecture, resource sharing and storage and nineteen input parameters. We chose 2-4 values per input parameter which corresponded to 20 millions of combinations tested through volunteer computing. We used three criteria to evaluate plant performance: plant total resource, ramet production and maximum length of one branch. The 1% top-performing plants were sorted according to these criteria. Plant total resource and ramet production were correlated while considering the top-performing plants. The maximum length of one branch was independent from the other two performance traits. We detected two processes promoting at least one of the plant performance traits: (i) a relatively high metabolic gain (high photosynthetic activity and low production cost for new growth units), a low resource storage and long integration distance for resource sharing; (ii) short spacer lengths and the predominance of elongation of existing branches over branching. Interactive effects between parameter values were demonstrated for more than half of the input parameters. Best performance was reached for plants with slightly different combinations of values for these parameters (i.e. different strategies) rather than a single one (i.e. unique strategy). This modeling approach with volunteer computing enabled us to proceed to large-scale virtual experiments which provided a new quality of insight into ecological processes linked with clonal plant growth.     

Forest dynamics in Oregon landscapes: evaluation and application of an individual-based model.

The FORCLIM model of forest dynamics was tested against field survey data for its ability to simulate basal area and composition of old forests across broad climatic gradients in western Oregon, USA. The model was also tested for its ability to capture successional trends in ecoregions of the west Cascade Range. It was then applied to simulate present and future (1990-2050) forest landscape dynamics of a watershed in the west Cascades. Various regimes of climate change and harvesting in the watershed were considered in the landscape application. The model was able to capture much of the variation in forest basal area and composition in western Oregon even though temperature and precipitation were the only inputs that were varied among simulated sites. The measured decline in total basal area from tall coastal forests eastward to interior steppe was matched by simulations. Changes in simulated forest dominants also approximated those in the actual data. Simulated abundances of a few minor species did not match actual abundances, however. Subsequent projections of climate change and harvest effects in a west Cascades landscape indicated no change in forest dominance as of 2050. Yet, climate-driven shifts in the distributions of some species were projected. The simulation of both stand-replacing and partial-stand disturbances across western Oregon improved agreement between simulated and actual data. Simulations with fire as an agent of partial disturbance suggested that frequent fires of low severity can alter forest composition and structure as much or more than severe fires at historic frequencies.     

Test of a behavior-based individual-based model: response of shorebird mortality to habitat loss.

In behavior-based individual-based models (IBMs), demographic functions are emergent properties of the model and are not built into the model structure itself, as is the case with the more widely used demography-based IBMs. Our behavior-based IBM represents the physiology and behavioral decision making of individual animals and, from that, predicts how many survive the winter nonbreeding season, an important component of fitness. This paper provides the first test of such a model by predicting the change in winter mortality of a charadriid shorebird following removal of intertidal feeding habitat, the main effect of which was to increase bird density. After adjusting one calibration parameter to the level required to replicate the observed mortality rate before habitat loss, the model predicted that mortality would increase by 3.65%, which compares well with the observed increase of 3.17%. The implication that mortality was density-dependent was confirmed by predicting mortality over a range of bird densities. Further simulations showed that the density dependence was due to an increase in both interference and depletion competition as bird density increased. Other simulations suggested that an additional area of mudflat, equivalent to only 10% of the area that had been lost, would be needed by way of mitigation to return mortality to its original level. Being situated at a high shore level with the flow of water in and out impeded by inlet pipes, the mitigating mudflat would be accessible to birds when all mudflats in the estuary were covered at high tide, thus providing the birds with extra feeding time and not just a small replacement mudflat. Apart from providing the first, and confidence-raising, test of a behavior-based IBM, the results suggest (1) that the chosen calibration procedure was effective; (2) that where no new fieldwork is required, and despite being parameter rich, a behavior-based IBM can be parameterized quickly (few weeks), and thus cheaply, because so many of the parameter values can be obtained from the literature and are embedded in the model; and (3) that behavior-based IBMs can be used to explore system behavior (e.g., the role of depletion competition and interference competition in density-dependent mortality).     

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.     

An individual-based stochastic hazard model of eastern king prawn (Melicertus plebejus) migration with spatially and temporally varying fishing effort

This paper describes an individual-based stochastic model of eastern king prawn migration along the eastern Australian coast. Migration is treated as one-dimensional diffusion with drift. Capture of a prawn is seen as a failure event driven by movement through a spatially and temporally variable fishing mortality hazard. This hazard is combined with a uniform natural mortality hazard. We use a Monte Carlo method to estimate parameters by comparing expected numbers of tag-returns predicted from the model with previously published tag-release data. As the previous study used a discrete compartmental model, with compartments corresponding to zones of constant fishing effort, we used the same zones and fishing effort in our comparison. The marginal distribution of yield in each zone per single recruit is determined, providing more information compared with the deterministic approach to yield-per-recruit. Using our model we also derive the constant fishing mortality rate equivalent to a spatially variable fishing mortality rate in its impact on the proportion of prawns surviving the migration to reach spawning grounds. Determination of this proportion could contribute significantly to a sustainability assessment of the fishery. It is demonstrated using the AIC that better fits to the data of the previous study and greater parsimony are obtained using our model than were found in the deterministic compartmental analysis of that study. This improvement results from the ability of our model to account separately for average speed of movement and average dispersal rate, whereas in the previous deterministic compartmental model, movement is governed by just one parameter. Our individual-based model includes a parameter that explicitly accounts for dispersal of prawns in migration, so it can distinguish between speed effects and dispersal effects in the data. It also models both types of mortality as processes distinct from those of movement. This enables it to better separate movement and mortality effects compared to the compartmental approach, in which movement and mortality are treated as similar departure processes from a compartment. This separation reduces confounding of movement and mortality effects when parameters are estimated.     

An individual-based analysis of the dynamics of two coexisting phytoplankton species in the mixed layer

In marine ecosystems ecological and environmental conditions continuously change, possibly supporting the wide range of phytoplankton species coexisting in aquatic environments. Phytoplankton communities are not homogeneously distributed in the water column due to the spatial and temporal variability of turbulent mixing and the concurrent biological response. In this paper an individual-based model (Lagrangian method) simulating the basic physiology of two coexisting phytoplankton species has been developed. The species, sharing the same availability of light and nutrient resource, are characterized by different photo-physiological parameters. The spatial and temporal evolution of turbulent mixing is simulated introducing vertical profiles of measured eddy diffusivity. Three case studies have been examined to analyze the role of environment–individual interactions in determining bloom conditions for both the selected species. The organisms experience recurrent fluctuations of light, temperature, and nutrient concentration gradients, due to the turbulent mixing in the water column, which have significant effects on the growth of the phytoplankton species. In all the numerical experiments, the temporal and spatial variability of different forcings do not support the prevalence of one species over the other over the time scale typical of a phytoplankton bloom.A well mixed water column favours the growth of both the populations while a variable mixing regime limits their growth reducing the photophysiological differences between the species.     

A spatiotemporal individual-based fish model to investigate emergent properties at the organismal and the population level

A spatiotemporal individual-based model (IBM) of roach (Rutilus rutilus) including bioenergetic principles was used to study emergent properties at the individual and the population level which appeared as a result of resource allocation and time scheduling of activities related to maintenance, growth, and reproduction in a seasonally changing environment. The model was used as a virtual laboratory to consider the impact of various parameters on vital rates and spatial behaviour of roach, which is particularly difficult to study in the field. The parameterisation based on field studies performed at Lake Belau (Schleswig-Holstein, Germany) and laboratory measurements. This allowed us to explore the relationship between population structure and environmental heterogeneity on an integrated base. At the individual level emergent properties such as spatial behaviour, growth, and food consumption could be identified. Emergent properties at the population level resulted as phenotypic consequences of a trophic bottleneck, the influence of lake morphology on the phenotype as well as size-dependent winter mortality rates and post-reproductive mortality rates.     

Circatidal swimming behavior of brachyuran crab zoea larvae: implications for ebb-tide transport

Larvae of the blue crab Callinectes sapidus and fiddler crab Uca pugilator are exported from estuaries and develop on the continental shelf. Previous studies have shown that the zoea-1 larvae of some crab species use selective tidal-stream transport (STST) to migrate from estuaries to coastal areas. The STST behavior of newly hatched larvae is characterized by upward vertical migration during ebb tide followed by a descent toward the bottom during flood. The objectives of the study were (1) to determine if newly hatched zoeae of U. pugilator and C. sapidus possess endogenous tidal rhythms in vertical migration that could underlie STST, (2) to determine if the rhythms persist in the absence of estuarine chemical cues, and (3) to characterize the photoresponses of zoeae to assess the impact of light on swimming behavior and vertical distribution. Ovigerous crabs with late-stage embryos were collected from June to August 2002 and maintained under constant laboratory conditions. Following hatching, swimming activity of zoeae was monitored in darkness for 72 h. U. pugilator zoeae displayed a circatidal rhythm in swimming with peaks in activity occurring near the expected times of ebb currents in the field. Conversely, C. sapidus zoeae exhibited no clear rhythmic migration patterns. When placed in a light field that simulated the underwater angular light distribution, C. sapidus larvae displayed a weak positive phototaxis at the highest light levels tested, while U. pugilator zoeae were unresponsive. Swimming behaviors and photoresponses of both species were not significantly influenced by the presence of chemical cues associated with offshore or estuarine water. These results are consistent with predictions based on species-specific differences in spawning and the proximity of hatching areas to the mouths of estuaries. U. pugilator larvae are released within estuaries near the adult habitat. Thus, ebb-phased STST behavior by zoeae is adaptive since it enhances export. Selective pressures for a tidal migration in C. sapidus larvae are likely weaker than for U. pugilator since ovigerous females migrate seaward prior to spawning and hatching occurs near inlets and in coastal waters.     

Diversity of swimming behavior in hydromedusae as related to feeding and utilization of space

Feeding behaviors of the following 4 species of hydromedusae are described from field and laboratory observations: Probosidactyla flavicirrata, Stomotoca atra, Phialidium gregarium and Polyorchis penicillatus. Feeding efficiency of medusae has previously been considered equivalent to fishing with a given amount (combined tentacle length) of adhesive fishing line; however, detailed observation shows that behavior of medusae greatly modifies the fishing capacity of each species. It is hypothesized that in addition to (1) tentacle number and length, the following factors strongly influence feeding efficiency: (2) tentacle posture, (3) velocity of tentacles moving through water (4) swimming pattern of medusa, (5) streamlining effects of medusa bell on water flow, (6) diameter of prey, (7) swimming pattern and velocity of prey. Each species of hydromedusa utilizes the above factors in different combinations.Mailing address     

Use of individual-based models for population parameters estimation

A method for parameters estimation of stage-specific mortality and fecundity rate functions in poikilotherm organisms, and in particular for arthropod structured population, is proposed. The application of this method requires three types of information: stage-frequency data of a sampled population, development rate function and time evolution of forcing variables affecting the rate functions. By means of an individual-based model (a microscopic model) the number of eggs produced by the adults is generated starting from the number of individuals collected at each sampling time. Using a compartmental model (a macroscopic model) a stage-structured population dynamics is described and compared with observations. Non-linear regression methods based on least square principle are used to estimate the optimal parameters of the mortality and fecundity rate functions combining microscopic and macroscopic models. As a case study, the parameter estimation of the temperature-dependent mortality function of olives fruit fly Bactrocera oleae is presented.     

An individual-based model to study the reproduction of egg bearing copepods: Application to Eurytemora affinis (Copepoda Calanoida) from the Seine estuary,France

Limited empirical studies have elucidated the daily egg production and associated reproductive processes of egg bearing copepod. Herein, we present an individual-based model which constitutes a realistic representation of the reproduction in egg bearing copepods. The model has been parameterized using an extensive set of experimental data obtained from the literature and from the laboratory and field experiments on the estuarine copepod Eurytemora affinis. The proposed model takes into account the adult female longevity, the clutch size and interclutch duration, which is a function of egg maturation time and latency time required by the female after egg hatching to produce a new clutch. The embryonic development time and hatching success are also taken into account. The effect of temperature on the means and variances of above-mentioned reproductive parameters has been also incorporated. A multi agent system based generic platform “Mobidyc” has been used to generate and calibrate the model. The model demonstrates the reproductive parameters of females of E. affinis which is validated through individual based experiments. Temperature specific simulations provide a dynamical explanation of temperature effect on the cumulative egg production. The daily survival principally affects the number of clutches produced per female during its life span. The results obtained in the present study by combining temperature and survival effects reveal the relatively greater importance of the first factor on the daily egg production of egg-carrying copepods. The present model is generic and hence easily applicable to other animals with comparable reproductive strategy.