Managing plant population spread: prediction and analysis using a simple model

Models can be used to direct the management of population spread for the control of invasives or to encourage species of conservation value. Analytical models are attractive because of their theoretical basis and limited data requirements, but there is concern that their simplicity may limit their practical utility. We address the applied use of simple models in a study of a declining annual herb, Rhinanthus minor. We parameterized a population-spread model using field data on demography and dispersal for four management systems: grazed only (GR), hay-cut once (H1), hay-cut twice (H2), and hay-cut with autumn grazing (HG). Within a replicated experiment we measured spread rates of introduced R. minor populations over eight years. The modeled and measured spread rates were very similar in terms of both patterns of management effects and absolute values, so that in both cases HG > H2, H1 > GR. The treatments affected both dispersal and demography (establishment and survival) and so we used decomposition approaches to analyze the major causes of differences in population spread. Increased dispersal under hay-cutting was more important than demographic changes and accounted for approximately 70% of the differences in spread rate between the hay-cut and grazed-only treatments. Furthermore, management effects on the tail of the dispersal curve were by far the most critical in governing spread. This study suggests that simple models can be used to inform practical conservation management, and we demonstrate straightforward uses of our model to predict the impacts of different management strategies. While simple models can give accurate projections, we emphasize that they must be parameterized with high-quality data gathered at the appropriate spatial scale.     

Seed terminal velocity, wind turbulence, and demography drive the spread of an invasive tree in an analytical model

Little is known about the relative importance of mechanistic drivers of plant spread, particularly when long-distance dispersal (LDD) events occur. Most methods to date approach LDD phenomenologically, and all mechanistic models, with one exception, have been implemented through simulation. Furthermore, the few recent mechanistically derived spread models have examined the relative role of different dispersal parameters using simulations, and a formal analytical approach has not yet been implemented. Here we incorporate an analytical mechanistic wind dispersal model (WALD) into a demographic matrix model within an analytical integrodifference equation spread model. We carry out analytical perturbation analysis on the combined model to determine the relative effects of dispersal and demographic traits and wind statistics on the spread of an invasive tree. Models are parameterized using data collected in situ and tested using independent data on historical spread. Predicted spread rates and direction match well the two historical phases of observed spread. Seed terminal velocity has the greatest potential influence on spread rate, and three wind properties (turbulence coefficient, mean horizontal wind speed, and standard deviation of vertical wind speed) are also important. Fecundity has marginal importance for spread rate, but juvenile survival and establishment are consistently important. This coupled empirical/theoretical framework enables prediction of plant spread rate and direction using fundamental dispersal and demographic parameters and identifies the traits and environmental conditions that facilitate spread. The development of an analytical perturbation analysis for a mechanistic spread model will enable multispecies comparative studies to be easily implemented in the future.     

Temporal limits to simulating the future spread pattern of invasive species: Buddleja davidii in Europe and New Zealand

The spread of invasive species is a major ecological and economic problem. Dynamic spread modelling is a potentially valuable tool to assist regional and central government authorities to monitor and control invasive species. To date a lack of suitable data has meant that most broad scale dispersal models have not been validated with independent datasets, and so their predictive ability and reliability has remained unscrutinised. A dynamic, stochastic dispersal model of the widely invasive plant Buddleja davidii was calibrated on European spread data and then used to project the temporal progression of B. davidii's distribution in New Zealand, starting from several different historical distributions. To assess the model's performance, we constructed an occupancy map based on the average number of simulation realisations that have a population present. The application of Receiver Operating Characteristic (ROC) curves to occupancy maps is introduced, but with specificity substituted by the proportion of available area used in a realisation. A derivative measure, the partial area under these curves when assessed through time (pAUC), is introduced and used to assess overall performance of the spread model. The model was able to attain a high level of model sensitivity, encompassing all of the known locations within the occupancy envelope. However, attempting to simulate the spread of this invasive species beyond a decade had very low model specificity. This is due to several factors, including the exponential process of spread (the further a population spreads the more sites exist from which it can spread stochastically), and the Markovian chain property of the stochastic system whereby differences between realisations compound through time. These features are seen in many reports of spread models, without being explicitly acknowledged. Our measure of pAUC through time allows a model's temporal performance and its specificity to be simultaneously assessed. While the rapid deterioration in model performance limits the utility of this type of modelling for forecasting long-term broad-scale strategic management of biological invasions, it does not necessarily limit its attractiveness for informing smaller scale and shorter term invasion management activities such as surveillance, containment and local eradication.     

The interplay of sex ratio, male success and density-independent mortality affects population dynamics

Environmental constraints can limit a population to a certain size, which is usually called the carrying capacity of a habitat. Besides to this ‘external’ factor, which is mainly determined by the limitation of resources, we investigate here another set of population-intrinsic factors that can limit a population size significantly below the maximum sustainable size. Firstly, density-independent mortality is a prominent factor in all organisms that show age-related and/or accidental death. Secondly, in sexually reproducing organisms the sex ratio and the success of pairing is important for finding reproductive partners. Using a simple model, we demonstrate how sex ratio, mating success and gender-specific mortality can strongly affect the speed of population growth and the maximum population size. In addition, we demonstrate that density-independent mortality, which is often neglected in population models, adds a very important feature to the system: it strongly enhances the negative influence of unbiased sex ratios and inefficient pairing to the maximum sustainable population size. A decrease of the maximum population size significantly affects a population's survival chance in inter-specific competition. Thus, we conclude that the inclusion of density-independent mortality is crucial, especially for models of species that reproduce sexually. We show that density-independent mortality, together with biased sex ratios, can significantly lower the abilities of a population to survive in conditions of strong inter-specific competition and due to the Allee effect. We emphasize that population models should incorporate the sex ratio, male success and density-independent mortality to make plausible predictions of the population dynamics in a gender-structured population. We show that the population size is limited by these intrinsic factors. This is of high ecological significance, because it means that there will always be resources available in any habitat that allows other species (e.g., invaders) to use these resources and settle successfully, if they are sufficiently adapted.     

Predicting regional spread of non-native species using oceanographic models: validation and identification of gaps

Predicting spread is a central goal of invasion ecology. Within marine systems, researchers have increasingly made use of oceanographic circulation models to estimate currents and track species dispersal. However, the accuracy of these models for predicting biological patterns, particularly for non-native species, has generally not been validated. Particularly, we wished to examine the ability of models to predict physical and biological processes, which jointly determine the spread of marine larval organisms. We conducted two empirical studies—a recruitment study and a drift card study—along the coast of New England, USA, focusing on two invaders of concern—the European green crab (Carcinus maenas) and the Asian shore crab (Hemigrapsus sanguineus), to explicitly evaluate the ability of oceanographic models to predict patterns of spread. We used data from the large-scale drift card study to validate our ability to capture dispersal patterns driven purely by physical processes. Next, we conducted a recruitment study to evaluate our ability to reproduce patterns of biological dispersal. We were generally capable of reproducing drift cards patterns—suggesting that the physical mechanics in the model were predictive. However, predicted biological patterns were inconsistent—we were able to predict dispersal patterns for H. sanguineus but not for C. maenas. Our results highlight the importance of validating models and suggest that more work is necessary before we can reliably use oceanographic models to predict biological spread of intertidal organisms.     

Importance of individual and environmental variation for invasive species spread: a spatial integral projection model

Plant survival, growth, and flowering are size dependent in many plant populations but also vary among individuals of the same size. This individual variation, along with variation in dispersal caused by differences in, e.g., seed release height, seed characteristics, and wind speed, is a key determinant of the spread rate of species through homogeneous landscapes. Here we develop spatial integral projection models (SIPMs) that include both demography and dispersal with continuous state variables. The advantage of this novel approach over discrete-stage spread models is that the effect of variation in plant size and size-dependent vital rates can be studied at much higher resolution. Comparing Neubert-Caswell matrix models to SIPMs allowed us to assess the importance of including individual variation in the models. As a test case we parameterized a SIPM with previously published data on the invasive monocarpic thistle Carduus nutans in New Zealand. Spread rate (c*) estimates were 34% lower than for standard spatial matrix models and stabilized with as few as seven evenly distributed size classes. The SIPM allowed us to calculate spread rate elasticities over the range of plant sizes, showing the size range of seedlings that contributed most to c* through their survival, growth and reproduction. The annual transitions of these seedlings were also the most important ones for local population growth (lambda). However, seedlings that reproduced within a year contributed relatively more to c* than to lambda. In contrast, plants that grow over several years to reach a large size and produce many more seeds, contributed relatively more to lambda than to c*. We show that matrix models pick up some of these details, while other details disappear within wide size classes. Our results show that SIPMs integrate various sources of variation much better than discrete-stage matrix models. Simpler, heuristic models, however, remain very valuable in studies where the main goal is to investigate the general impact of a life history stage on population dynamics. We conclude with a discussion of future extensions of SIPMs, including incorporation of continuous time and environmental drivers.     

Spatial uncertainty analysis of population models

This paper describes an approach for conducting spatial uncertainty analysis of spatial population models, and illustrates the ecological consequences of spatial uncertainty for landscapes with different properties. Spatial population models typically simulate birth, death, and migration on an input map that describes habitat. Typically, only a single “reference” map is available, but we can imagine that a collection of other, slightly different, maps could be drawn to represent a particular species’ habitat. As a first approximation, our approach assumes that spatial uncertainty (i.e., the variation among values assigned to a location by such a collection of maps) is constrained by characteristics of the reference map, regardless of how the map was produced. Our approach produces lower levels of uncertainty than alternative methods used in landscape ecology because we condition our alternative landscapes on local properties of the reference map. Simulated spatial uncertainty was higher near the borders of patches. Consequently, average uncertainty was highest for reference maps with equal proportions of suitable and unsuitable habitat, and no spatial autocorrelation. We used two population viability models to evaluate the ecological consequences of spatial uncertainty for landscapes with different properties. Spatial uncertainty produced larger variation among predictions of a spatially explicit model than those of a spatially implicit model. Spatially explicit model predictions of final female population size varied most among landscapes with enough clustered habitat to allow persistence. In contrast, predictions of population growth rate varied most among landscapes with only enough clustered habitat to support a small population, i.e., near a spatially mediated extinction threshold. We conclude that spatial uncertainty has the greatest effect on persistence when the amount and arrangement of suitable habitat are such that habitat capacity is near the minimum required for persistence.     

Unveiling human-assisted dispersal mechanisms in invasive alien insects: Integration of spatial stochastic simulation and phenology models

Capturing the spread of biological invasions in heterogeneous landscapes is a complex modelling task where information on both dispersal and population dynamics needs to be integrated. Spatial stochastic simulation and phenology models have rarely been combined to assist in the study of human-assisted long-distance dispersal events.Here we develop a process-based spatially explicit landscape-extent simulation model that considers the spread and detection of invasive insects. Natural and human-assisted dispersal mechanisms are modelled with an individual-based approach using negative exponential and negative power law dispersal kernels and gravity models. The model incorporates a phenology sub-model that uses daily temperature grids for the prediction and timing of the population dynamics in each habitat patch. The model was applied to the study of the invasion by the important maize pest western corn rootworm (WCR) Diabrotica virgifera ssp. virgifera in Europe. We parameterized and validated the model using maximum likelihood and simulation methods from the historical invasion of WCR in Austria.WCR was found to follow stratified dispersal where international transport networks in the Danube basin played a key role in the occurrence of long-distance dispersal events. Detection measures were found to be effective and altitude had a significant effect on limiting the spread of WCR. Spatial stochastic simulation combined with phenology models, maximum likelihood methods and predicted versus observed regression showed a high degree of flexibility that captured the salient features of WCR spread in Austria. This modelling approach is useful because it allows to fully exploit and the often limited and heterogeneous information available regarding the population dynamics and dispersal of alien invasive insects.     

A Comparison of Corridors and Intrinsic Connectivity to Promote Dispersal in Transient Successional Landscapes

Low-vagility organisms that specialize on transitory successional habitats may be especially dependent upon habitat connectivity to maintain population viability. We analyzed the theoretical intrinsic connectivity of successional landscapes (i.e., the natural juxtaposition of similar habitats that allows dispersal) as a function of patch geometry coupled with the disperser's habitat specificity. Habitat specialists living in poorly connected landscapes (approximating hexagonal patches) have only a 26.5% chance of colonizing a new site when their resident patch becomes unsuitable. In contrast, generalists living in well connected landscapes can virtually always colonize a new site when needed. We infer from our simulation that for some habitat specialists, such as the rare, endemic Florida scrub lizard (Sceloporus woodi), anthropogenic control of successional dynamics for commercial logging may significantly reduce intrinsic connectivity. Lizard population viability may now depend upon the extrinsic connectivity provided by artificial corridors. However, the use of corridors will not serve as a general solution to the problem of anthropogenically reduced intrinsic connectivity until key logistical design problems have been resolved. Moreover, efforts to enhance intrinsic connectivity by modifying patch geometry may produce undesirable edge effects and conflict with old-growth preservation. Future research should focus on developing spatially explicit corridor models, documenting natural levels of intrinsic connectivity, quantifying anthropogenic disruption of natural connectivity, and describing species-specific mechanisms of inter-patch dispersal.     

Is spread of invasive species regulated? Using ecological theory to interpret statistical analysis

We investigate a recent proposal that invasive species display patterns of spatial "spread regulation" analogous to density-dependent regulation of population abundances. While invasive species do offer valuable tests of ecological theories about spatial spread, we argue that the statistical approach used in the study is not useful, and that the proposed definition of "spread regulation" is likely to be confusing. While concepts of negative feedbacks in spatial spread may be reasonable, the proposed definition of "spread regulation" encompasses accelerating, constant, or decelerating spread. There is no compelling biological or practical reason to adopt such a definition. Moreover, we show that the statistical patterns (from time series of ratios of newly to recently invaded sites) proposed as evidence of spread regulation are predictable from basic diffusion models or other common models of constant spread with some stochasticity in dynamics and/or observations. Because such a wide range of processes would generate the observed patterns, no clear biological conclusions emerge from the proposed approach to spread analysis. When regarded in the context of the impacts and management of invasive species, the proposed regulation concept has the potential to create costly misunderstandings.     

Local population dynamics of an invasive tree species with a complex life-history cycle: A stochastic matrix model

Biological invasions are widely accepted as having a major impact on ecosystem functioning worldwide, giving urgency to a better understanding of the factors that control their spread. Modelling tools have been developed for this purpose but are often discrete-space, discrete-time spatial-mechanistic models that adopt a computer simulation approach and resist mathematical analysis. We constructed a simple demographic matrix model to explore the local population dynamics of an invasive species with a complex life history and whose invasive success depends on resource availability, which occurs stochastically. As a case study we focused on the American black cherry (Prunus serotina Ehrh.), a gap-dependent tree able both to constitute a long-living seedling bank under unfavourable light conditions and to resprout vigorously once cut-down, which is invading European temperate forests. The model used was a stage-classified matrix population model (i.e., Lefkovitch matrix), integrating environmental stochasticity. Stochastic matrix projection analysis was combined with elasticity analysis and stochastic simulations to search for the species’ ‘Achille heel’. As expected, the population growth rate (i.e., Lyapunov exponent), which measures the risk of P. serotina invasion at the stand scale, increased with light frequency. There was a critical value above which the population of P. serotina explodes and below which it locally goes extinct. The resprouting capacity usually speed up the invasion but appeared to play a minor role. The mean duration of stand invasion was measured and important life stage transitions that mostly contribute to the local stochastic growth rate were identified. Some relevant management implications are discussed and the interest of such models for the understanding of demographic characteristics of invasive species is stressed.     

The growth response of a model Gymnodinium splendens in stationary and wavy water columns

A computer model is used to investigate the simulated growth of a theoretical dinoflagellate resembling Gymnodinium splendens in response to a variety of field conditions. Literature data on G. splendens are combined with probable estimates of organism response (where direct data are lacking) to yield light-and temperature-dependent production curves. These production curves are superimposed on a physical model characterized by a diurnally variable light cycle, by a two-layered water column (16°C water overlaying 12°C water) of variable layer thicknesses, and by variable extinction coefficients in the upper layer. The water column is either stationary or perturbed by a semidiurnal (12.4 h) internal wave. Organism behavior ranges from the continuous occupation of selected strata (stationary or wavy) to diurnal vertical migrations within the upper layer or across the thermocline. In stationary water columns, species patchiness depends on spatial differences in the depth preferences of nonmigrating organisms or in the details of the behavior of migrating organisms. In water columns perturbed by a semidiurnal internal wave, spatial differences in the phase relationship between the wave form and daylight supplement organism behavior as a source of patchiness. The models result in their most complex spatial patterns when a population migrates through a thermocline perturbed by a semidiurnal internal wave.University of Texas Marine Science Institute Contribution No. 280.     

A general random walk model for the leptokurtic distribution of organism movement: Theory and application

The movement of organisms is usually leptokurtic in which some individuals move long distances while the majority remains at or near the area they are released. There has been extensive research into the origin of such leptokurtic movement, but one important aspect that has been overlooked is that the foraging behaviour of most organisms is not Brownian as assumed in most existing models. In this paper we show that such non-Brownian foraging indeed gives rise to leptokurtic distribution. We first present a general random walk model to describe the organism movement by breaking the foraging of each individual into events of active movement and inactive stationary period; its foraging behaviour is therefore fully characterized by a joint probability of how far the individual can move in each active movement and the duration it remains stationary between two consecutive movements. The spatio-temporal distribution of the organism can be described by a generalized partial differential equation, and the leptokurtic distribution is a special case when the stationary period is not exponentially distributed. Empirical observations of some organisms living in different habitats indicated that their rest time shows a power-law distribution, and we speculate that this is general for other organisms. This leads to a fractional diffusion equation with three parameters to characterize the distributions of stationary period and movement distance. A method to estimate the parameters from empirical data is given, and we apply the model to simulate the movement of two organisms living in different habitats: a stream fish (Cyprinidae: Nocomis leptocephalus) in water, and a root-feeding weevil, Sitona lepidus in the soil. Comparison of the simulations with the measured data shows close agreement. This has an important implication in ecology that the leptokurtic distribution observed at population level does not necessarily mean population heterogeneity as most existing models suggested, in which the population consists of different phenotypes; instead, a homogeneous population moving in homogeneous habitat can also lead to leptokurtic distribution.     

Modeling range dynamics in heterogeneous landscapes: invasion of the hemlock woolly adelgid in eastern North America

Range expansion by native and exotic species will continue to be a major component of global change. Anticipating the potential effects of changes in species distributions requires models capable of forecasting population spread across realistic, heterogeneous landscapes and subject to spatiotemporal variability in habitat suitability. Several decades of theory and model development, as well as increased computing power and availability of fine-resolution GIS data, now make such models possible. Still unanswered, however, is the question of how well this new generation of dynamic models will anticipate range expansion. Here we develop a spatially explicit stochastic model that combines dynamic dispersal and population processes with fine-resolution maps characterizing spatiotemporal heterogeneity in climate and habitat to model range expansion of the hemlock woolly adelgid (HWA; Adelges tsugae). We parameterize this model using multiyear data sets describing population and dispersal dynamics of HWA and apply it to eastern North America over a 57-year period (1951-2008). To evaluate the model, the observed pattern of spread of HWA during this same period was compared to model predictions. Our model predicts considerable heterogeneity in the risk of HWA invasion across space and through time, and it suggests that spatiotemporal variation in winter temperature, rather than hemlock abundance, exerts a primary control on the spread of HWA. Although the simulations generally matched the observed current extent of the invasion of HWA and patterns of anisotropic spread, it did not correctly predict when HWA was observed to arrive in different geographic regions. We attribute differences between the modeled and observed dynamics to an inability to capture the timing and direction of long-distance dispersal events that substantially affected the ensuing pattern of spread.     

Smashing tests? Patterns and mechanisms of adult mortality in a declining echinoid population

Mass mortality of echinoids is well documented, and has potentially profound effects on benthic communities. However, no study to date has quantitatively investigated how regular, predictable events such as winter storms might lead to large mortality events in pivotal echinoid species. Hydrodynamic disturbances can be major drivers of crucial biological processes in benthic communities. For echinoid populations in particular, wave action in shallow waters generated by high winds (winter storms) can cause displacement, damage and even death to individuals. However, evidence for displacement-mediated mortality is scant in the literature, in part because it is so difficult to demonstrate in exposed environments where echinoids are frequently found. In this study, we examined mortality in a sheltered subtidal population of the European purple sea urchin Paracentrotus lividus over a 3-year period, and examined the role that dislodgement by wave action or predation might play in these mortality patterns. Because our study population has been in decline for the past three decades, we considered it important to evaluate its current status in addition to assessing the contribution that adult mortality makes to that decline. We sampled twice per month, using the density of freshly dead echinoid material to assess the extent of adult mortality. The Irish Meteorological Service provided our estimates of wind speed data. We compared historical and recent data on P. lividus size frequency data to investigate change the population structure (Poor recruitment would be caused by failure to spawn over a prolonged period). Our data suggest ongoing declines in this population, and support the theory that the decline of the P. lividus population of Lough Hyne is a result of persistent recruitment failure linked to repeated cool maximum sea surface temperatures. Although we found peaks of P. lividus mortality were coincident with spikes in wind speed, mortality was low, and seems unlikely to have contributed significantly to the dramatic decline in P. lividus in the past three decades.Communicated by J.P. Thorpe, Port Erin     

Ecotoxicology and population dynamics: Using DEBtox models in a Leslie modeling approach

Although the ecological risks of toxic chemicals are usually assessed on the basis of individual responses, such as survival, reproduction or growth, ecotoxicologists are now attempting to assess the impact of environmental pollution on the dynamics of naturally exposed populations. The main issue is how to infer the likely impact on the population of the toxic effects observed at the individual level. Dynamic energy budget in toxicology (DEBtox) is the most user-friendly software currently available to analyze the experimental data obtained in toxicity tests performed on individuals. Because toxic effects are diverse and because the sensitivity of individuals varies considerably depending on life-cycle stage, Leslie models offer a convenient way of predicting toxicant effects on population dynamics.In the present study, we first show how parameter inputs, estimated from individual data using DEBtox, can be coupled using a Leslie matrix population model. Then, using experimental data obtained with Chironomus riparius, we show how the effects of a pesticide (methiocarb) on the population growth rate of a laboratory population can be estimated. Lastly, we perform a complex sensitivity analysis to pinpoint critical age classes within the population for the purposes of the field management of populations.     

Estimating dispersal potential for marine larvae: dynamic models applied to scleractinian corals

Dispersal influences ecological dynamics, evolution, biogeography, and biodiversity conservation, but models of larval dispersal in marine organisms make simplifying assumptions that are likely to approximate poorly the temporal dynamics of larval survival and capacity for settlement. In particular, larval mortality rates are typically assumed to be constant throughout larval life; and all larvae are frequently assumed to acquire and lose competence at the same time. To improve upon these assumptions, we here develop simple models of dispersal potential that incorporate rates of mortality, and acquisition and loss of settlement competence. We fit these models to empirical competence and survival data for five scleractinian coral species, to test the models' ability to characterize empirical survival and competence patterns, and to estimate the dispersal potential implied by those patterns. The models fit the data well, incorporating qualitative features of competence and survival that traditional approaches to modeling dispersal do not, with important implications for dispersal potential. Most notably, there was high within-cohort variation in the duration of the competent period in all species, and this variation increases both self-recruitment and long-distance dispersal compared with models assuming a fixed competent period. These findings help to explain the seeming paradox of high genetic population structure, coupled with large geographic range size, observed in many coral species. More broadly, our approach offers a way to parsimoniously account for variation in competence dynamics in dispersal models, a phenomenon that our results suggest has important effects on patterns of connectivity in marine metapopulations.     

遥感水文耦合模型的研究进展

遥感水文的耦合模型在目前生态环境领域,特别是在水资源的应用和管理中其作用日益重要,具有大流域尺度上快速应用、实时动态监测等优点。结合国内外近年来取得的研究成果,文章综述了遥感水文耦合模型的研究进展。首先介绍了遥感技术在水文学中的应用,讨论了它的分类发展概况,接着介绍了几种主要的遥感水文耦合模型及其应用实例,包括SCS(SoilConservationServices)模型、SiB2(SimpleBiosphereModelversion2)简化生物圈模型、SRM(SnowmeltRunoffModel)融雪径流模型以及SWAT(SoilandWaterAssessmentTool)模型,最后展望了遥感水文耦合模型未来的发展趋势,指出尺度问题上的时空变异性仍是其发展的关键,与GIS(Geographicinformationsystem)及其他空间技术的相结合是其未来发展的重要方向,从而为水文学、水资源的预测评价等研究提供参考。     

Composite forces shape population dynamics of copepod crustaceans

Understanding the processes that control species abundance and distribution is a major challenge in ecology, yet for a large number of potentially important organisms, we know little about the biotic and abiotic factors that influence population size. One group of aquatic organisms that defies traditional demographic analyses is the Crustacea, particularly those with complex life cycles. We used likelihood techniques and information theoretics to evaluate a suite of models representing alternative hypotheses on factors controlling the abundance of two copepod crustaceans in a small, tropical floodplain lake. Quantitative zooplankton samples were collected at three stations in a Venezuelan floodplain lake from June through December 1984; the average sampling interval was two days. We constructed a series of models with stage structure that incorporated six biotic and abiotic covariates in various combinations to account for temporal changes in abundance of these target species and in their population growth rates. Our analysis produced several novel insights into copepod population dynamics. We found that multiple forces affected the abundance of particular stages, that these factors differed between species as well as among stages within each species, and that biotic processes had the largest effects on copepod population dynamics. Density dependence had a large effect on the survival of Oithona amazonica copepodites and on population growth rate of Diaptomus negrensis.     

A distance dependent contagion function for vector-based data

Landscape pattern is of primary interest to landscape ecologists and landscape metrics are used to quantify landscape pattern. Metrics are commonly defined and calculated on raster-based land cover maps. One metric is the contagion, existing in several versions, e.g., unconditional and conditional, used as a measure of fragmentation. However, mapped data is sometimes in vector-based format or there may be no mapped data but only a point sample. In this study a definition of contagion for such cases is investigated. The metric is an extension of the usual contagion, based on pairs of points at varying distances and gives a function of the distance. In this study the extended contagion is calculated for vector-based delineated real landscapes and for simulated ones. Both unconditional and conditional contagions are studied using two classification systems. The unconditional contagion function was decreasing and convex, with upper and lower limits highly correlated to the Shannon diversity index, thus carrying only area proportion information. The spatial information lies in the speed by which the function converges to the lower limit; using a proxy function this can be expressed by a single parameter b, with high values for fragmented landscapes. No proxy function was found for the conditional contagion, for which only qualitative information was found. The extended contagion is applicable both in patch mosaic models of landscapes and in gradient-based models, where landscape characteristics change continuously without distinct borders between patches. The extended contagion can be useful in sample based surveys where there no map of the entire landscape is available.