Assessing the impact of biological control of Plutella xylostella through the application of Lotka–Volterra model

The Lotka–Volterra model was applied to the population densities of diamondback moth (DBM), Plutella xylostella (L.) and its exotic larval parasitoid Diadegma semiclausum (Hellen) data that was collected earlier by icipe's DBM biological control team. The collections were done for 15 months before the release and 36 months after release of the parasitoid in two areas; in Werugha, Coast Province of Kenya and Tharuni, Central Province of Kenya, respectively. For each area in pre- and post-release periods, we estimated Lotka–Volterra model parameters from the minimization of the loss function between the theoretical and experimental time-series datasets following the Nelder-Mead multidimensional method. The model estimated a reduction in the value of the steady state of DBM population from 4.86 to 2.17 in Werugha and from 6.11 to 3.76 and 3.45 (with and without exclusion of the time before D. semiclausum recovery) in Tharuni when transiting from the pre- and post-release periods, respectively. This change was a consequence of the newly introduced parasitoid, in the areas. The study presented a successful and detailed technique for non-linear model parameters restoration which was demonstrated by the correct mimicking of empirical datasets from the classical biological control with D. semiclausum, in different areas of Kenya. The applied model has measured the parasitoids impact on the DBM biological control through a quantitative estimate of the effectiveness of the newly introduced species D. semiclausum. These equations may therefore be used as tool for decision making in the implementation for such pests’ management system strategy.     

Impact of bias in predicted height on tree volume estimation: A case-study of intrinsic nonlinearity

Bias originating from intrinsic nonlinearity in nonlinear models is caused by excess curvature in the solution locus of parameter estimates derived from least squares procedures. Bias due to intrinsic nonlinearity varies according to sample size as well as model specification. This paper analyses consequences of fractionising data into smaller sub-samples. Based on measurements of stem diameter and total tree height from the first Danish national forest inventory, it is demonstrated how data splitting at random may cause the intrinsic nonlinear curvature to exceed the critical F-value. Application of a Taylor-series expansion shows that, for all practical purposes, the bias in predictions of individual tree volume (based on stem diameter and tree height) is negligible. To minimize residual variance, intrinsic curvature and, in turn, prediction bias, it is recommended that data be stratified according to site conditions, stand characteristics or other relevant criteria. Finally, the preferred model should exhibit close-to-linear behaviour.     

Studying ecological communities from a neutral standpoint: A review of models’ structure and parameter estimation

Neutral models provide an alternative to niche-based assembly rules of ecological communities by assuming that communities’ properties are shaped by the stochastic interplay between ecological drift, migration and speciation. The recent and ongoing interest about neutral assumptions has produced many developments on the theoretical side, with nevertheless limited echoes in terms of analyses of real-world data. The present review paper aims to help bridge the widening gap between modellers and field ecologists through two objectives. First, to provide a multi-criteria typology of the main neutral models, including those from population genetics that have not yet been transposed to ecology, by considering how the fundamental processes of ecological drift, speciation and migration are modelled and, specifically, how space is taken into account. Second, to review methods recently proposed to estimate models parameters from field data, a point that should be mastered to allow for broader applications.     

Recruitment and attrition of associated plants under a shading crop canopy: Model selection and calibration

Associated plant and animal diversity provides ecosystem services within crop production systems. The importance of the maintenance or restoration of diversity is therefore increasingly acknowledged. Here we study the population dynamics of associated annual plants (‘weeds’) during the growth of a crop in a season and introduce a minimal model to characterize the recruitment and attrition of the associated plants under the influence of shading by the crop. A mechanistically based, logistic, light interception model was parameterized with light interception measurements in two single crops (barley and rye) and in mixtures of these cereals with peas. Population dynamics data were collected for the annuals Papaver rhoeas, Centaurea cyanus, Chrysanthemum segetum, and Misopates orontium. A minimal population dynamics model was identified for each annual plant species, using system identification techniques as model selection and calibration.     

Incentive compatibility tests of choice experiment value elicitation questions

This paper uses laboratory experiments with induced values to address fundamental issues related to the incentive compatibility of choice experiment value elicitation questions. In particular, we compare two- versus three-option choice sets and the effect of using alternative provision rules, including one where the outcome is influenced by both participant and “regulator” votes. We find the overall proportion of choices that are inconsistent with induced preferences is rather low. However, there are more deviations from induced preferences for two-option choice sets, and for alternatives to a simple plurality vote implementation rule. A multinomial probit analysis of choices in tandem with a mixed logit welfare analysis suggests there is a statistically significant but modest degree of bias towards selecting the status quo option.     

Evaluation of discrete host–parasitoid models for diamondback moth and Diadegma semiclausum field time population density series

The performance of discrete mathematical models to describe the population dynamics of diamondback moth (DBM) (Plutella xylostella L.) and its parasitoid Diadegma semiclausum was investigated. The parameter values for several well-known models (Nicholson–Bailey, Hassell and Varley, Beddington, Free and Lawton, May, Holling type 2, 3 and Getz and Mills functional responses) were estimated. The models were tested on 20 consecutive sets of time series data collected at 14 days interval for pest and parasitoid populations obtained from a highland cabbage growing area in eastern Kenya. Model parameters were estimated from minimized squared difference between the numerical solution of the model equations and the empirical data using Powell's method. Maximum calculated DBM growth rates varied between 0.02 and 0.07. The carrying capacity determined at 16.5 DBM/plant by the Beddington et al. model was within the range of field data. However, all the estimated parameter values relating to the parasitoid, including the instantaneous searching rate (0.07–0.28), per capita searching efficiency (0.20–0.27), search time (5.20–5.33), handling time (0.77–0.90), and parasitism aggregation index (0.33), were well outside the range encountered empirically. All models evaluated for DBM under Durbin–Watson criteria, except the May model, were not autocorrelated with respect to residuals. In contrast, the criteria applied to the parasitoid residuals showed strong autocorrelations. Thus, these models failed to estimate parasitoid dynamics. We conclude that the interactions of the DBM with its parasitoid cannot be explained by any of the models tested. Two factors may be associated with this failure. First, the parasitoid in this integrated biological control system may not be playing a major role in regulating DBM population. Second, and perhaps more likely, poor correlations reflect gross inadequacies in the theoretical assumptions that underlie the existing models.     

Urban expansion and its contribution to the regional carbon emissions: Using the model based on the population density distribution

The method is used for calculating regional urban area dynamics and the resulting carbon emissions (from the land-conversion) for the period of 1980 till 2050 for the eight world regions. This approach is based on the fact that the spatial distribution of population density is close to the two-parametric Γ-distribution [Kendall, M.G., Stuart, A., 1958. The Advanced Theory of Statistics, vol. 1.2. Academic Press, New York; Vaughn, R., 1987. Urban Spatial Traffic Patterns, Pion, London]. The developed model provides us with the scenario of urbanisation, based on which the regional and world dynamics of carbon emissions and export from cities, and the annual total urban carbon balance are estimated. According to our estimations, world annual emissions of carbon as a result of urbanisation increase up to 1.25 GtC in 2005 and begin to decrease afterwards. If we compare the emission maximum with the annual emission caused by deforestation, 1.36 GtC per year, then we can say that the role of urbanised territories (UT) in the global carbon balance is of a comparable magnitude. Regarding the world annual export of carbon from UT, we observe its monotonous growth by three times, reaching 505 MtC. The latter, is comparable to the amount of carbon transported by rivers into the ocean (196–537 MtC). The current model shows that urbanisation is inhibited in the interval 2020–2030, and by 2050 the growth of urbanised areas would almost stop. Hence, the total balance, being almost constant until 2000, then starts to decrease at an almost constant rate. By the end of the XXI century, the total carbon balance will be equal to zero, with the exchange flows fully balanced, and may even be negative, with the system beginning to take up carbon from the atmosphere, i.e., becomes a “sink”. The regional dynamics is somewhat more complex, i.e., some regions, like China, Asia and Pacific are being active sources of Carbon through the studied period, while others are changing from source to sink or continue to be neutral in respect the GCC.     

Population as an oscillating system

In this paper we present a new approach describing population dynamics based on the view of a population as an oscillating system. To develop a mathematical model of an oscillating population, we applied a third-order differential equation. Our model describes population dynamics within a parametric-temporal continuum, formed by the relative values of population growth and decrease over time. In this paper we also illustrate how our oscillative model effectively compliments the existing suite of models in population dynamics.     

On the use of correlated beta random variables with animal population modelling

We give reasons why demographic parameters such as survival and reproduction rates are often modelled well in stochastic population simulation using beta distributions. In practice, it is frequently expected that these parameters will be correlated, for example with survival rates for all age classes tending to be high or low in the same year. We therefore discuss a method for producing correlated beta random variables by transforming correlated normal random variables, and show how it can be applied in practice by means of a simple example. We also note how the same approach can be used to produce correlated uniform, triangular, and exponential random variables.