Delay dynamics of the slug Deroceras reticulatum,an agricultural pest

Slugs are devastating agricultural and horticultural pests. However, their population dynamics are not well understood and this hinders the construction of efficient control strategies. This is especially true with organic farming for which biological controls are preferred. Moreover, the dominant species, Deroceras reticulatum, does not follow a regular annual life cycle, as do the majority of the other slug species. Its dominance may be associated with this fact. In this paper, we investigate whether mechanisms associated with the slugs’ time-delayed population dynamics are responsible for the large variations in numbers, with particular emphasis on their sensitivity to environmental conditions. In order to do this, several versions of a non-autonomous delay differential equation model are developed in which we highlight some of the contentious issues in slug modelling. Analyses of the models are combined with numerical experiments using parameters based upon controlled laboratory experiments. In the absence of seasonal forcing, we find that the delay term may be neglected in the simplest models. However, the presence of a predator dramatically increases the impact of the delay term and may drive a delay induced instability. Notably, we find that in all cases the delay term is of considerable qualitative importance in models which incorporate seasonal fluctuations. We highlight the fact that the models are capable of producing a large range of solution behaviour and, furthermore, discuss the conditions for, and thus the likelihood of their relevance.     

A simulation model of rhizome networks for Fallopia japonica (Japanese knotweed) in the United Kingdom

Fallopia japonica (Japanese knotweed) is an aggressively invasive herbaceous perennial that causes substantial economic and environmental damage in the United Kingdom (UK). As such, it is of considerable concern to councils, environmental groups, private landowners and property developers. We construct a 3D correlated random walk model of the development of the subterranean rhizome network for a single stand of F. japonica. The formulation of this model uses detailed knowledge of the morphology and physiology of the plant, both of which differ in the UK to that of its native habitat due to factors including a lack of predation and competition, longer growth seasons and favourable environmental conditions in the UK. Field data obtained as a part of this study are discussed and used in the model for parameterisation and validation. The simulation captures the field data well and predicts, for example, quadratic growth in time for the stand area. Furthermore, the role of a selection of parameters on long-term stand development are discussed, highlighting some key factors affecting vegetative spread rates.     

Population dynamics of natural colonies of <Emphasis Type="Italic">Aurelia</Emphasis> sp. scyphistomae in Tasmania,Australia

The aim of this study was to identify potential environmental controls of the asexual phases of reproduction by measuring the rates of asexual reproduction (budding and strobilation) and mortality in naturally occurring populations of Aurelia sp. scyphistomae at different spatial and temporal scales. The percentage cover, density of colonies of Aurelia sp. scyphistomae, and density of the population of two naturally occurring colonies of Aurelia sp. scyphistomae were examined over 2 years in southern Tasmania. Artificial substrates were also deployed to investigate colony dynamics when density dependent effects were reduced. Clear spatial and temporal differences in the population dynamics of the colonies were observed. Density dependent effects controlled budding and recruitment of new scyphistomae to the substrate when populations were dense and space limiting. In contrast, environmental controls of budding and strobilation were more apparent in a colony with significantly greater area of bare substrate and hence room for expansion. Water temperature and rainfall (as a proxy for salinity) were linked to changes in population size. Annual and seasonal differences in population dynamics were not observed in a colony limited by space but were apparent in a colony where space was not limited. When space was removed as a limiting factor by deploying artificial substrates, a seasonal environmental effect on the rate of growth of the colony was observed. These studies suggest that the growth, survival and reproduction of the sessile colonial phase of Aurelia sp. is regulated by a combination of density dependent factors and environmental conditions, which are consequently important to the formation of jellyfish blooms.     

Habitat and population modelling of roe deer using an interactive geographic information system

Management of German roe deer (Capreolus capreolus) populations is a challenge for wildlife managers and foresters because population densities are difficult to estimate in forests and forest regeneration can be negatively affected when roe deer density is high. We describe a model to determine deer population densities compatible with forest management goals, and to assess harvest rates necessary to maintain desired deer densities. A geographic information system (GIS) was used to model wildlife habitat and population dynamics over time. Our model interactively incorporates knowledge of field biologists and foresters via a graphical user interface (GUI). Calibration of the model with deer damage maps allowed us to evaluate density dependence of a roe deer population. Incorporation of local knowledge into temporally dynamic and spatial models increases understanding of population dynamics and improves wildlife management.     

Predicting changes in the Antarctic krill, Euphausia superba, population at South Georgia

Variability in the Southern Ocean is frequently reflected in changes in the abundance of Antarctic krill Euphausia superba and subsequent effects on dependent predators. However, the nature and consequences of changes in krill population dynamics that accompany fluctuations in its abundance are essentially unknown. A conceptual model, developed from quantitative measures of krill length in the diet of predators at South Georgia from 1991 to 1997, allowed predictions to be made about the abundance and population structure of krill in 1998 and the consequences for predators. Consistent with model predictions, in 1998 there was a serial change in krill population structure, low krill biomass and low reproductive performance of predators. The change in the modal size of krill, from 56 mm in December to 42 mm in March, was apparently a result of the transport of krill into the region. This is the first occasion when the future status and structure of the krill population at South Georgia has been successfully predicted. By representing local krill population dynamics, which may also reflect large-scale physical and biological processes, predators have a potential key role as indicators of environmental variation in the Southern Ocean at a range of spatial scales. Received: 6 March 1999 / Accepted: 3 September 1999     

Microclimate influence in a physiological model of cattle-fever tick (Boophilus spp.) population dynamics

Since their official eradication from the US in 1943, the cattle-tick species Boophilus microplus and Boophilus annulatus, vectors of bovine babesiosis, frequently have penetrated a quarantine zone established along the Texas–Mexico border designed to exclude them. Inspection and quarantine procedures have eradicated reinfestations successfully within the US, but increasing acaricide resistance in Mexican B. microplus populations poses a threat to future eradication efforts. Better understanding of interrelationships among Boophilus populations, their hosts, and vegetation communities in south Texas could improve prediction of the behavior of reintroduced Boophilus populations and increase management options. To this end, we constructed a simulation model to evaluate how microclimate, habitat (i.e. vegetation) heterogeneity, and within-pasture cattle movement may influence dynamics of Boophilus ticks in south Texas. Unlike previous Boophilus tick models, this model simulates dynamics at an hourly time-step, calculates all off-host dynamics as functions of temperature and relative humidity, and runs with ground-level microclimate data collected bi-hourly in three different habitat types. Sensitivity analysis of the model showed that temperatures and relative humidities created by habitat type, as well as engorged female mass, influenced tick population dynamics most strongly. Host habitat selection, initial number of larvae per cow, and the number of cells into which the simulated pasture was divided also had a strong influence. Population dynamics appeared moderately sensitive to the proportion of Bos indicus in cattle genotypes and the larval attachment rate, while appearing relatively insensitive to factors such as mortality rate of engorged females. When used to simulate laboratory experiments from the literature, the model predicted most observed life-history characteristics fairly well; however, it tended to underestimate oviposition duration, incubation duration, and egg mortality and overestimate larval longevity, especially at low temperatures and high humidities. Use of the model to predict Boophilus population dynamics in hypothetical south Texas pastures showed that it reasonably generated qualitative patterns of stage-wise abundances but tended to overestimate on-host tick burdens. Collection and incorporation of data that appear not to exist for Boophilus ticks, such as larval lipid content and lipid-use rates, may improve model accuracy. Though this model needs refinements such as a smaller spatial resolution, it provides insight into responses of B. microplus or B. annulatus populations to specific weather patterns, habitat heterogeneity, and host movement.     

The scale transition: scaling up population dynamics with field data

Applying the recent developments of scale transition theory, we demonstrate a systematic approach to the problem of scaling up local scale interactions to regional scale dynamics with field data. Dynamics on larger spatial scales differ from the predictions of local dynamics alone because of an interaction between nonlinearity in population dynamics at the local scale and spatial variation in density and environmental factors over the regional population. Our systematic approach to scaling up involves the following five steps. First, define a model for dynamics on the local spatial scale. Second, apply scale transition theory to identify key interactions between nonlinearity and spatial variation that translate local dynamics to the regional scale. Third, measure local-scale model parameters to determine nonlinearities at local scales. Fourth, measure spatial variation. Finally, combine nonlinearity and variation measures to obtain the scale transition. Using field data for the dynamics of grazers and periphyton in a freshwater stream, we show that scale transition terms greatly reduce the growth and equilibrium density of the periphyton population at the stream scale compared to rock scale populations, confirming the importance of spatial mechanisms to stream-scale dynamics.     

A nonparametric procedure for analyzing repeated measures of spatially correlated data

Many agricultural, biological, and environmental studies involve detecting temporal changes of a response variable, based on data observed at sampling sites in a spatial region and repeatedly over several time points. That is, data are repeated measures over time and are potentially correlated across space. The traditional repeated-measures analysis allows for time dependence but assumes that the observations at different sampling sites are mutually independent, which may not be suitable for field data that are correlated across space. In this paper, a nonparametric large-sample inference procedure is developed to assess the time effects while accounting for the spatial dependence using a block bootstrap. For illustration, the methodology is applied to describe the population changes of root-lesion nematodes over time in a production field in Wisconsin.     

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.     

Non-linear biological responses to disturbance: consequences on population dynamics

We assessed how non-linear biological responses to environmental noise, or “noise filtering”, impact the spectra of density-dependent population dynamics, and the correlation between noise and population dynamics. The noise was assumed to affect population growth rate in a discrete-time population model by Hassell [J. Anim. Ecol. 44 (1975) 283–295] where the population growth rate was linked to the environment with an optimum type filter. When compared to unfiltered noise, the filtered noise can distort the stationary distribution of population values. The optimum type filter can make cyclic population dynamics more regular and low population values can become more frequent or rare depending on the strength of density dependence. Filtering can cause blue shifted and red shifted population dynamics and determine the strength of correlation between environmental noise and population size. In most cases, optimum type filtering makes linear correlation between population dynamics and noise weaker. The filter effect on population spectra and noise versus population correlation is sensitive to changes in population model parameters, the location where noise hits the filter, and noise colour.     

Effect of sheep grazing and fire on sage grouse populations in southeastern Idaho

This paper describes the development, evaluation, and use of a model that simulates the effect of grazing and fire on temporal and spatial aspects of sagebrush community vegetation and sage grouse population dynamics. The model is represented mathematically as a discrete-time, stochastic compartment model based on difference equations with a time interval of 1 week. In the model, sheep graze through sage grouse breeding habitat during spring and fall, and different portions of the area can burn at different frequencies, creating a habitat mosaic of burned and unburned areas.The model was evaluated by examining predictions of (1) growth of sagebrush canopy cover after fire, (2) seasonal dynamics of grass and forb biomass under historical environmental conditions, and (3) sage grouse population dynamics associated with selected sagebrush canopy covers. Simulated changes in sagebrush canopy cover following fire correspond well with qualitative reports of long-term trends, simulated seasonal dynamics of herbaceous biomass correspond well with field data, and simulated responses of sage grouse population size and age structure to changing sagebrush canopy cover correspond well to qualitative field observations.Simulation results suggest that large fires occurring at high frequencies may lead to the extinction of sage grouse populations, whereas fires occurring at low frequencies may benefit sage grouse if burned areas are small and sheep grazing is absent. Sheep grazing may contribute to sage grouse population decline, but is unlikely to cause extinction under fire regimes that are favorable to sage grouse.     

Modelling crayfish population dynamics using catch data: A size-structured model

In this study we explore a rather unique time series (1979–2002) of catch data of the crayfish Astacus astacus in Lake Steinsfjorden (SE Norway) in combination with temperature data and data on Canadian pondweed Elodea canadensis coverage. In 1977, E. canadensis was for the first time observed in the lake. Over the following years, the plant established dense covers over large parts of the shallow areas, excluding the crayfish from these areas and causing a sudden drop in population size. A size-structured model with bi-stability including a range of observed stage-specific life-cycle attributes (e.g. growth, fecundity, fertility, sex-ratio), population specific parameters and density-dependant (shelters, cannibalism, unspecified predators, competition between individuals, catch, number of traps) as well as density independent factors (temperature and Elodea coverage) were constructed to evaluate the various drivers for the population dynamics, and as a predictive tool for assessing the effects of future changes. Our model revealed that the decline primarily was due to density-dependant effect of the Elodea expansion with reduced number of hides and thus increased risk for predation and cannibalism, but also that temperature played an important role related to recruitment. The model should be relevant for crayfish stock management in general, and by demonstrating the major role of temperature, it is also relevant for predicting population responses under a changing climate. The model should also be applicable to other crustaceans and species with discrete growth and late maturation.     

Spatial and temporal dynamics at manakin leks: reconciling lek traditionality with male turnover

Leks, display grounds where males congregate and females visit to copulate, are typically traditional in location, despite often high turnover of individual males. How leks can persist in face of male turnover is not well understood, in part due to a lack of detailed field data allowing for a clear understanding of lek dynamics. We followed the fate of individual males at 11 to 15 leks of the blue-crowned manakin Lepidothrix coronata across four breeding seasons to gain insights on how leks are formed and changed in space and time. Between years, leks were traditional in location despite changes in territory ownership due to male disappearance and recruitment. New males were equally likely to recruit by taking over existing territories or by establishing new territories. Recruitment was influenced by age, as recruits were more likely to be adults than subadults. Lek size did not affect the probabilities of a male recruiting or persisting at a territory, and vocalization rate, a correlate of mating success in this population, did not affect male persistence. We used our field data to model changes in lek size and composition over longer periods of time (100 years) to understand how lek traditionality can be reconciled with high male turnover. Our simulations showed that leks in our population rapidly stabilize in size despite changes in territory ownership and that rates of male recruitment and disappearance compensate each other, such that leks have the potential to persist for several decades after the original males have disappeared from them.     

Evaluation and application of a three-dimensional water quality model in a shallow lake with complex morphometry

Fundamental hydrodynamic and ecological processes of a lake or reservoir could be adequately depicted by one-dimensional (1D) numerical simulation models. Whereas, lakes with significant horizontal water quality and hydrodynamic gradients due to their complex morphometry, inflow or water level fluctuations require a three-dimensional (3D) hydrodynamics and ecological analyses to accurately simulate their temporal and spatial dynamics. In this study, we applied a 3D hydrodynamic model (ELCOM) coupled with an ecological model (CAEDYM) to simulate water quality parameters in three bays of the morphologically complex Lake Minnetonka. A considerable effort was made in setting up the model and a systematic parameterization approach was adopted to estimate the value of parameters based on their published values. Model calibration covered the entire length of the simulation periods from March 29 to October 20, 2000. Sensitivity analysis identified the top parameters with the largest contributions to the sensitivity of model results. The model was next verified with the same setup and parameter values for the period of April 25 to October 10, 2005 against field data. Spatial and temporal dynamics were well simulated and model output results of water temperature (T), dissolved oxygen (DO), total phosphorus (TP) and one group of algae (Cyanobacteria) represented as chlorophyll a (Chla) compared well with an extensive field data in the bays. The results show that the use of the model along with an accurate bathymetry, a systematic calibration and corroboration (verification) process will help to analyze the hydrodynamics and geochemical processes of the morphologically complex Lake Minnetonka. An example of an ecological application of the model for Lake Minnetonka is presented by examining the effect of spatial heterogeneity on coolwater fish habitat analysis in 3D and under a scenario where horizontal spatial heterogeneity was eliminated (1D). Both analyses captured seasonal fish habitat changes and the total seasonal averages differed moderately. However, the 1D analysis did not capture local and short duration variabilities and missed suitable fish habitat variations of as much as 20%. The experiment highlighted the need for a 3D analysis in depicting ecological hot spots such as unsuitable fish habitats in Lake Minnetonka.     

Temporal patterns of populations in a warming world: a modelling framework

In this paper, we present an approach for describing the environmentally induced temporal pattern of structured populations by partial integro-differential equations. Populations are structured according to size or stage. Growth, energy allocation and stage transitions are affected by environmental conditions of which temperature, photoperiod, water depth and food supply were taken into account. The resulting modelling framework was applied to describe, analyse and predict alterations in populations with continuous development, populations with distinct state structures and interacting populations. Our exemplary applications consider populations of freshwater Amphipoda, Isopoda and Odonata. The model was capable of simulating life cycle alterations in dependence on temperature in interaction with other environmental factors: (1) population dynamics, (2) seasonal regulation, (3) water depth-dependent dispersal, (4) intraguild predation and (5) consumer-resource dynamics.     

Atypical plant–herbivore association of algal food and a kleptoplastic sea slug (Elysia clarki) revealed by DNA barcoding and field surveys

The identity of food sources and feeding preferences of specialist herbivores have been commonly inferred from spatial associations between consumer and food items. However, such basic information for well-known marine herbivores, sacoglossans (sea slugs), and their algal diets remains disappointingly lacking, especially from field studies. The sacoglossan, Elysia clarki (Pierce et al. in Molluscan Res 26:23–38, 2006), is kleptoplastic and sequesters chloroplasts from algal food to photosynthesize, so DNA identification of sequestered chloroplasts was employed to verify the algal species fed upon by the slug across its geographic range. The molecular information on the algae consumed by E. clarki was combined with field surveys of slugs and algae in slug habitats in the Florida Keys in July and August of 2008 in order to evaluate whether the diet of this herbivore could be predicted based on its spatial association with algae in the field. A considerable mismatch between food availability and kleptoplast identity was recorded. E. clarki commonly occupied areas devoid of potential food and often contained symbiotic plastids from algal species different from those most frequently found in the surveyed habitats. In three of the four study sites, algal species present were poor predictors of slug diet. These findings suggest that the photosynthetic capability of E. clarki may release the slug from the constraint of requiring proximity to its food sources and may allow for the potential lack of spatial coupling between this herbivore and its algal food. This combination of field surveys and DNA barcoding provided critical and previously unavailable information on herbivore feeding in this marine system.     

Spatial variation in population dynamics in a colonial ascidian (Botryllus schlosseri)

Recent interest in the dynamics of marine invertebrate populations has focused largely on taxa with an open population structure. However, in many colonial taxa with limited larval dispersal, settlers may be locally derived. Consequently, dynamics may vary among sites that are separated by relatively short distances. This study explored spatial variation in temporal dynamics of colonial ascidians (Botryllus schlosseri Pallas) inhabiting five sites distributed along a ≈ 17-km temperature and phytoplankton gradient in the Damariscotta River estuary, Maine, USA. Settlement and population densities and sexual reproductive status were assayed throughout the summer seasons of 1996 and 1997. Sexual reproduction and larval settlement commenced earlier in the summer in up-river populations, which subsequently underwent a seasonal population explosion that was much smalier in down-river populations. Two peaks in settlement density up-river (in early July and early September) suggest that colonies there may have completed two sexual generations, in contrast to a single generation at down-river sites. Similar spatial variation is expected among populations of other taxa with limited larval dispersal when they are distributed across environmental gradients. Published online: 18 September 2002     

Modeling individual and population dynamics in a consumer–resource system: Behavior under food limitation and crowding and the effect on population cycling in Daphnia

In population modeling, a considerable level of complexity is often required to provide trustworthy results, comparable with field observations. By assuring sufficient detail at the individual level while preserving the potential to explore the consequences at higher levels, individual-based modeling may thus provide a useful tool to investigate dynamics at different levels of organization. Still, population dynamics resulting from such models are often at odds with observations from the field. This may be partly caused by a lack of focus on the individual dynamics under conditions of food stress and starvation. I developed a physiologically structured, individual-based simulation model to investigate life history of Daphnia and its effect on population dynamics in response to the productivity of the system. In verifying model behavior with available literature data on life history and physiology, I paid special attention to the dynamics of food intake and the verification of individual level results under conditions of food limitation and starvation. I show that the maximum filtering rates under low food levels used in the current model are much closer to measured filtering rates than the ones used in other models. Being consistent with results on physiology and life history from experiments at a wide range of food availability (including starvation), the model generates low amplitude or high amplitude population density cycles depending on the productivity of the system, as observed in field and experimental populations of Daphnia and with the minimum population densities being one to two orders of magnitude lower in the high amplitude than in the low amplitude cycles. To generate results which are not only qualitatively but also quantitatively comparable to experimental and field observations, however, a crowding effect on the filtering response has to be incorporated in the model.     

Estimating the functional form for the density dependence from life history data

Two contrasting approaches to the analysis of population dynamics are currently popular: demographic approaches where the associations between demographic rates and statistics summarizing the population dynamics are identified; and time series approaches where the associations between population dynamics, population density, and environmental covariates are investigated. In this paper, we develop an approach to combine these methods and apply it to detailed data from Soay sheep (Ovis aries). We examine how density dependence and climate contribute to fluctuations in population size via age- and sex-specific demographic rates, and how fluctuations in demographic structure influence population dynamics. Density dependence contributes most, followed by climatic variation, age structure fluctuations and interactions between density and climate. We then simplify the density-dependent, stochastic, age-structured demographic model and derive a new phenomenological time series which captures the dynamics better than previously selected functions. The simple method we develop has potential to provide substantial insight into the relative contributions of population and individual-level processes to the dynamics of populations in stochastic environments.     

Chromium in intertidal sediments of the Clyde,UK: potential for remobilisation and bioaccumulation

Detailed surveys of intertidal sediments have been performed along the north and south shores of the Inner Clyde estuary, UK. Surface sediment data reveal significant spatial variation in Cr content and an association with major sediment characteristics and location within the estuary. Depth variation for Cr and other heavy metals cannot be explained by variation in major geochemical controls such as grain size and organic matter and highlights the impact of historical contamination on sediment quality. These elevated levels at depth may still have environmental impact through redox-reactivity, in association with iron and manganese. Sequential extraction of sediments and pore water analysis of Cr(VI) and Cr(III) provide detailed information on release potential from the sediments. The implication of Cr mobility for biota in the estuary has been assessed by the analysis of a common marine bivalve, Mytilus edulis (Blue Mussel) and a burrowing polychaete, Nereis diversicolor (rag worm) from a number of survey sites. Bioconcentration factors for Mytilus indicate that the weakly held portion of sediment Cr is available for uptake and in the case of Nereis, bioaccumulation appears to be inhibited by sediment organic matter.