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 Nesidiocoris 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.

Abstract. The paper is aimed at a methodological development in biological pest control. The 10 considered one pest two-agent system is modelled as a verticum-type system. Originally, linear 11 verticum-type systems were introduced by one of the authors for modelling certain industrial 12 systems. These systems are hierarchically composed of linear subsystems such that a part of the 13 state variables of each subsystem affect the dynamics of the next subsystem. Recently, 14 verticum-type system models have been applied to population ecology as well, which required 15 the extension of the concept a verticum-type system to the nonlinear case. 16In the present paper the general concepts and technics of nonlinear verticum-type control 17 systems are used to obtain biological control strategies in a two-agent system. For the 18 illustration of this verticum-type control, these tools of mathematical systems theory are applied 19 to a dynamic model of interactions between the egg and larvae populations of the sugarcane 20 borer (Diatraea saccharalis) and its parasitoids: the egg parasitoid Trichogramma galloi and the 21 larvae parasitoid Cotesia flavipes. 22In this application a key role is played by the concept of controllability, which means that it is 23 possible to steer the system to an equilibrium in given time. In addition to a usual linearization, 24 the basic idea is a decomposition of the control of the whole system into the control of the 25 subsystems, making use of the verticum structure of the population system. The main aim of 26 this study is to show several advantages of the verticum (or decomposition) approach over the 27 classical control theoretical model (without decomposition). For example, in the case of 28 verticum control the pest larval density decreases below the critical threshold value much 29 quicker than without decomposition. Furthermore, it is also shown that the verticum approach 30 may be better even in terms of cost effectiveness. The presented optimal control methodology 31 also turned out to be an efficient tool for the "in silico" analysis of the cost-effectiveness of 32 different biocontrol strategies, e.g. by answering the question how far it is cost-effective to 33 speed up the reduction of the pest larvae density, or along which trajectory this reduction should 34 be carried out. 35 36

Relationships between the omnivorous predator Nesidiocoris tenuis (Reuter) and the egg parasitoid Trichogramma achaeae Nagaraja and Nagarkatti were studied in the laboratory (no-choice and choice assays, and functional responses) and in a greenhouse experiment. Both natural enemies are utilized in the biological control of tomato pinworm on greenhouse-grown tomato crops. Three different food items were offered to the predator: nonparasitized prey, prey parasitized for less than 4 d by T. achaeae, and prey parasitized for more than 4 d by the parasitoid. There were significant differences in consumption of food types, with highest consumption for nonparasitized prey, followed by parasitized (<4 d) and then parasitized (>4 d), both in no-choice and choice trials. At the same time, the predator causes a significant mortality in the prey (over 80%) regardless of previous parasitism, resulting in a very coincidental intraguild predation detrimental to the parasitoid. It has also been observed that there was a change in the functional response by the predator from Type II in presence of nonparasitized prey to Type I when there was a combination of parasitized and nonparasitized prey. This represents an increase of instantaneous search rate (a') and a decrease of handling time (Th), which indicates a change in feeding behavior on the two prey types. Under greenhouse conditions, the intraguild predation reduced the percentage of parasitism by T. achaeae in just over 20%. However, when both natural enemies were present, a better control of pest Tuta absoluta (Meyrick) was achieved than in the case of application of any of them alone.

1Sib cannibalism seems to be paradoxical behaviour, since it decreases the survival rate of the 2 closest relative juveniles, so the rate of sib cannibalism changes the demography of the 3 cannibal phenotype. In the general kin demographic selection model presented here, the long-4 term growth rate of a phenotype is determined by a Leslie matrix that depends on the life 5 history strategy, and a uniform density-dependent selection process takes place, keeping the 6 total population size at the level of the carrying capacity. Using this model, where different 7 phenotypes are described by different Leslie matrices, we point out that the phenotype 8 optimizing the phenotypic long-term growth rate will select out any other optimizing 9 phenotype. We find that sib cannibalism is adaptive if the sib cannibal can decrease its 10 developmental time, and the shorter development time can increase the rate of survival from 11 sib cannibal juvenile to adult, and also when sib cannibalism increases fecundity in the adult 12 stage. Cannibalism between the closest relatives can be considered as a mutualistic kin 13 strategy when the benefit of cannibalism is greater than the cost of it. 14 Keywords: collector hypothesis, kin demography, Leslie model 15 16 3

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