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.     

Does song reflect age and viability? A comparison between two populations of the great reed warbler Acrocephalus arundinaceus

Song complexity is often regarded as a sexually selected trait that reflects the overall quality of a male. In many passerine species, old males possess larger song repertoires than younger males. This may be either because individual males improve their performance as they get older (longitudinal increase) or because poor singers have reduced viability and, hence, are underrepresented in old age classes (cross-sectional increase). We studied the age dependence of repertoire size and other song traits in a German and a Swedish great reed warbler (Acrocephalus arundinaceus) population. We found marked differences between longitudinal and cross-sectional approaches, as well as between the two study populations. In the German population, we found that syllable switching, a measure of immediate versatility and strophe length, increased with age in a cross-sectional analysis. This was not because birds improved with age (longitudinally) but because syllable switching was positively correlated with male longevity. However, in Sweden, syllable switching seemed to be unrelated to age and longevity. In the Swedish population, individual males increased their repertoire size as they got older (longitudinal increase), but this did not happen in the German population. Hence, two populations, even when belonging to the same subspecies, may differ in whether or not they show delayed song maturation.     

A model of nematode dynamics in the Westerschelde Estuary

We developed a time dynamic model to investigate the temporal dynamics of nematode community in the brackish zone of the Westerschelde Estuary. The biomass of four nematode feeding groups observed from March 1991 to February 1992 is used to calibrate the model. Using environmental data as the input, the model predicts the temporal modification and interrelation of four nematode feeding groups. Nematodes achieve a dominant position in the community because of their lower loss rate (in respiration, excretion and natural death). Predators which are deposit-feeding macrobenthos control the variations of dominant nematodes, such as omnivores and non-selective deposit feeders. Food availability causes modification only for rare nematodes such as epigrowth feeders and selective deposit feeders. Temperature is a factor affecting both predation death and a loss including respiration, excretion and natural death. Overall, the modification of nematode community by food availability is much lower than by predator. The macrobenthos in the Westerschelde Estuary decrease from upstream to the estuarine mouth. The stability and standing stock of nematode population follow the opposite gradient of their predators. They increase from upstream to the estuarine mouth.     

A process-convolution approach to modelling temperatures in the North Atlantic Ocean

This paper develops a process-convolution approach for space-time modelling. With this approach, a dependent process is constructed by convolving a simple, perhaps independent, process. Since the convolution kernel may evolve over space and time, this approach lends itself to specifying models with non-stationary dependence structure. The model is motivated by an application from oceanography: estimation of the mean temperature field in the North Atlantic Ocean as a function of spatial location and time. The large amount of this data poses some difficulties; hence computational considerations weigh heavily in some modelling aspects. A Bayesian approach is taken here which relies on Markov chain Monte Carlo for exploring the posterior distribution.     

Population dynamics models based on cumulative density dependent feedback: A link to the logistic growth curve and a test for symmetry using aphid data

Density dependent feedback, based on cumulative population size, has been advocated to explain and mathematically characterize “boom and bust” population dynamics. Such feedback results in a bell-shaped population trajectory of the population density. Here, we note that this trajectory is mathematically described by the logistic probability density function. Consequently, the cumulative population follows a time trajectory that has the same shape as the cumulative logistic function. Thus, the Pearl–Verhulst logistic equation, widely used as a phenomenological model for density dependent population growth, can be interpreted as a model for cumulative rather than instantaneous population. We extend the cumulative density dependent differential equation model to allow skew in the bell-shaped population trajectory and present a simple statistical test for skewness. Model properties are exemplified by fitting population trajectories of the soybean aphid, Aphis glycines. The linkage between the mechanistic underpinnings of the logistic probability density function and cumulative distribution function models could open up new avenues for analyzing population data.     

Response of American redstarts (suborder Passeri) and least flycatchers (suborder Tyranni) to heterospecific playback: the role of song in aggressive interactions and interference competition

Least flycatchers (Empidonax minimus) and American redstarts (Setophaga ruticilla) overlap in the use of food resources on their breeding grounds, promoting high levels of interspecific aggression by the socially dominant flycatcher. We examined the role of song in this interspecific aggression by using repeated-measures-designed playback experiments and observational data on induced aggressive interactions. Flycatchers were more likely to approach the speaker during presentation of redstart song than during intervals of no song or presentation of control song. Approach was close enough to enable visual contact with a singing redstart. In contrast, redstarts made significantly fewer flights following presentation of flycatcher song, when risk of flycatcher attack may be greatest. Reducing the number of flights likely reduces the risk of flycatcher attack on the redstart, as flycatchers do not attack stationary redstart models and are apparently dependent on cues from redstart flight for visual heterospecific recognition. Flycatcher-specific responses of redstarts and marked differences in song morphology rule out misdirected intraspecific aggression as a proximate or ultimate cause of interspecific response to song. Results indicate that song is an important component in aggressive interactions between these two species, and reflect the dominant role of the flycatcher in such interactions. Our results also illustrate the capacity for interspecific interference competition to influence behavior and heterospecific song recognition in two distant avian taxa. Received: 10 January 1995/Accepted after revision: 8 June 1996     

A model-based approach to determine the long-term effects of multiple interacting stressors on coral reefs

The interaction between multiple stressors on Caribbean coral reefs, namely, fishing effort and hurricane impacts, is a key element in the future sustainability of reefs. We develop an analytic model of coral-algal interactions and explicitly consider grazing by herbivorous reef fish. Further, we consider changes in structural complexity, or rugosity, in addition to the direct impacts of hurricanes, which are implemented as stochastic jump processes. The model simulations consider various levels of fishing effort corresponding to' several hurricane frequencies and impact levels dependent on geographic location. We focus on relatively short time scales so we do not explicitly include changes in ocean temperature, chemistry, or sea level rise. The general features of our approach would, however, apply to these other stressors and to the management of other systems in the face of multiple stressors. It is determined that the appropriate management policy, either local reef restoration or fisheries management, greatly depends on hurricane frequency and impact level. For sufficiently low hurricane impact and macroalgal growth rate, our results indicate that regions with lower-frequency hurricanes require stricter fishing regulations, whereas management in regions with higher-frequency hurricanes might be less concerned with enhancing grazing and instead consider whether local-scale restorative activities to increase vertical structure are cost-effective.     

A finite element method to solve a population dynamics stage-structured model of intertidal barnacles

Many marine organisms are fixed or highly sedentary as adults but the adult population may be strongly dependent on the oceanic transport of planktonic larvae. In order to assess interactions between oceanographic and biological processes that determine the population dynamics of marine organisms with a sessile adult phase restricted to the coastline and a planktonic larval phase, we present a stage-structured finite element model for the barnacle Balanus glandula that inhabits the rocky intertidal zone of central California, USA.     

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.     

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.     

Sex ratio dynamics and fluctuating selection pressures in natural populations of the Trinidadian guppy,<Emphasis Type="Italic"> Poecilia reticulata</Emphasis>

In many species, population sex ratios have far-reaching consequences for a wide variety of population-level and behavioural processes and can directly influence sexual selection through differential effects on male and female mating behaviour. Although sex ratios are often treated as more or less stable population characteristics, recent theoretical evidence suggests that sex ratios fluctuate under many conditions, and that the amplitude of these fluctuations can be considerable. Few studies have attempted to quantify this variation in systems with prominent, sex ratio-dependent sexual conflict. One of the species with the greatest potential to integrate these factors in the wild is the Trinidadian guppy, Poecilia reticulata. In this study, we quantified natural sex ratio variation both as detailed longitudinal studies of focal guppy populations and as snapshot estimates across a range of freshwater habitats. In line with theoretical predictions, we expected to detect significant sex ratio variation over time. We also investigated the association between juvenile and adult sex ratios to quantify a possible compensatory feedback implied in standard models of sex ratio evolution. Our results confirm that population-level sex ratios in wild guppy populations have a range of dynamic features, with all four focal populations showing significant variation in sex ratio over time. The survey showed that juveniles were generally close to equal (50:50) sex ratios whereas 7 out of 11 adult sex ratios differed significantly from equality. We found no evidence that a surplus of juveniles of the locally rarer sex had been produced. The results indicate that sex ratios and hence the balance between sexual selection and sexual coercion is normally fluctuating in nature, despite juvenile ratios being close to equality.Communicated by J. Krause     

Modeling the brown bear population in Slovenia: A tool in the conservation management of a threatened species

In this paper, we address three aspects of the brown bear population in Slovenia: its size (and its evolution over time), its spatial expansion out of the core area, and its potential habitat based on natural habitat suitability. Data collected through measurement/observation of the bear population and from the literature are used. A model is developed for each aspect. The results are estimates of population size, a picture of the spatial expansion of the population and maps of its optimal and maximal potential habitat (based on natural suitability). Overall, the brown bear population has been increasing since the establishment of a core protective area and has been expanding outside this area. The habitat suitability maps show that there is room for further expansion. Based on habitat suitability and bear population density, as well as human activity and current damage reports, we recommend that the Alps should be temporarily kept free of the bears, until the necessary mitigation measures regarding human–bear conflicts are carried out. On the other hand it is of crucial importance to adapt human activities and improve bear management in the optimal habitat, with which the goals of successful conservation of the species might be achieved.     

A metapopulation approach of the dynamics of arthropods from Mediterranean-type ecosystems

In this paper we developed a general stage-structured, Leslie-type model, suitable to simulate dynamics of soil arthropods under typical Mediterranean conditions. In order to explore arthropods’ life-history strategies in relation to enhanced spatial heterogeneity of the Mediterranean ecosystems, metapopulation characteristics were considered and different habitat quality regimes, in terms of dominant microclimatic conditions, were taken into account. Environmental stochasticity in temperature and humidity was incorporated into the model, and an elasticity analysis was conducted to quantify contribution of different life-history traits to metapopulation growth rate. The application of the model revealed well-known life-cycle characteristics of Mediterranean arthropods, such as seasonally fluctuating population sizes and skewing phenologies, a fact that confirms models’ reliability. Furthermore, the model seems able to elucidate controversial points of the animals’ life-cycle development, such as the long-term maintenance of populations in the field and the underlying mechanisms related to the adjustment to the specific features of the Mediterranean ecosystem. Subpopulations inhabiting various microsites display different dynamics and the interaction between these subpopulations, via dispersion, seems to be able to ensure stochastic equilibrium for the system. Dispersal appears to play a decisive role, allowing arthropods to conform to spatial severities and habitats fragmentation, rescuing individuals and recolonizing previously extinct habitats.     

An estimating function approach to the inference of catch-effort models

A class of catch-effort models, which allows for heterogeneous removal probabilities, is proposed for closed populations. The model includes three types of removal probabilities: multiplicative, Poisson and logistic. The usual removal and generalized removal models then become special cases. The equivalence of the proposed model and a special type of capture-recapture model is discussed. A unified estimating function approach is used to estimate the initial population size. For the homogeneous model, the resulting population size estimator based on optimal estimating functions is asymptotically equivalent to the maximum likelihood estimator. One advantage for our approach is that it can be extended to handle the heterogeneous populations in which the maximum likelihood estimators do not exist. The bootstrap method is applied to construct variance estimators and confidence intervals. We illustrate the method by two real data examples. Results of a simulation study investigating the performance of the proposed estimation procedure are presented.     

The response of the woodpigeon (Columba palumbus) to relaxation of intraspecific competition: A hybrid modelling approach

The recent rapid growth of the woodpigeon population in the British Isles is a cause for concern for environmental managers. It is unclear what has driven their increase in abundance. Using a mathematical model, we explored two possible mechanisms, reduced intraspecific competition for food and increased reproductive success. We developed an age-structured hybrid model consisting of a system of ordinary differential equations that describes density-dependent mortality and a discrete component, which represents the birth-pulse. We investigated equilibrium population dynamics using our model. The two hypotheses predict contrasting population age profiles at equilibrium. We adapted the model to examine the impacts of control measures. We showed that an annual shooting season that follows the period of density-dependent mortality is the most effective control strategy because it simultaneously removes adult and juvenile woodpigeons. The model is a first step towards understanding the processes that influence the dynamics of woodpigeon populations.     

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.     

Sensitivity of stand dynamics to grazing in mixed Pinus sylvestris and Quercus pubescens forests: A modelling study

Only recently, studies of forest succession have started to include the effects of browsing by wild or domestic ungulates. We aim to contribute to this topic by analysing the influence of goat grazing on the long-term coexistence of Scots pine (Pinus sylvestris L.) and pubescent oak (Quercus pubescens Willd.) in the low-elevation forests of an inner-Alpine dry valley. The forest gap model ForClim was first adapted to these site conditions by examining the site-dependent sensitivity of the model with regard to the species-specific parameterisation of the drought tolerance as well as the light demand of establishing and adult trees. In a second step, the behaviour of the model was investigated with respect to different grazing intensities and species-specific browsing susceptibilities. The last step was the application of a grazing scenario based on forest history, with 150 years of heavy browsing (by goats) at the beginning of the simulated forest succession, followed by less intensive grazing pressure.     

Effects of pollinator density-dependent preferences on field margin visitations in the midst of agricultural monocultures: A modelling approach

Managed field margins offer a means of reducing the impact of agricultural monocultures within intensively managed environments. By providing refuge for wild plants and the pollinators associated with them, field margins can also contribute to enhancing the pollination services within the monoculture. However, the effects of the monoculture on pollinator behaviour need to be carefully considered. It is known that pollinators may show density-dependent preferences such as neophobia (an avoidance of unfamiliar items) when different types of flower are available within their environment, and the dominance of monoculture crops within the environment may consequently have adverse effects upon the preferences shown by pollinators living in the field margins within them. In order to examine how pollinator preferences for wild flowers are affected by monocultures, we modelled the effects of density-dependent preferences, flower densities, and the geometry of field margins within a monoculture landscape using numerical simulations. This was done by considering how the placement of pollinator nests within a simple, spatially explicit landscape consisting of fields of monoculture crops separated by margins containing wild flowers affected the ratio of wild and monoculture crops experienced by the pollinator, given that it could only forage within a limited distance from its nest. Increasing field margin width and decreasing monoculture field width both led to an increase in pollinators visiting wild flowers (which levelled off as width increased). The size of the monoculture fields had little additional effect once they had passed an intermediate width. Increasing wild flower density within the margins led to a shift away from preferring monocultures. When wild flowers were at low densities compared to the monoculture, even the addition of small amounts of extra wild flowers had a large effect in shifting foraging preferences away from the monoculture. The distance which pollinators normally forage over only has an effect upon preferences for wild flowers when the travel distance is small. This suggests that careful consideration of margin design might be extremely important for those species which do not travel far. Innate preferences for density-dependence and particular crop types may also have an effect on preference behaviour. We demonstrate that the way in which resources are presented to indigenous pollinators may be extremely important in influencing where they choose to forage within agricultural landscapes. Careful margin design, as well as increasing the density of wild flowers (such as by enhancing the wild seed bank within the margins), may lead to overall improvements in ecosystem function within intensively farmed monocultures.     

The effects of disturbance based management on the dynamics of Mediterranean vegetation: A hierarchical and spatially explicit modeling approach

The eastern Mediterranean region has been subjected to intensive human disturbance in the past 10,000 years, mainly in the forms of agro-pastoral activities such as grazing, shrub clearing, and prescribed burning. This disturbance history resulted in the formation of highly heterogeneous landscapes, characterized by high biodiversity. Recent changes in human activities have resulted in a decrease of landscape heterogeneity, leading to decreasing biodiversity and increasing fire risk. To conserve heterogeneity, land managers apply disturbance based management practices, using the same activities that created and maintained landscape heterogeneity in the past. However, the long-term and large-scale outcomes of these disturbances are often unknown, due to the complex response of Mediterranean vegetation to disturbance. Here we report on a spatially explicit, hybrid, and spatially hierarchical ecological model developed by us. The model attempts to predict the outcome of various disturbance based management activities on the long-term spatio-temporal dynamics of five common Mediterranean vegetation types. The model uses a spatially explicit state and transition formulation, with continuous transition functions. Model simulations were conducted on a Mediterranean landscape in Northern Israel, incorporating various disturbance practices that are common in the region. Simulation results highlight the potential of disturbance based management as a tool for conserving landscape heterogeneity, as well as the complex interactions between disturbances and the spatial structure of the landscape in Mediterranean regions.     

A simulation model to evaluate the impacts of invasive earthworms on soil carbon dynamics

Recent studies have reported that earthworm invasions alter native communities and impact nutrient cycling in terrestrial ecosystems. We developed a simulation model to evaluate the potential impacts of earthworm invasions on carbon dynamics, taking into consideration earthworm feeding strategies and priming effects on the microorganisms through their casting activities. Responses of carbon stocks (forest litter, soil organic matter, microbial biomass and earthworm populations) and carbon fluxes (litter decomposition, earthworm consumption, and microbial respiration) were used to evaluate an earthworm invasion of a forest ecosystem. Data from a northern temperate forest (Arnot Forest, New York) were adapted for model calibration and evaluation. Simulation results suggest that the impact and outcome of earthworm invasions are affected by pre-invasion resource availability (litter and soil organic matter), invasive earthworm assemblages (particularly feeding strategy), and invasion history (associated with earthworm population dynamics). The abovementioned factors may also determine invasion progress of earthworm species. The accuracy of the model could be improved by the addition of environmental modules (e.g., soil water regimes), precise parameters accounting for individual species attributes under different environmental conditions (e.g. utilization ability of different types of food resources), as well as earthworm population dynamics (size and structure) and interactions with predators and other invasive/indigenous species during the invasion progress. Such an earthworm invasion model could provide valuable evaluation of the complicated responses of carbon dynamics to earthworm invasions in a range of forest ecosystems, particularly under global change scenarios.