Influence of host migration between woodland and pasture on the population dynamics of the tick Ixodes ricinus: A modelling approach

Ticks act as vectors of pathogens that can be harmful to animals and/or humans. Epidemiological models can be useful tools to investigate the potential effects of control strategies on diseases such as tick-borne diseases. The modelling of tick population dynamics is a prerequisite to simulating tick-borne diseases and the corresponding spread of the pathogen. We have developed a dynamic model to simulate changes in tick density at different stages (egg, larva, nymph and adult) under the influence of temperature. We have focused on the tick Ixodes ricinus, which is widespread in Europe. The main processes governing the biological cycles of ticks were taken into account: egg laying, hatching, development, host (small, mainly rodents, or large, like deer and cattle, mammals) questing, feeding and mortality. This model was first applied to a homogeneous habitat, where simulations showed the ability of the model to reproduce the general patterns of tick population dynamics. We considered thereafter a multi-habitat model, where three different habitats (woodland, ecotone and meadow) were connected through host migration. Based on this second application, it appears that migration from woodland, via the ecotone, is necessary to sustain the presence of ticks in the meadow. Woodland can therefore be considered as a source of ticks for the meadow, which in turn can be regarded as a sink. The influence of woodland on surrounding tick densities increases in line with the area of this habitat before reaching a plateau. A sensitivity analysis to parameter values was carried out and demonstrated that demographic parameters (sex ratio, development, mortality during feeding and questing, host finding) played a crucial role in the determination of questing nymph densities. This type of modelling approach provides insight into the influence of spatial heterogeneity on tick population dynamics.     

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

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

Assessing competition between Steller sea lions and the commercial groundfishery in Alaska: A bioenergetics modelling approach

In the last three decades the western stock of the Steller sea lion (Eumetopias jubatus) has declined by more than 85%. Nutritional stress resulting in increased juvenile mortality is one of the leading hypotheses to account for this decline. Competition between Steller sea lions and the commercial groundfishery for walleye pollock (Theragra chalcogramma) has been proposed as a mechanism underlying the nutritional stress. In order to examine the competition component of the nutritional stress hypothesis, we developed a bioenergetics-based model to project the population trends of Steller sea lions under various scenarios of continued groundfish harvest. Annual energy budgets were calculated for the Gulf of Alaska population of Steller sea lions, and compared with projected available energy from walleye pollock under a variety of harvest scenarios. Model simulations produced 50-year Steller sea lion population projections consistent with current trends, as well as with published projections for stable and increasing populations from stable age distribution life table models. Model simulations were unable to produce energy deficits sufficient to account for the decline in Steller sea lions, but do suggest areas where existing data need supplementing.     

A resource-based approach to modelling the dynamics of interacting populations

The procedure for modelling the growth of single-species populations [Sakanoue, S., 2007. Extended logistic model for growth of single-species populations. Ecol. Model. 205, 159–168] is improved to be applicable to the study of the dynamics of interacting populations. The improved procedure is based on three assumptions: resource availability changes with population size as a variable, resource supply to populations and population demand for resources are defined as functions of resource availability and population size, and the variables of resource availability and population size shift in the supply function attracted to the demand function. These assumptions are organized into three equations. The equations can generate the dynamics models of plant, herbivore, and detritivore populations, and their own resources. The models can be used to describe prey–predator dynamics. They naturally contain nonlinear terms for the predator’s numerical and functional responses. Depending on the terms, the fluctuations in resource availability and population size stabilize. The three equations can also generate the dynamics models of different populations consuming the same resources. The analysis of zero isoclines of the models shows that a superior population can be simply defined as one with a higher intrinsic rate of natural increase, that a stable coexistence may be realized with the intraspecific interference or the interspecific facilitation of superiors, and that the interspecific interference or the intraspecific facilitation of inferiors may make the coexistence unstable and the inferiors winners depending on their initial population size.     

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 population model for the peach fruit moth, Carposina sasakii Matsumura (Lepidoptera: Carposinidae), in a Korean orchard system

A population model for the peach fruit moth, Carposina sasakii Matsumura, was constructed to understand the population dynamics of this pest species and to develop an effective management strategy for various orchard (apple, peach, apple + peach) systems. The model was structured by the five developmental stages of C. sasakii: egg, larva, pupa, larval-cocoon (overwintering larva), and adult. The model consisted of a series of component models: (1) a bimodal spring adult emergence model, (2) an adult oviposition model, (3) stage emergence models of eggs, larvae, and pupae, (4) a larval survival rate model in fruits, (5) a larval-cocoon formation model, and (6) an insecticide effect model. Simulations using the model described the typical patterns of C. sasakii adult abundance in various orchard systems well, and was specific to the composition of host plants: three adult abundance peaks (first peak, mid-season peak, and last peak) a year with decreased peaks after the first peak in monoculture orchards of late apple, two adult peaks a year with a much higher last peak in monoculture orchards of early peach, and three adult peaks a year with much higher later peaks in mixed orchards of late apple and early peach. The average deviation between model outputs and actual records for first and second adult peak dates was 2.8 and 3.9 d, respectively, in simulations without an insecticide effect. The deviation decreased when insecticide effects were incorporated into the model. We also performed a sensitivity analysis of our model, and suggest possible applications of the model.     

Sanitary felling of Norway spruce due to spruce bark beetles in Slovenia: A model and projections for various climate change scenarios

A model is presented to predict sanitary felling of Norway spruce (Picea abies) due to spruce bark beetles (Ips typographus, Pityogenes chalcographus) in Slovenia according to different climate change scenarios. The model incorporates 21 variables that are directly or indirectly related to the dependent variable, and that can be arranged into five groups: climate, forest, landscape, topography, and soil. The soil properties are represented by 8 variables, 4 variables define the topography, 4 describe the climate, 4 define the landscape, and one additional variable provides the quantity of Norway spruce present in the model cell. The model was developed using the M5′ model tree. The basic spatial unit of the model is 1 km², and the time resolution is 1 year. The model evaluation was performed by three different measures: (1) the correlation coefficient (51.9%), (2) the Theil's inequality coefficient (0.49) and (3) the modelling efficiency (0.32). Validation of the model was carried out by 10-fold cross-validation. The model tree consists of 28 linear models, and model was calculated for three different climate change scenarios extending over a period until 2100, in 10-year intervals. The model is valid for the entire area of Slovenia; however, climate change projections were made only for the Maribor region (596 km²). The model assumes that relationships among the incorporated factors will remain unchanged under climate change, and the influence of humans was not taken into account. The structure of the model reveals the great importance of landscape variables, which proved to be positively correlated with the dependent variable. Variables that describe the water regime in the model cell were also highly correlated with the dependent variable, with evapotranspiration and parent material being of particular importance. The results of the model support the hypothesis that bark beetles do greater damage to Norway spruce artificially planted out of its native range in Slovenia, i.e., lowlands and soils rich in N, P, and K. The model calculation for climate change scenarios in the Maribor region shows an increase in sanitary felling of Norway spruce due to spruce bark beetles, for all scenarios. The model provides a path towards better understanding of the complex ecological interactions involved in bark beetle outbreaks. Potential application of the results in forest management and planning is discussed.     

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.     

Analysis of annual fluctuations of C. nodosa in the Venice lagoon: Modeling approach

A simple simulation model was developed to describe the growth trends of Cymodocea nodosa (Ucria) Ascherson based on data sets from the Venice lagoon. The model reproduces the seasonal fluctuations in the above and belowground biomass and in shoot density. The modeling results are in good agreement with data on net production, growth rates and chemical–physical parameters of water. It was assumed that light and temperature are the most important factors controlling C. nodosa development, and that the growth was not limited by nutrient availability. The aim was to simulate biomass production as a function of external forcing variables (light, water temperature) and internal control (plant density). A series of simulation experiments were performed with the basic model showing that among the most important phenomena affecting C. nodosa growth are: (1) inhibition of production and recruitment of new shoots by high temperature and (2) light attenuation due to seasonal fluctuation.     

A process-based population dynamics model to explore target and non-target impacts of a biological control agent

The risks and benefits associated with efforts to control invasive alien species using classical biological control are being subjected to increasing scrutiny. A process-based population dynamics model was developed to explore the interactions between a folivorous biological control agent, Cleopus japonicus, and its plant host Buddleja davidii. The model revealed that climate could have a significant impact upon the interactions between B. davidii and C. japonicus. At the coolest sites, the impact of C. japonicus on B. davidii was slowed, but it was still eventually capable of controlling populations of B. davidii. At the warmer sites where both B. davidii and C. japonicus grew faster, B. davidii succumbed rapidly to weevil damage. We hypothesise that barring an encounter with a natural enemy, C. japonicus will eventually be able to provide sustained control B. davidii throughout the North Island of New Zealand. The model scenarios illustrate the potential for the C. japonicus population to attain high densities rapidly, and to defoliate patches of B. davidii, creating the potential for spill-over feeding on non-target plants. The potential magnitude of this threat will depend partly on the climate suitability for C. japonicus, the pattern by which it migrates in response to a reduction in the available leaf resource, and the suitability of non-target plants as hosts. In all migration scenarios considered, the pattern of population growth and resource consumption by C. japonicus was exponential, with a strong tendency toward complete utilisation of resource patches more quickly at the warmer compared to colder sites. In addition to providing some useful hypotheses about the effects of climate on the biological control system, and the non-target risks, it also provides some insight into the mechanisms by which climate affects the system.     

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.     

Modeling the role of macroalgae in a shallow sub-estuary of Narragansett Bay, RI (USA)

Proliferation of macroalgal mats is a frequent consequence of nutrient-driven eutrophication in shallow, photic coastal marine ecosystems. These macroalgae have the potential to significantly modify water quality, plankton productivity, nutrient cycling, and dissolved oxygen dynamics. We developed a model for Ulva lactuca and Gracilaria tikvahiae in Greenwich Bay, RI (USA), a shallow sub-estuary of Narragansett Bay, as part of a larger estuarine ecosystem model. The model predicts the biomass of both species in units of carbon, nitrogen, and phosphorus as a function of primary production, respiration, grazing, decay, and physical exchange, with particular attention to the effects of biomass layering on light attenuation and suppression of metabolic rates. The model successfully reproduced the magnitude and seasonal cycle of area-weighted and peak biomass in Greenwich Bay along with tissue C:N ratios, and highlighted the importance of grazing and inclusion of self-limitation primarily in the form of self-shading to overcome an order of magnitude difference in rates of production and respiration. Inclusion of luxury nutrient uptake demonstrated the importance of internal nutrient storage in fueling production when nutrients are limiting. Macroalgae were predicted to contribute a small fraction of total system primary production and their removal had little effect on predicted water quality. Despite a lack of data for calibration and a fair amount of sensitivity to individual parameter values, which highlights the need for further autecological studies to constrain formulations, the model successfully predicted macroalgal biomass dynamics and their role in ecosystem functioning. Our formulations should be exportable to other temperate systems where macroalgae occur in abundance.     

A simple individual model for simulating weight gain dynamics in response to intake rate and daily behavior

It is often necessary to estimate the weight that an individual may be capable of gaining depending on its degree of activity. A simple individual-based model was developed for studying the dynamics of weight in terms of daily behavior and ingestion rate. It was based on the balance between the individual's energy intake and the cost of its daily activities. Costs depend on the weight of the individual and the photoperiod, as well as on the time spent on each activity. Different combinations of ingestion rate, individual's weight, photoperiod length, and time assigned to different activities were used for simulating the weight dynamics, taking the species Rhea americana as a study case. Estimations of energetic costs of the activities were obtained from specialized literature. Using different photoperiods and individual behaviors, the model yields field metabolic rate (FMR) values in agreement with those obtained from direct measurements for other omnivorous bird species.     

Uncertainty analysis of transient population dynamics

Two types of demographic analyses, perturbation analysis and uncertainty analysis, can be conducted to gain insights about matrix population models and guide population management. Perturbation analysis studies how the perturbation of demographic parameters (survival, growth, and reproduction parameters) may affect the population projection, while uncertainty analysis evaluates how much uncertainty there is in population dynamic predictions and where the uncertainty comes from. Previously, both perturbation analysis and uncertainty analysis were conducted on the long-term population growth rate. However, the population may not reach its equilibrium state, especially when there is management by harvesting or hunting. Recently, there has been an increased interest in short-term transient dynamics, which can differ from asymptotic long-term dynamics. There are currently techniques to conduct perturbation analyses of short-term transient dynamics, but no techniques have been proposed for uncertainty analysis of such dynamics. In this study, we introduced an uncertainty analysis technique, the general Fourier Amplitude Sensitivity Test (FAST), to study uncertainties in transient population dynamics. The general FAST is able to identify the amount of uncertainty in transient dynamics and contributions by different demographic parameters. We applied the general FAST to a mountain goat (Oreamnos americanus) matrix population model to give a clear illustration of how uncertainty analysis can be conducted for transient dynamics arising from matrix population models.     

Computer simulation applied to the biological control of the insect Aphis gossypii for the parasitoid Lysiphlebus testaceipes

In integrated pest management (IPM), biological control is one of the possible options for the prevention or remediation of an unacceptable pest activity or damage. The success of forecast models in IPM depends, among other factors, on the knowledge of temperature effect over pests and its natural enemies. In this work, we simulated the effects of parasitism of Lysiphlebus testaceipes (Cresson, 1880) (Hymenoptera: Aphidiidae) on Aphis gossypii (Glover, 1877) (Hemiptera: Aphididae), a pest that is associated to crops of great economic importance in several parts of the world. We made use of experimental data relative to the host and its parasitoid at different temperatures. Age structure was incorporated into the dynamics through the Penna model. The results obtained showed that simulation, as a forecast model, can be a useful tool for biological control programs.     

Simulation modeling to understand how selective foraging by beaver can drive the structure and function of a willow community

Beaver–willow (Castor-Salix) communities are a unique and vital component of healthy wetlands throughout the Holarctic region. Beaver selectively forage willow to provide fresh food, stored winter food, and construction material. The effects of this complex foraging behavior on the structure and function of willow communities is poorly understood. Simulation modeling may help ecologists understand these complex interactions. In this study, a modified version of the SAVANNA ecosystem model was developed to better understand how beaver foraging affects the structure and function of a willow community in a simulated riparian ecosystem in Rocky Mountain National Park, Colorado (RMNP). The model represents willow in terms of plant and stem dynamics and beaver foraging in terms of the quantity and quality of stems cut to meet the energetic and life history requirements of beaver. Given a site where all stems were equally available, the model suggested a simulated beaver family of 2 adults, 2 yearlings, and 2 kits required a minimum of 4 ha of willow (containing about10 stems m⁻²) to persist in a steady-state condition. Beaver created a willow community where the annual net primary productivity (ANPP) was 2 times higher and plant architecture was more diverse than the willow community without beaver. Beaver foraging created a plant architecture dominated by medium size willow plants, which likely explains how beaver can increase ANPP. Long-term simulations suggested that woody biomass stabilized at similar values even though availability differed greatly at initial condition. Simulations also suggested that willow ANPP increased across a range of beaver densities until beaver became food limited. Thus, selective foraging by beaver increased productivity, decreased biomass, and increased structural heterogeneity in a simulated willow community.