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.     

Hidden process models for animal population dynamics.

Hidden process models are a conceptually useful and practical way to simultaneously account for process variation in animal population dynamics and measurement errors in observations and estimates made on the population. Process variation, which can be both demographic and environmental, is modeled by linking a series of stochastic and deterministic subprocesses that characterize processes such as birth, survival, maturation, and movement. Observations of the population can be modeled as functions of true abundance with realistic probability distributions to describe observation or estimation error. Computer-intensive procedures, such as sequential Monte Carlo methods or Markov chain Monte Carlo, condition on the observed data to yield estimates of both the underlying true population abundances and the unknown population dynamics parameters. Formulation and fitting of a hidden process model are demonstrated for Sacramento River winter-run chinook salmon (Oncorhynchus tshawytsha).     

Mathematical equivalence of geometric mean fitness with probabilistic optimization under environmental uncertainty

Natural selection can be considered as optimising fitness. Because ‘mean’ fitness is maximized with respect to the genotypes of carriers, traditional theory can be viewed as a statistical theory of natural selection. Probabilistic optimisation is a way to incorporate such uncertainty into optimality analyses of natural selection, where environmental uncertainty is expressed as a probability distribution. Its canonical form is a weighted average of fitness with respect to a given probabilistic distribution. This concept should be applicable to three different levels of uncertainty: (1) behavioural variations of an individual, (2) individual variations within a generation, and (3) temporal change over generations (geometric mean fitness). The former two levels are straightforward with many empirical evidences, but the last category, the geometric mean fitness, has not well understood. Here we studied the geometric mean fitness by taking its logarithm, where the log growth rates become the fitness value. By further transforming the log growth rates, the fitness of log growth rates becomes its linear function. Therefore, a simple average of these distributions becomes the fitness measure across generations and consideration of variance discount or the entire probability distributions becomes unnecessary. We discuss some characteristic features of probabilistic optimization in general. Our view is considered a probabilistic view of natural selection, in contrast with the traditional statistical view of natural selection.     

Modelling of spatio-temporal population dynamics of earthworms under wetland conditions—An integrated approach

Both the effects of earthworms on soils and the effects of soil conditions on earthworms have been studied with the help of experiments and modelling. This paper provides a model architecture allowing coupling both effects to a dynamic interaction in changing environmental conditions. We chose for a spatio-temporally explicit model and focussed on wetland conditions. Soil temperature and humidity have been modelled by means of finite volumes and were used to determine the spatial habitat suitability. The life cycles of earthworms have been modelled by Leslie matrices where soil humidity, soil temperature and population densities have been used to parametrize survival and transition probabilities. Earthworm dispersion has been described by a cellular automaton of the domain providing spatial population densities for both the life cycle submodel and the soil conditions submodel.     

Complex dynamics of the population with a simple age structure

The effects of the following modes of density-dependent control of population growth: density-dependent birth rate, adult survival rate, juvenile survival rate are compared based on the mathematical model of population dynamics. It is shown that the most efficient mechanisms limiting population size are decreasing with the growth of the adult population birth rate and/or the decreasing survival rate of the offspring with the increase in their number. However, these same mechanisms are responsible for oscillations of the population size and its chaotic change. The density-dependence of the adult survival rate is not efficient in constraining the population growth, but it can substantially limit the magnitude of oscillations of the population size.     

Suspended particulate matter dynamics in a particle framework

Suspended particulate matter (SPM) dynamics in ocean models are usually treated with an advection–diffusion equation for one or more sediment size classes coupled to the hydrodynamical part of the model. Numerical solution of these additional partial differential equations unavoidably introduces numerical diffusion, i.e. in the case of sharp gradients the possible occurrence of artificial oscillations and non-positivity. A Lagrangian particle-tracking model has been developed to simulate short-term SPM dynamics. Modelling individual sediment particles allows a straightforward physical interpretation of the processes. The tracking of large numbers of individual and independent particles (up to 25 million in total in a single sediment class) can be achieved on high performance computer clusters, due to efficient parallelisation of particle tracking. The movement of the particles is described by a stochastic differential equation, which is consistent with the advection–diffusion equation. Here, the concentration profile is represented by a set of independent moving particles, which are advected according to the 3D velocity field, while the diffusive displacements of the particles are sampled from a random distribution, which is related to the eddy diffusivity field. To account for erosion a new parameterisation is proposed. Three numerical particle tracking schemes (EULER, MILSTEIN and HEUN) are presented and validated in idealised test cases. Finally, the particle tracking algorithms are applied to a realistic scenario, a severe winter storm in the East Frisian Wadden Sea (southern North Sea). The comparison with observations and an Eulerian SPM transport model seems to indicate a somewhat better fidelity of the Lagrangian approach.     

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.     

Modelling coupled peach tree-aphid population dynamics and their control by winter pruning and nitrogen fertilization

Nitrogen fertilization and winter pruning are commonly used to control crop production in peach [Prunus persica (L.) Batsch] orchards. They are also known to affect the dynamics of Myzus persicae (Sulzer) (Homoptera: Aphididae) aphid populations via bottom-up regulation processes. Interactions between crops and pests can cause complex system behaviour in response to management practices. An integrated approach will therefore improve the understanding of the effects of these two cultural practices on aphid and peach performances.We developed a simulation model that describes the cultural control of interacting peach tree and aphid population dynamics. It uses the principles of common trophic models while gathering available knowledge and explicit assumptions on peach and aphid functioning and the effects of cultural practices.The model was able to qualitatively reproduce the system behaviour observed in the field. It accounted for actions and feedback such as stimulation of foliar growth by winter pruning, consecutive aphid population increase, subsequent damage to foliage, and partial compensatory growth of foliage. The model also reproduced low losses in fruit production due to aphid infestations. However, it called for further integration of ‘long-term’ effects. Analysis of the model showed the complexity of peach tree and aphid responses to leaf N × winter pruning interactions. Simulations indicated that fruit production losses remained low within a range of realistic values of leaf N and pruning intensity, whereas manipulating peach and aphid dynamics, their interactions and their relationships to practices could result in higher losses.The model is useful to evaluate the relevance of cultural practices for a bottom-up regulation of aphid dynamics in crop-pest management. After considering other control methods and fruit quality, it can be used to find a combination of practices that optimises trade-offs between fruit production and environmental conservation goals. A modelling approach that links crop growth and pest population dynamics and integrates management practice effects has strong potential for improving crop-pest management in an integrated crop production context.     

Fitting probability models to population dynamics data

Methods for modeling population dynamics in probability using the generalized point process approach are developed. The life history of these populations is such that seasonal reproduction occurs during a short time. Several models are developed and analyzed. Data about two species: colonial spiders (Stegodyphus dumicola) and a migratory bird (wood thrush, Hylocichla mustelina) are used to estimate model parameters with appropriate log maximum likelihood functions. For the spiders, the model is fitted to provide evolutionary feasible colony size based on maximum likelihood estimates of fecundity and survival data. For the migratory bird species, a maximum likelihood estimates are derived for the fecundity and survival rates of young and adult birds and immigration rate. The presented approach allows computation of quantities of interest such as probability of extinction and average time to extinction.     

Using citizen science butterfly counts to predict species population trends

Citizen scientists are increasingly engaged in gathering biodiversity information, but trade‐offs are often required between public engagement goals and reliable data collection. We compared population estimates for 18 widespread butterfly species derived from the first 4 years (2011–2014) of a short‐duration citizen science project (Big Butterfly Count [BBC]) with those from long‐running, standardized monitoring data collected by experienced observers (U.K. Butterfly Monitoring Scheme [UKBMS]). BBC data are gathered during an annual 3‐week period, whereas UKBMS sampling takes place over 6 months each year. An initial comparison with UKBMS data restricted to the 3‐week BBC period revealed that species population changes were significantly correlated between the 2 sources. The short‐duration sampling season rendered BBC counts susceptible to bias caused by interannual phenological variation in the timing of species’ flight periods. The BBC counts were positively related to butterfly phenology and sampling effort. Annual estimates of species abundance and population trends predicted from models including BBC data and weather covariates as a proxy for phenology correlated significantly with those derived from UKBMS data. Overall, citizen science data obtained using a simple sampling protocol produced comparable estimates of butterfly species abundance to data collected through standardized monitoring methods. Although caution is urged in extrapolating from this U.K. study of a small number of common, conspicuous insects, we found that mass‐participation citizen science can simultaneously contribute to public engagement and biodiversity monitoring. Mass‐participation citizen science is not an adequate replacement for standardized biodiversity monitoring but may extend and complement it (e.g., through sampling different land‐use types), as well as serving to reconnect an increasingly urban human population with nature.     

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.     

Organochlorines in urban soils from Central India: probabilistic health hazard and risk implications to human population

This study presents distribution of organochlorines (OCs) including HCH, DDT and PCBs in urban soils, and their environmental and human health risk. Forty-eight soil samples were extracted using ultrasonication, cleaned with modified silica gel chromatography and analyzed by GC-ECD. The observed concentrations of ∑HCH, ∑DDT and ∑PCBs in soils ranged between?<?0.01–2.54, 1.30–27.41 and?<?0.01–62.8 µg kg^?1, respectively, which were lower than the recommended soil quality guidelines. Human health risk was estimated following recommended guidelines. Lifetime average daily dose (LADD), non-cancer risk or hazard quotient (HQ) and incremental lifetime cancer risk (ILCR) for humans due to individual and total OCs were estimated and presented. Estimated LADD were lower than acceptable daily intake and reference dose. Human health risk estimates were lower than safe limit of non-cancer risk (HQ?<?1.0) and the acceptable distribution range of ILCR (10^?6–10^?4). Therefore, this study concluded that present levels of OCs (HCH, DDT and PCBs) in studied soils were low, and subsequently posed low health risk to human population in the study area.     

Fish population dynamics in a seasonally varying wetland

Small fishes in seasonally flooded environments such as the Everglades are capable of spreading into newly flooded areas and building up substantial biomass. Passive drift cannot account for the rapidity of observed population expansions. To test the ‘reaction-diffusion’ mechanism for spread of the fish, we estimated their diffusion coefficient and applied a reaction-diffusion model. This mechanism was also too weak to account for the spatial dynamics. Two other hypotheses were tested through modeling. The first—the ‘refuge mechanism’—hypothesizes that small remnant populations of small fishes survive the dry season in small permanent bodies of water (refugia), sites where the water level is otherwise below the surface. The second mechanism, which we call the ‘dynamic ideal free distribution mechanism’ is that consumption by the fish creates a prey density gradient and that fish taxis along this gradient can lead to rapid population expansion in space. We examined the two alternatives and concluded that although refugia may play an important role in recolonization by the fish population during reflooding, only the second, taxis in the direction of the flooding front, seems capable of matching empirical observations. This study has important implications for management of wetlands, as fish biomass is an essential support of higher trophic levels.     

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.     

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.     

Modelling the effects of green macroalgae blooms on the population dynamics of Cyathura carinata (Crustacea: Isopoda) in an eutrophied estuary

A population dynamics model was developed to simulate the effects of benthic macroalgae blooms (mostly Enteromorpha spp.) on the productivity of Cyathura carinata (Crustacea: Isopoda), a possible keystone species in the benthic communities of the Mondego estuary. The model describes C. carinata population dynamics, as well as the relationships between Enteromorpha biomass, Enteromorpha decaying rates, organic matter content in the sediments and detritus consumption by C. carinata, a detritic feeder. Model results support the idea that seasonal blooms of Enteromorpha determine a significant increase of organic matter content in the sediments, due to macroalgae decay, which initially contributes to enhance C. carinata consumption and growth rates, determining a significant increase in the biomass. Nevertheless, later, following the algae bloom, C. carinata biomass decreases, and reaches its lowest value, close to 0, when the algae crash. This effect is probably related with strong anoxic conditions, especially during night, due to high algal decomposition rates. In accordance with the model, migration of new individuals from adjacent areas must occur in order to recolonise the area affected by the algae bloom. Therefore, it seems reasonable to conclude that macroalgae blooms that are limited in space may favour C. carinata populations, but extensive blooms affecting the whole area of distribution of this species will determine its disappearance.     

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.     

Spatial selection and inheritance: applying evolutionary concepts to population dynamics in heterogeneous space

Organisms in highly suitable sites generally produce more offspring, and offspring can inherit this suitability by not dispersing far. This combination of spatial selection and spatial inheritance acts to bias the distribution of organisms toward suitable sites and thereby increase mean fitness (i.e., per capita population increase). Thus, population growth rates in heterogeneous space change over time by a process conceptually analogous to evolution by natural selection, opening avenues for theoretical cross-pollination between evolutionary biology and ecology. We operationally define spatial inheritance and spatial selective differential and then combine these two factors in a modification of the breeder's equation, derived from simple models of population growth in heterogeneous space. The modified breeder's equation yields a conservative criterion for persistence in hostile environments estimable from field measurements. We apply this framework for understanding gypsy moth population persistence amidst abundant predators and find that the predictions of the modified breeder's equation match initial changes in population growth rate in independent simulation output. The analogy between spatial dynamics and natural selection conceptually links ecology and evolution, provides a spatially implicit framework for modeling spatial population dynamics, and represents an important null model for studying habitat selection.     

Enchytraeid population dynamics: Resource limitation and size-dependent mortality

Enchytraeids are regarded as keystone soil organisms in forest ecosystems. Their abundance and biomass fluctuate widely. Predicting the consequences of anthropogenic disturbances requires an understanding of the mechanisms underlying enchytraeid population dynamics. Here I develop a simple model, which predicts that the type of dynamics is controlled by resource input rate. If fungal resource input is a discrete event once a year, an exponential growth phase is followed by starvation and sharp decline of enchytraeid abundance. Model simulations with three different forcing functions were compared to field data. Initial parameter values were obtained from various independent sources, and parameters were estimated by minimizing the residual sum of squares. The best fitting model with resource addition once a year explained 39% of the variation in enchytraeid biomass over an 8-year study period. Further, variation in rainfall explained 59% of the variation in R² of the exponential phase models, which is also an index of the stability of population size-structure. The results emphasize the importance of resource limitation for enchytraeid population dynamics and support the hypothesis that the mortality during the decline phase is size-dependent.