József Garay - Academia.edu (original) (raw)

Papers by József Garay

Mathematics

This paper is a contribution to the modeling–methodological development of the application of mat... more This paper is a contribution to the modeling–methodological development of the application of mathematical systems theory in population biology. A discrete-time nonlinear Leslie-type model is considered, where both the reproduction and survival rates decrease as the total population size increases. In this context, the monitoring problem means that, from the observation of the size of certain age classes as a function of time, we want to recover (estimate) the whole state process (i.e., the time-dependent size of the rest of the classes). First, for the linearization approach, conditions for the existence and asymptotic stability of a positive equilibrium are obtained, then the discrete-time observer design method is applied to estimate an unknown state trajectory near the equilibrium, where we could observe a single age class. It is also shown how the observer design can be used to detect an unknown change in the environment that affects the population dynamics. The environmental c...

Agriculture, 2022

The potato tuber moth (PTM), Phthorimaea operculella, is the main potato pest in the world, havin... more The potato tuber moth (PTM), Phthorimaea operculella, is the main potato pest in the world, having managed to adapt to a wide range of climatic conditions, and causing damage to stored tubers. The effectiveness of a biological control using the parasitoid Trichogramma cacaeciae and the predatory mite Blattisocius mali was evaluated in PTM under conditions that simulated those of tubers in storage. The number of adults found at the end of the trial was significantly higher in the control (181.75 ± 11.00 adults/container) than in treatments where B. mali (24.50 ± 7.22) or T. cacaeciae (102.00 ± 14.61) were released. The biological control’s effectiveness using the Abbot formula was 86.52% for the predator and 43.88% for the parasitoid. In addition, the PTM population data was fitted by logistic models, and the best fit was found for the simple logistic function. Using the data generated from these functions, the control efficiencies for the mite and the parasitoid were 94.85% and 73.7...

Agronomy, 2021

Rhynchophorus ferrugineus (Olivier, 1790) is an invasive pest species that constitutes one of the... more Rhynchophorus ferrugineus (Olivier, 1790) is an invasive pest species that constitutes one of the most important problems around the Mediterranean region and has been responsible for the loss of over 100,000 palm trees with an estimated annual cost of EUR several hundred million since its introduction into Europe. Methodological approaches of conservation ecology, such as multidisciplinary modelling, also apply in the management of cultural landscapes concerning ornamental plants, such as palm trees of the area. In this paper, we propose a dynamic model for the control of the red palm weevil, contributing in this way to the sustainability of an existing cultural landscape. The primary data set collected is a sample from the density-time function of a two-cohort pest population. This data set suggests a bimodal analytic description. If, from this data set, we calculate a sample from the accumulated density-time function (the integral of the density-time function), it displays a doubl...

Data for the evaluation of functional response of the parasitoid species Chelonus oculator: (b) g... more Data for the evaluation of functional response of the parasitoid species Chelonus oculator: (b) greenhouse trial. MS Excel 2007 File (read only). Data include host densities (X) (no. eggs/patch), parasitoid densities (Y) (female adults/m2), and parasitized host (Xa) (replications 1 to 12) (parasitized egg/patch)

Data for parasitoid transition, Chelonus oculator, found at the corresponding stages in laborator... more Data for parasitoid transition, Chelonus oculator, found at the corresponding stages in laboratory trials. MS Excel 2007 File (read only). Data include accumulated degree-days (º C x day), number inside host, number outside host+pupa, and total immatures

Data for host transition, Spodoptera exigua, found at the corresponding stages in greenhouse pepp... more Data for host transition, Spodoptera exigua, found at the corresponding stages in greenhouse pepper crop. MS Excel 2007 File (read only). Data include cage number, accumulated degree-days (º C x day), number of eggs, I-instar, II-instar, III-instar, IV-instar, V-instar, total larvae, number of pupae, and adults (no. individuals / cage)

Data for evaluation of biological parameters of the parasitoid species Chelonus oculator: (a) Lab... more Data for evaluation of biological parameters of the parasitoid species Chelonus oculator: (a) Laboratory trial, fecundity of adults. MS Excel 2007 File (read only). Data include temperature (º C), and fecundity (no. eggs/female)

Monitoring of ecological systems is one of the major issues in ecosystem research. The concepts a... more Monitoring of ecological systems is one of the major issues in ecosystem research. The concepts and methodology of mathematical systems theory provide useful tools to face this problem. In many cases, state monitoring of a complex ecological system consists in observation (measurement) of certain state variables, and the whole state process has to be determined from the observed data. The solution proposed in the paper is the design of an observer system, which makes it possible to approximately recover the state process from its partial observation. The method is illustrated with a trophic chain of resource – producer – primary consumer type and a numerical example is also presented.

Bulletin of Mathematical Biology, 2021

We consider matrix games with two phenotypes (players): one following a mixed evolutionarily stab... more We consider matrix games with two phenotypes (players): one following a mixed evolutionarily stable strategy and another one that always plays a best reply against the action played by its opponent in the previous round (best reply player, BR). We focus on iterated games and well-mixed games with repetition (that is, the mean number of repetitions is positive, but not infinite). In both interaction schemes, there are conditions on the payoff matrix guaranteeing that the best reply player can replace the mixed ESS player. This is possible because best reply players in pairs, individually following their own selfish strategies, develop cycles where the bigger payoff can compensate their disadvantage compared with the ESS players. Well-mixed interaction is one of the basic assumptions of classical evolutionary matrix game theory. However, if the players repeat the game with certain probability, then they can react to their opponents’ behavior. Our main result is that the classical mixe...

Agronomy, 2021

We propose a conceptual model for pollination and fertilization of tomato flowers in greenhouses ... more We propose a conceptual model for pollination and fertilization of tomato flowers in greenhouses crops by hoverflies, when the maximal number of adult pollinators maintained by the crops is less than what is needed for an economically successful pollination in greenhouses. The model consists of a two-stage process for additional feeding of hoverfly to maintain the pollinator density at the economically desired level. First, with a stochastic model, we calculate the density of flies necessary for the economically successful pollination, determined according to the economically expected yield. Second, using a deterministic optimal control model, we find a minimum cost supplementary feeding strategy. In summary, we theoretically demonstrate, at the present stage of the research without validations in case studies, that optimal supplementary feeding can maintain the economically desired hoverfly density.

Insects, 2020

Cannibalism in insects plays an important role in ecological relationships. Nonetheless, it has n... more Cannibalism in insects plays an important role in ecological relationships. Nonetheless, it has not been studied as extensively as in other arthropods groups (e.g., Arachnida). From a theoretical point of view, cannibalism has an impact on the development of more realistic stage-structure mathematical models. Additionally, it has a practical application for biological pest control, both in mass-rearing and out in the field through inoculative releases. In this paper, the cannibalistic behavior of two species of predatory bugs was studied under laboratory conditions—one of them a generalist predator (strictly carnivorous), Nabis pseudoferus, and the other a true omnivore (zoophytophagous), Nesidiocoris tenuis—and compared with the intraguild predation (IGP) behavior. The results showed that cannibalism in N. pseudoferus was prevalent in all the developmental stages studied, whereas in N. tenuis, cannibalism was rarely observed, and it was restricted mainly to the first three nymphal ...

Tobbfajos evoluciookologiai modellt dolgoztunk ki, amely alkalmas az invaziv fajok es a paleontol... more Tobbfajos evoluciookologiai modellt dolgoztunk ki, amely alkalmas az invaziv fajok es a paleontologia „szakaszos egyensulyi” fogalmanak vizsgalatara. Megmutattuk, hogy az adaptiv dinamikai stabilitas specialis esetkent adodik az altalunk bevezetett dinamikus stabilitasbol. Kimutattuk, hogy a nem kooperalo egyedek kellően hatasos buntetesevel stabilizalhato a kooperacio. Igazoltuk, hogy a termeszetes szelekcio folyaman az „optimalizalo” (sajat bevetelet maximalizalo) tipust kiszelektalja a „versengőt” (aki relativ előnyet maximalizalja). Egy evolucios jatekelmeleti modellel kimutattuk, hogy kis csoportletszam mellett az altruista segitseg tobbszori ragadozotamadas eseten ESS. Igazoltuk, hogy mind a Ewens-fele parcialis ratermettseg, mind a relativ előny novekedesi rataja egyarant aranyos a ratermettsegek varianciajaval. Peldat adtunk olyan parameterekre, amelyek eseten a mehek optimalis nektargyűjtesi viselkedese nem garantalja a koegzisztenciat, ha ket novenyfaj nektarjaert ket mehf...

The m onitoring and analysis of the processes taking place in an ecosystem is a key issue for a s... more The m onitoring 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 methodologic...

Journal of Theoretical Biology, 2020

Dynamic Games and Applications, 2019

Applied Mathematics and Computation, 2018

Scientific reports, Jan 20, 2018

We consider two types of optimal foragers: a random searcher and a search image user. A search im... more We consider two types of optimal foragers: a random searcher and a search image user. A search image user can find its desired prey with higher and undesired prey with lower probability than a random searcher. Our model considers the density-dependent travelling time and the time duration of reproduction (oviposition). In the framework of optimal foraging theory for one predator-two prey systems, we find that there are ranges of prey densities in which the search image user has a higher net energy intake, and there are other ranges of prey densities in which the random searcher has higher net energy intake. The damsel bug Nabis pseudoferus Remane (Hemiptera: Nabidae) is a generalist predator rather than an omnivore. This species has a wide range of arthropod prey (predominantly insects and mites). Several aspects of the biology of this species have been studied, especially its cannibalistic behaviour, which is a quite important feature because N. pseudoferus is often used as a biolo...

Journal of Theoretical Biology, 2017

Journal of the Franklin Institute, 2017

Mathematics

This paper is a contribution to the modeling–methodological development of the application of mat... more This paper is a contribution to the modeling–methodological development of the application of mathematical systems theory in population biology. A discrete-time nonlinear Leslie-type model is considered, where both the reproduction and survival rates decrease as the total population size increases. In this context, the monitoring problem means that, from the observation of the size of certain age classes as a function of time, we want to recover (estimate) the whole state process (i.e., the time-dependent size of the rest of the classes). First, for the linearization approach, conditions for the existence and asymptotic stability of a positive equilibrium are obtained, then the discrete-time observer design method is applied to estimate an unknown state trajectory near the equilibrium, where we could observe a single age class. It is also shown how the observer design can be used to detect an unknown change in the environment that affects the population dynamics. The environmental c...

Agriculture, 2022

The potato tuber moth (PTM), Phthorimaea operculella, is the main potato pest in the world, havin... more The potato tuber moth (PTM), Phthorimaea operculella, is the main potato pest in the world, having managed to adapt to a wide range of climatic conditions, and causing damage to stored tubers. The effectiveness of a biological control using the parasitoid Trichogramma cacaeciae and the predatory mite Blattisocius mali was evaluated in PTM under conditions that simulated those of tubers in storage. The number of adults found at the end of the trial was significantly higher in the control (181.75 ± 11.00 adults/container) than in treatments where B. mali (24.50 ± 7.22) or T. cacaeciae (102.00 ± 14.61) were released. The biological control’s effectiveness using the Abbot formula was 86.52% for the predator and 43.88% for the parasitoid. In addition, the PTM population data was fitted by logistic models, and the best fit was found for the simple logistic function. Using the data generated from these functions, the control efficiencies for the mite and the parasitoid were 94.85% and 73.7...

Agronomy, 2021

Rhynchophorus ferrugineus (Olivier, 1790) is an invasive pest species that constitutes one of the... more Rhynchophorus ferrugineus (Olivier, 1790) is an invasive pest species that constitutes one of the most important problems around the Mediterranean region and has been responsible for the loss of over 100,000 palm trees with an estimated annual cost of EUR several hundred million since its introduction into Europe. Methodological approaches of conservation ecology, such as multidisciplinary modelling, also apply in the management of cultural landscapes concerning ornamental plants, such as palm trees of the area. In this paper, we propose a dynamic model for the control of the red palm weevil, contributing in this way to the sustainability of an existing cultural landscape. The primary data set collected is a sample from the density-time function of a two-cohort pest population. This data set suggests a bimodal analytic description. If, from this data set, we calculate a sample from the accumulated density-time function (the integral of the density-time function), it displays a doubl...

Data for the evaluation of functional response of the parasitoid species Chelonus oculator: (b) g... more Data for the evaluation of functional response of the parasitoid species Chelonus oculator: (b) greenhouse trial. MS Excel 2007 File (read only). Data include host densities (X) (no. eggs/patch), parasitoid densities (Y) (female adults/m2), and parasitized host (Xa) (replications 1 to 12) (parasitized egg/patch)

Data for parasitoid transition, Chelonus oculator, found at the corresponding stages in laborator... more Data for parasitoid transition, Chelonus oculator, found at the corresponding stages in laboratory trials. MS Excel 2007 File (read only). Data include accumulated degree-days (º C x day), number inside host, number outside host+pupa, and total immatures

Data for host transition, Spodoptera exigua, found at the corresponding stages in greenhouse pepp... more Data for host transition, Spodoptera exigua, found at the corresponding stages in greenhouse pepper crop. MS Excel 2007 File (read only). Data include cage number, accumulated degree-days (º C x day), number of eggs, I-instar, II-instar, III-instar, IV-instar, V-instar, total larvae, number of pupae, and adults (no. individuals / cage)

Data for evaluation of biological parameters of the parasitoid species Chelonus oculator: (a) Lab... more Data for evaluation of biological parameters of the parasitoid species Chelonus oculator: (a) Laboratory trial, fecundity of adults. MS Excel 2007 File (read only). Data include temperature (º C), and fecundity (no. eggs/female)

Monitoring of ecological systems is one of the major issues in ecosystem research. The concepts a... more Monitoring of ecological systems is one of the major issues in ecosystem research. The concepts and methodology of mathematical systems theory provide useful tools to face this problem. In many cases, state monitoring of a complex ecological system consists in observation (measurement) of certain state variables, and the whole state process has to be determined from the observed data. The solution proposed in the paper is the design of an observer system, which makes it possible to approximately recover the state process from its partial observation. The method is illustrated with a trophic chain of resource – producer – primary consumer type and a numerical example is also presented.

Bulletin of Mathematical Biology, 2021

We consider matrix games with two phenotypes (players): one following a mixed evolutionarily stab... more We consider matrix games with two phenotypes (players): one following a mixed evolutionarily stable strategy and another one that always plays a best reply against the action played by its opponent in the previous round (best reply player, BR). We focus on iterated games and well-mixed games with repetition (that is, the mean number of repetitions is positive, but not infinite). In both interaction schemes, there are conditions on the payoff matrix guaranteeing that the best reply player can replace the mixed ESS player. This is possible because best reply players in pairs, individually following their own selfish strategies, develop cycles where the bigger payoff can compensate their disadvantage compared with the ESS players. Well-mixed interaction is one of the basic assumptions of classical evolutionary matrix game theory. However, if the players repeat the game with certain probability, then they can react to their opponents’ behavior. Our main result is that the classical mixe...

Agronomy, 2021

We propose a conceptual model for pollination and fertilization of tomato flowers in greenhouses ... more We propose a conceptual model for pollination and fertilization of tomato flowers in greenhouses crops by hoverflies, when the maximal number of adult pollinators maintained by the crops is less than what is needed for an economically successful pollination in greenhouses. The model consists of a two-stage process for additional feeding of hoverfly to maintain the pollinator density at the economically desired level. First, with a stochastic model, we calculate the density of flies necessary for the economically successful pollination, determined according to the economically expected yield. Second, using a deterministic optimal control model, we find a minimum cost supplementary feeding strategy. In summary, we theoretically demonstrate, at the present stage of the research without validations in case studies, that optimal supplementary feeding can maintain the economically desired hoverfly density.

Insects, 2020

Cannibalism in insects plays an important role in ecological relationships. Nonetheless, it has n... more Cannibalism in insects plays an important role in ecological relationships. Nonetheless, it has not been studied as extensively as in other arthropods groups (e.g., Arachnida). From a theoretical point of view, cannibalism has an impact on the development of more realistic stage-structure mathematical models. Additionally, it has a practical application for biological pest control, both in mass-rearing and out in the field through inoculative releases. In this paper, the cannibalistic behavior of two species of predatory bugs was studied under laboratory conditions—one of them a generalist predator (strictly carnivorous), Nabis pseudoferus, and the other a true omnivore (zoophytophagous), Nesidiocoris tenuis—and compared with the intraguild predation (IGP) behavior. The results showed that cannibalism in N. pseudoferus was prevalent in all the developmental stages studied, whereas in N. tenuis, cannibalism was rarely observed, and it was restricted mainly to the first three nymphal ...

Tobbfajos evoluciookologiai modellt dolgoztunk ki, amely alkalmas az invaziv fajok es a paleontol... more Tobbfajos evoluciookologiai modellt dolgoztunk ki, amely alkalmas az invaziv fajok es a paleontologia „szakaszos egyensulyi” fogalmanak vizsgalatara. Megmutattuk, hogy az adaptiv dinamikai stabilitas specialis esetkent adodik az altalunk bevezetett dinamikus stabilitasbol. Kimutattuk, hogy a nem kooperalo egyedek kellően hatasos buntetesevel stabilizalhato a kooperacio. Igazoltuk, hogy a termeszetes szelekcio folyaman az „optimalizalo” (sajat bevetelet maximalizalo) tipust kiszelektalja a „versengőt” (aki relativ előnyet maximalizalja). Egy evolucios jatekelmeleti modellel kimutattuk, hogy kis csoportletszam mellett az altruista segitseg tobbszori ragadozotamadas eseten ESS. Igazoltuk, hogy mind a Ewens-fele parcialis ratermettseg, mind a relativ előny novekedesi rataja egyarant aranyos a ratermettsegek varianciajaval. Peldat adtunk olyan parameterekre, amelyek eseten a mehek optimalis nektargyűjtesi viselkedese nem garantalja a koegzisztenciat, ha ket novenyfaj nektarjaert ket mehf...

The m onitoring and analysis of the processes taking place in an ecosystem is a key issue for a s... more The m onitoring 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 methodologic...

Journal of Theoretical Biology, 2020

Dynamic Games and Applications, 2019

Applied Mathematics and Computation, 2018

Scientific reports, Jan 20, 2018

We consider two types of optimal foragers: a random searcher and a search image user. A search im... more We consider two types of optimal foragers: a random searcher and a search image user. A search image user can find its desired prey with higher and undesired prey with lower probability than a random searcher. Our model considers the density-dependent travelling time and the time duration of reproduction (oviposition). In the framework of optimal foraging theory for one predator-two prey systems, we find that there are ranges of prey densities in which the search image user has a higher net energy intake, and there are other ranges of prey densities in which the random searcher has higher net energy intake. The damsel bug Nabis pseudoferus Remane (Hemiptera: Nabidae) is a generalist predator rather than an omnivore. This species has a wide range of arthropod prey (predominantly insects and mites). Several aspects of the biology of this species have been studied, especially its cannibalistic behaviour, which is a quite important feature because N. pseudoferus is often used as a biolo...

Journal of Theoretical Biology, 2017

Journal of the Franklin Institute, 2017