Characterisation of a nonlinear Leslie matrix model for predicting the dynamics of biological populations in polluted environments: Applications to radioecology (original) (raw)
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Journal of Environmental Radioactivity, 2013
The present work describes the application of a non-linear Leslie model for predicting the effects of ionising radiation on wild populations. The model assumes that, for protracted chronic irradiation, the effect-dose relationship is linear (the increase in the mortality of the individuals is proportional to the dose rate). The model was tested using independent data and information from a series of experiments that were aimed at assessing the response to radiation of wild populations of meadow voles and whose results were described in the international literature. The values of the effect-dose proportionality factor, C, which relates the mortality rates to the dose, was estimated by a suitable calibration of the model results to the time dependent data of the population size. Such estimates were lower than the corresponding values of C assessed by accounting for the median lethal dose (L 50 ) determined by laboratory experiments on small mammals subjected to acute and protracted irradiation. Most likely a wild population can more efficiently respond to the radiation effects by profiting from the non-expressed biotic potential of the species whose growth is limited by processes of environmental resistance, such as the competition among the individuals of the same or of different species for the exploitation of the available resources, which are nonlinearly dependent on the population size.
In this paper, a non-linear mathematical model is proposed and analyzed to study the existence and survival of a biological population when the resource and population is being affected by a toxicant (pollutant), emitted into the environment from external sources. Although the resource biomass density is also affected, here in the model we have only considered the adverse effects of biological population taking up the consideration of the uptake of toxicants by population.
Journal of Environmental Radioactivity, 2009
The present work describes a model for predicting the population dynamics of the main components (resources and consumers) of terrestrial ecosystems exposed to ionising radiation. The ecosystem is modelled by the Lotka-Volterra equations with consumer competition. Linear dose-response relationships without threshold are assumed to relate the values of the model parameters to the dose rates. The model accounts for the migration of consumers from areas characterised by different levels of radionuclide contamination. The criteria to select the model parameter values are motivated by accounting for the results of the empirical studies of past decades. Examples of predictions for long-term chronic exposure are reported and discussed.
Matrix Population Models as Relevant Modeling Tools in Ecotoxicology
Emerging Topics in Ecotoxicology, 2009
Nowadays, one of the big challenge in ecotoxicology is to understand how individually measured effects can be used as predictive indices at the population level. A particular interesting aspect is to evaluate how individual measures of fitness and survival under various toxic conditions can be used to estimate the asymptotic population growth rate known as one of the most robust endpoint in population risk assessment. Among others, matrix population models are now widely recognized as a convenient mathematical formalism dedicated to the characterization of the population demographic health. They offer the advantage of simplicity, not only in the modeling process of underlying biological phenomena, but also in the sensitivity analyses and the simulation running. On the basis of different biological systems among aquatic animal species (from fish to zooplankton), we illustrate the use of matrix population models to quantify environmental stress effects of toxic type. We also show how critical demographic parameters for the population dynamics can be highlighted by sensitivity analyses. The first example will focus on coupled effects of food amount and exposure concentration on chironomid population dynamics in laboratory. The second example will exemplify the use of energy-based models coupled with matrix population ones to properly describe toxic effects on daphnid populations. Last, we will show how to introduce a spatial dimension in Leslie type models to describe space-specific aspects of contaminant induced population dynamics alteration with the case of brown trout population modeling at the river network scale.
In this paper, a non-linear mathematical model is proposed and analyzed to study the effect of a toxicant (pollutant) which is emitted into the environment from various external sources at a constant rate and whose concentration is augmented due to transformation of a precursor produced by the species. It is shown that if the rate of emission of toxicant and rate of its transformation from precursor into the environment increases, the density of the biological population settles down to a lower equilibrium than its original carrying capacity and its magnitude decreases as the equilibrium level of concentration of toxicant increases. It is pointed out that for very large emission and transformation rates of the toxicant from the above mentioned processes, the survival of the biological species is threatened.
Ecotoxicology and population dynamics: Using DEBtox models in a Leslie modeling approach
Ecological Modelling, 2005
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.
This report describes in details the basic concepts, needs and data treatment for the population modeling approaches that have been implemented under WP-5 dedicated to “ecologically-relevant low doses effects to non-human species” as part of Task 5.1 devoted to the derivation of population-level protection criteria. Two modeling approaches are presented for extrapolating radiation dose effects from individuals to populations of non-human biota. The first approach, developed as part of the STAR programme, is inspired from methods which are increasingly used in ecotoxicology to address population effects of chemical contaminants. The approach applies Leslie matrix techniques to the case of chronic external gamma irradiation on a range of wildlife species, based on effect data available in the FREDERICA database and interpreted as dose rate response curves. Considered species cover 14 species representing four taxonomic groups (aquatic and soil invertebrates, fish and terrestrial mam...
Journal of Environmental Radioactivity, 2008
This study evaluated the potential effect of ionising radiation on population growth using simple population models and parameter values derived from chronic exposure experiments in two invertebrate species with contrasting life-history strategies. In the earthworm Eisenia fetida, models predicted increasing delay in population growth with increasing gamma dose rate (up to 0.6 generation times at 11 mGy h À1 ). Population extinction was predicted at 43 mGy h À1 . In the microcrustacean Daphnia magna, models predicted increasing delay in population growth with increasing alpha dose rate (up to 0.8 generation times at 15.0 mGy h À1 ), only after two successive generations were exposed. The study examined population effects of changes in different individual endpoints (including survival, number of offspring produced and time to first reproduction). Models showed that the two species did not respond equally to equivalent levels of change, the fast growing daphnids being more susceptible to reduction in fecundity or delay in reproduction than the slow growing earthworms. This suggested that susceptibility of a population to ionising radiation cannot be considered independent of the species' life history.
In this paper, a non-linear mathematical model is proposed and analyzed to study the survival of a biological population (Plants, trees etc.) when it is affected by a toxicant (pollutant), emitted into the environment from external sources. It is shown that as the rates of emission and formation of a toxicant in the environment increases, the density of the plant population settles down to lower equilibria than their initial carrying capacity and their magnitude decreases as the equilibrium level of toxicant increases.