Manuel Gámez

Biological Control Strategies for the South American Tomato Moth (Lepidoptera: Gelechiidae) in Greenhouse Tomatoes

ABSTRACT The South American tomato pinworm, Tuta absoluta (Meyrick) has been introduced into new geographic areas, including the Mediterranean region, where it has become a serious threat to tomato production. Three greenhouse trials conducted in tomato crops during 2009 and 2010 explored control strategies using the egg-parasitoid Trichogramma achaeae Nagaraja and Nagarkatti compared with chemical control. The effectiveness of the predator Nesidiocoiis tenuis (Reuter) was also tested. In greenhouses with early pest infestations (discrete generations), periodic inundative releases (eight releases at a rate of 50 adults/m2, twice a week) were necessary to achieve an adequate parasitism level (85.63 ± 5.70%) early in the growing season. However, only one inoculative release (100 adults/m2) was sufficient to achieve a comparatively high parasitism level (91.03 ± 12.58%) under conditions of high pest incidence and overlapping generations. Some intraguild competition was observed between T. achaeae and the predator, N. tenuis. This mirid species is commonly used in Mediterranean greenhouse tomato crops for the control of the sweetpotato whitefly, Bemisia tabaci (Gennadius). Tomato cultivars were also observed to influence the activity of natural enemies, mainly N. tenuis (whose average numbers ranged between 0.17 ± 0.03 and 0.41 ± 0.05 nymphs per leaf depending on the cultivar). This may be because of differences in plant nutrients in different cultivars, which may affect the feeding of omnivorous insects. In contrast, cultivar effects on T. achaeae were less apparent or possibly nonexistent. Nevertheless, there was an indirect effect in as much as T. achaeae was favored in cultivars not liked by N. tenuis.

Observability and observers in a food web

The problem of the possibility of recovering the time-dependent state of a whole population system from the observation of certain components has been studied in earlier publications, in terms of the observability concept of mathematical systems theory. In the present note a method is proposed for effectively calculating the state process. For an illustration an observer system for a simple food web is numerically constructed.

Observation and control in a model of a cell population affected by radiation

The effect of radiation on a cell population is described by a two-dimensional nonlinear system of differential equations. If the radiation rate is not too high, the system is known to have an asymptotically stable equilibrium. First, for the monitoring of this effect, the concept of observability is applied. For the case when the total number of cells is observed, without distinction between healthy and affected cells, a so-called observer system is constructed, which, at least near the equilibrium state, makes it possible to recover the dynamics of both the healthy and the affected cells, from the observation of the total number of cells without distinction. Results of simulations with illustrative data are also presented. If we want to control the system into a required new equilibrium state, and maintain this new equilibrium by a constant control, a technique of theory of optimal control can be applied to construct a feedback control system.

Monitoring environmental change in an ecosystem

The monitoring and analysis of the processes taking place in an ecosystem is a key issue for a sustainable human activity. A system of populations, as the biotic component of a complex ecosystem is usually affected by the variation of its abiotic environment. Even in nearly natural ecosystems an abiotic effect like climatic implications of global warming may cause important changes in the dynamics of the population system. In ecosystems involving field cultivation or any industrial activity; the abiotic parameter in question may be the concentration of a substance, changing, e.g. as a result of pollution, application of a pesticide, or a fertilizer, etc. In many cases the observation of the densities of each population may be technically complicated or expensive, therefore the question arises whether from the observation of the densities of certain (indicator) populations, the whole state process of the population system can be uniquely recovered. The paper is aimed at a methodological development of the state monitoring, under the conditions of a changing environment. It is shown, how the technique of mathematical systems theory can be applied not only for the approximate calculation of the state process on the basis of the observed data, even under the effect of an exogene abiotic change with known dynamics; but in certain cases, also for the estimation of the unknown biological effect of the change of an abiotic parameter. The proposed methodology is applied to simple illustrative examples concerning a three-species predator-prey system.

Observability in strategic models of viability selection

Strategic models of frequency-dependent viability selection, in terms of mathematical systems theory, are considered as a dynamic observation system. Using a general sufficient condition for observability of nonlinear systems with invariant manifold, it is studied whether, observing certain phenotypic characteristics of the population, the development of its genetic state can be recovered, at least near equilibrium.

Application of change-point problem to the detection of plant patches.

In ecology, if the considered area or space is large, the spatial distribution of individuals of a given plant species is never homogeneous; plants form different patches. The homogeneity change in space or in time (in particular, the related change-point problem) is an important research subject in mathematical statistics. In the paper, for a given data system along a straight line, two areas are considered, where the data of each area come from different discrete distributions, with unknown parameters. In the paper a method is presented for the estimation of the distribution change-point between both areas and an estimate is given for the distributions separated by the obtained change-point. The solution of this problem will be based on the maximum likelihood method. Furthermore, based on an adaptation of the well-known bootstrap resampling, a method for the estimation of the so-called change-interval is also given. The latter approach is very general, since it not only applies in the case of the maximum-likelihood estimation of the change-point, but it can be also used starting from any other change-point estimation known in the ecological literature. The proposed model is validated against typical ecological situations, providing at the same time a verification of the applied algorithms.

Stock estimation, environmental monitoring and equilibrium control of a fish population with reserve area

For sustainable exploitation of renewable resources, the separation of a reserve area is a natural idea. In particular, in fishery management of such systems, dynamic modelling, monitoring and control has gained major attention in recent years. In this paper, based on the known dynamic model of a fish population with reserve area, the methodology of mathematical systems theory and optimal control is applied. In most cases, the control variable is fishing effort in the unreserved area. Working with illustrative data, first a deterministic stock estimation is proposed using an observer design method. A similar approach is also applied to the estimation of the effect of an unknown environmental change. Then it is shown how the system can be steered to equilibrium in given time, using fishing effort as an open-loop control. Furthermore, a corresponding optimal control problem is also solved, maximizing the harvested biomass while controlling the system into equilibrium. Finally, a closed-loop control model is applied to asymptotically control the system into a desired equilibrium, intervening this time in the reserve area.

Verticum-type systems applied to ecological monitoring

In the paper ecological interaction chains of the type resource - producer - primary user - secondary consumer are considered. The dynamic behaviour of these four-level chains is modelled by a system of differential equations, the linearization of which is a verticum-type system introduced for the study of industrial verticums. Applying the technique of such systems, for the monitoring of the considered ecological system, an observer system is constructed, which makes it possible to recover the whole state process from the partial observation of the ecological interaction chain.

Iterative scheme for the observation of a competitive Lotka–Volterra system

Abstract In this work, in terms of the model parameters, sufficient conditions are established to construct a sequence of approximate observers for a two-species competitive Lotka–Volterra system. This iterative approach makes it possible to localize the solution of the system, and reveal its long-term behaviour. The main results are also illustrated by numerical simulations.

Monitoring and control in a spatially structured population model

In the paper methods of Mathematical Systems Theory are applied to the dynamical analysis of a harvested population with a reserve area. Although the methodology also applies to rather general spatially structured populations, for a concrete interpretation, we consider a fish population living in a free fishing area and in a reserved area, with migration between them. Using a fishing effort model based on logistic growth in both areas, from the catch, by the construction of an auxiliary system called observer, we dynamically estimate the total fish stock. A similar method also applies to the case of a changing environment, when there is a time-dependent abiotic environmental effect described by an additional exosystem. Furthermore, we also consider the problem of steering the population into a desired new equilibrium. To this end an optimal control problem is set up, which is numerically solved using an optimal control toolbox developed for MatLab.