Estimative of Podisus nigrispinus (Dallas) (Heteroptera: Pentatomidae) development time with non linear models

Estimativa do tempo de desenvolvimento de Podisus nigrispinus (Dallas) (Heteroptera: Pentatomidae) através de modelos não lineares

Abstracts

The objective of this study was to evaluate the precision of the non linear models of Davidson (1942, 1944), Stinner et al. (1974), Sharpe & DeMichele (1977), and Lactin et al. (1995) to describe relationship between developmental rate of different stages of Podisus nigrispinus (Dallas) and temperature. Lower values of R² for the models of Davidson (0.1593 to 0.2672, and 0.1406 to 0.2804 for males and females, respectively) and of Stinner et al. (0.2136 to 0.6389, and 0.1417 to 0.3045 for males and females, respectively) showed that these models were not adequate to estimate developmental rate of P. nigrispinus as function of temperature. However, high values of R² for the models of Sharpe & DeMichele (0.9226 to 0.9893, and 0.8818 to 0.9914 for males and females, respectively), and of Lactin et al. (0.9485 to 0.9997, and 0.8961 to 0.9997 for males and females, respectively) showed that these models are suitable to estimate developmental rate of P. nigrispinus as function of temperature. Females of P. nigrispinus showed high tolerance to high temperature which is represented by high values of H H for immature stage of this insect obtained with the Sharpe & DeMichele model. According to this model females of P. nigrispinus present thermal stress at 33.3ºC, which indicates that maximum thermal estimated by this model was close to the real one.

Asopinae; biological control; Alabama argillacea; developmental rate; predator

O objetivo deste estudo foi avaliar a precisão dos modelos não lineares de Davidson (1942, 1944), Stinner et al. (1974), Sharpe & DeMichele (1977) e Lactin et al. (1995) no estudo da relação entre as taxas de desenvolvimento das diferentes fases de Podisus nigrispinus (Dallas) e a temperatura. Os menores valores de R² para os modelos de Davidson (0,1593 a 0,2672, e de 0,1406 a 0,2804 para machos e fêmeas, respectivamente) e de Stinner et al. (0,2136 a 0,6389, e de 0,1417 a 0,3045 para machos e fêmeas, respectivamente), indicaram que esses modelos não são adequados para a estimativa do tempo de desenvolvimento de P. nigrispinus, em função da temperatura. Entretanto, os altos valores de R² para os modelos de Sharpe & DeMichele (0,9226 a 0,9893, e de 0,8818 a 0,9914 para machos e fêmeas, respectivamente), e de Lactin et al. (0,9485 a 0,9997, e de 0,8961 a 0,9997 para machos e fêmeas, respectivamente), indicaram que esses modelos são adequados para a estimativa do tempo de desenvolvimento de P. nigrispinus, em função da temperatura. Fêmeas de P. nigrispinus, na fase imatura, mostraram maior tolerância à alta temperatura, a qual é representada pelo parâmetro H H obtido do modelo de Sharpe & DeMichele. De acordo com este modelo, fêmeas de P. nigrispinus na fase imatura apresentam estresse térmico a 33,3°C, indicando que a estimativa da ação térmica máxima foi bastante realista.

Asopinae; controle biológico; Alabama argillacea; taxa de desenvolvimento; predador

ECOLOGY, BEHAVIOR AND BIONOMICS

Estimative of Podisus nigrispinus (Dallas) (Heteroptera: Pentatomidae) development time with non linear models

Estimativa do tempo de desenvolvimento de Podisus nigrispinus (Dallas) (Heteroptera: Pentatomidae) através de modelos não lineares

Rômulo S. Medeiros^I; Francisco S. Ramalho^II; José E. Serrão^III; José C. Zanuncio

^IDepto. Biologia Animal, Universidade Federal de Viçosa, 36571-000, Viçosa, MG, e-mail: [e-mail]

^IIEmbrapa Algodão, Rua Osvaldo Cruz, 1143, Centenário, C. postal 174, 58107-720, Campina Grande, PB, e-mail: [e-mail]

^IIIDepto. Biologia Geral, Universidade Federal de Viçosa, 36571-000, Viçosa, MG, e-mail: [e-mail]

ABSTRACT

The objective of this study was to evaluate the precision of the non linear models of Davidson (1942, 1944), Stinner et al. (1974), Sharpe & DeMichele (1977), and Lactin et al. (1995) to describe relationship between developmental rate of different stages of Podisus nigrispinus (Dallas) and temperature. Lower values of R² for the models of Davidson (0.1593 to 0.2672, and 0.1406 to 0.2804 for males and females, respectively) and of Stinner et al. (0.2136 to 0.6389, and 0.1417 to 0.3045 for males and females, respectively) showed that these models were not adequate to estimate developmental rate of P. nigrispinus as function of temperature. However, high values of R² for the models of Sharpe & DeMichele (0.9226 to 0.9893, and 0.8818 to 0.9914 for males and females, respectively), and of Lactin et al. (0.9485 to 0.9997, and 0.8961 to 0.9997 for males and females, respectively) showed that these models are suitable to estimate developmental rate of P. nigrispinus as function of temperature. Females of P. nigrispinus showed high tolerance to high temperature which is represented by high values of H_H for immature stage of this insect obtained with the Sharpe & DeMichele model. According to this model females of P. nigrispinus present thermal stress at 33.3^oC, which indicates that maximum thermal estimated by this model was close to the real one.

Key words: Asopinae, biological control, Alabama argillacea, developmental rate, predator

RESUMO

O objetivo deste estudo foi avaliar a precisão dos modelos não lineares de Davidson (1942, 1944), Stinner et al. (1974), Sharpe & DeMichele (1977) e Lactin et al. (1995) no estudo da relação entre as taxas de desenvolvimento das diferentes fases de Podisus nigrispinus (Dallas) e a temperatura. Os menores valores de R² para os modelos de Davidson (0,1593 a 0,2672, e de 0,1406 a 0,2804 para machos e fêmeas, respectivamente) e de Stinner et al. (0,2136 a 0,6389, e de 0,1417 a 0,3045 para machos e fêmeas, respectivamente), indicaram que esses modelos não são adequados para a estimativa do tempo de desenvolvimento de P. nigrispinus, em função da temperatura. Entretanto, os altos valores de R² para os modelos de Sharpe & DeMichele (0,9226 a 0,9893, e de 0,8818 a 0,9914 para machos e fêmeas, respectivamente), e de Lactin et al. (0,9485 a 0,9997, e de 0,8961 a 0,9997 para machos e fêmeas, respectivamente), indicaram que esses modelos são adequados para a estimativa do tempo de desenvolvimento de P. nigrispinus, em função da temperatura. Fêmeas de P. nigrispinus, na fase imatura, mostraram maior tolerância à alta temperatura, a qual é representada pelo parâmetro H_H obtido do modelo de Sharpe & DeMichele. De acordo com este modelo, fêmeas de P. nigrispinus na fase imatura apresentam estresse térmico a 33,3°C, indicando que a estimativa da ação térmica máxima foi bastante realista.

Palavras - chave: Asopinae, controle biológico, Alabama argillacea, taxa de desenvolvimento, predador

Podisus nigrispinus (Dallas) is a generalist predator which occurs in many countries of Central and South America (Thomas 1992) as an important biological control agent in several crops. Michel (1994) emphasized the importance of this predator against Alabama argillacea (Hübner) (Lepidoptera: Noctuidae) in Paraguay. The occurrence of this predator in Brazil is mentioned in many crops of economic importance such as tomato (Lycopersicum esculentum Mill.) (Bergam et al. 1984), soybean (Glycine max L.) (Panizzi et al. 1977), and cotton (Gossypium hirsutum L.) (Medeiros et al. 1998). For this reason, studies with this predator have been showing its potential to control populations of A. argillacea (Santos et al. 1995, 1996, Medeiros et al. 2000, 2003, Lemos et al. 2001).

The relationship between developmental rate of insects and temperature represents an important ecological tool to modelling population dynamics of these organisms (Uvarov 1931, Howe 1967). Several authors (Davidson 1942, 1944, Stinner et al. 1974, Sharpe & DeMichele 1977, Lactin et al. 1995) have formulated mathematical models to describe the relationship between developmental rate of insects and temperature. The knowledge of such relationships is important to determine seasonal occurrences of insect populations as strategies for integrated pest management (Marco et al. 1997).

Linear models were the first ones developed for insects (Howe 1967). However, the lack of linearity of the developmental rate of insects at low and high temperatures suggests that these models are inadequate to describe such parameters for these organisms. This has led to increasing development of non linear phenological models in programs of integrated pest management from the beginning of 1980 (Wagner et al. 1984, Worner 1992).

Non linear models (Logan et al. 1976, Hilbert & Logan 1983) have been developed for different species of insects submitted to certain circumstances. Davidson (1942, 1944) described developmental rate of insects as function of temperature through the use of logistic equations. Stinner et al. (1974) described the effect of temperature on developmental rate as a modified sigmoid equation which results in a symmetrical curve at high temperatures. Sharpe & DeMichele (1977) formulated a complex biophysical model, later modified by Schoolfield et al. (1981), which describes a non linear response of developmental rate of insects exposed to low and high temperatures as well as a linear response at intermediate temperatures. Lactin et al. (1995) modified the non linear model of Logan et al. (1976) by eliminating the parameter y, which is the direct measurable rate of the temperature-dependent physiological process at T_b, and introducing the parameter intercept l which allowed the estimative of developmental threshold.

Linear models can not supply precise information on inhibition of development at extreme temperatures and, with a few exceptions, they have been applied to study such rates for insect pest species as function of temperature but not of their natural enemies (Gould & Elkinton 1990). For this reason, the purpose of this research was to determine which non linear model (Davidson, 1942, 1944, Stinner et al. 1974, Sharpe & DeMichele 1977, Lactin et al. 1995) can better describe the effect of temperature on P. nigrispinus development.

Material and Methods

The research was developed at the Biological Control Unit (BCU)/Embrapa Algodão, in Campina Grande, State of Paraíba, Brazil. Data used were obtained from Medeiros et al. (1998). The developmental rate from egg to adult was studied under the following constant temperatures: 17, 20, 23, 25, 28, 30, 33, and 35^oC (60 ±10% RH, and a photoperiod of 14:10 [L:D] h).

Mean developmental rate of P. nigrispinus at different temperatures was estimated with the formula:

where r(T) is the mean developmental rate at temperature T (°C), di, individual observations of developmental time in days, and n, number of observations. This method is recommended by Logan et al. (1976) to account for linearity in the transformation from developmental time to developmental rate.

Developmental rate is the reciprocal of developmental time in days and it is represented by values from 0 to 1. These rates are used in developmental models where data are added each day. The development of an organism is completed when the sum of their daily rate of development reaches value 1 (Curry & Feldman 1987). Therefore, the integral of the function of developmental rate along time (as the models of Davidson, 1942, 1944, Stinner et al. 1974, Sharpe & DeMichele 1977, Lactin et al. 1995) can be used to simulate the development of an organism submitted to changes in temperature. For this reason, descriptive non linear procedures have been used to analyse relationship between developmental rate of P. nigrispinus and temperature as described:

Logistic equation of Davidson (1942, 1944):

where r(T) is the mean developmental rate at temperature T (°C), a, value which defines the place of the regression line in relation to the x axis, b, the slope of curve line, k, a constant defining the upper limit of the sigmoid line, Ti, temperature in environmental chamber. Parameters a, b and k were estimated with regression of non linear model of Marquardt with the PROC NLIN (Sas Institute Inc. 2000). This method is used to determine the minimum square of the parameters estimated with this model.

Sigmoid equation of Stinner et al.(1974):

where r(T) is the mean developmental rate at temperature T (°C), c, (1/T_max) x (e ^{k1 + k2Tmax}) (asymptote), k₁ and k₂, empirical constants and T' = T, for T < T_max and T' = 2 x T_max - T, for T > T_max. The parameters c, k₁ and k₂were estimated by Marquardt's method using PROC NLIN (Sas Institute Inc. 2000).

where r(T) is the mean developmental rate at temperature T (°K), R, universal gas constant (1.987 cal degree^-1mole^-1), RHO₂₅, the developmental rate at 25°C (298.15°K), assuming no enzyme inativation, H_A, the enthalpy of activation of the reaction that is catalyzed by a rate-controlling enzyme, T_L, Kelvin temperature at which the rate-controlling enzyme is half active and half low-temperature inactive, H_L, the change in the enthalpy associated with low temperature inativation of the enzyme, T_H, Kelvin temperature at which the rate-controlling enzyme is half active and half high-temperature inactive, and H_H, the change in the enthalpy associated with high-temperature inactivation of the enzyme. The parameters RHO₂₅, H_A, T_H, and H_H were estimated by Marquardt's method using PROC NLIN (Sas Institute Inc. 2000) with the procedure adopted by Wagner et al. (1984).

The numerator of the fourth equation explains the dependent developmental rates of the temperature in the absence of inactivation at low or high temperatures, while first and second exponential equations in the denominator explain respectively, the inhibition at low and high temperatures (Wagner et al. 1984). These authors developed a method to determine if data are adjusted by a model constituted of six, four or two parameters. This method tests the non linearity of data to extreme temperatures (low and high), which would indicate inhibition at extreme temperatures. The model is constituted by six parameters and it is better adjusted to the data if both extreme temperatures have significant effect in the inhibition. When high temperatures have no significant effect in the inhibition, the parameters T_H and H_H will assume constant values of 1,000 and 100,000,000, respectively. If low temperature has no significant effect in the inhibition, the parameters T_L and H_L will receive constant values of 100 and 100,000,000, respectively. Therefore, in both cases, the model constituted of four parameters will be better adjusted to the data. When low and high temperatures have no effect in the inhibition, the model with two parameters will be better adjusted to the data; then, the four parameters T_H, H_H, T_L and H_L will receive constant values of 1,000; 100,000,000; 100, and 100,000,000, respectively.

Model of Lactin et al. (1995) resulted from the modification of the non linear model of Logan et al. (1976):

where r(T) is the mean developmental rate at temperature T (°C), T_L, lethal temperature (°C), r, rate of increase at optimal temperature, DT, difference between lethal and optimal temperature of development, and l, the parameter that makes the curve intercept the x-axis, allowing to estimate developmental threshold. Parameters TL, r, DT and l were estimated by Marquardt's method using PROC NLIN (Sas Institute Inc. 2000).

R² of these models were calculated as R² = 1-(S²_y/S²_td ), where S²_y is the variance of the residues of the model and S²_td is the variance of means of developmental rates.

Results

Except for some instars [2^nd (30°C), 3^rd (30°C and 33°C), 4^th (33°C) and 5^th (28°C and 33^oC) of P. nigrispinus that originated males; and 1^st (30°C), 4^th (33°C) and 5^th (28°C) instars for those that originated females], developmental rates of this insect increased as the temperature rose (Table 1). On the other hand, developmental rates of eggs and nymphs of P. nigrispinus increased as the temperature rose for both sexes (Table 2). At the highest tested temperature (35^oC) all the predator eggs died before hatching and no evidence of development was observed. Therefore, the development time at 35^oC was not feasible because of the deleterious effect this constant high temperature had on the eggs of this predator. The lethality of this temperature was not instantaneous, and the predators probably died as a consequence of long time exposure to high temperature stress. High mortality at extreme constant temperatures may result from different mortality agents and inactivation of enzymes (Sharpe & DeMicele 1977).

Low values of R² of the logistic model of Davidson (1942, 1944) (from 0.1593 to 0.2672, and 0.1406 to 0.2804 for males and females, respectively) (Table 3) and for the sigmoid model of Stinner et al. (1974) (from 0.2136 to 0.6389, and from 0.1417 to 0.3045 for males and females, respectively) (Table 4) indicate that these models are not adjusted for the data obtained for P. nigrispinus.

Inhibition of P. nigrispinus development occurred at the highest temperature (35°C) while in the lowest temperature (17°C) this was not significant. Since the inhibition of developmental rate of this predator was only significant at higher temperature, we used the version of Sharpe & DeMichele (1977) model, with constants T_L and H_L assuming the values of 100 and 100,000,000, respectively. Linear correlation between developmental rate and temperature up to 33°C was significant (as for instance, immature males: R² = 0.95; F = 99.76; df = 1,5; P = 0.0002 and immature females: R² = 0.97; F = 187.19; df = 1,5; P = 0.0001) with no deviation in linearity at lower temperatures.

High values of R² for the biophysical model of Sharpe & DeMichele (1977) (from 0.9226 to 0.9893, and from 0.8818 to 0.9914 for males and females, respectively) (Table 5) and for the model of Lactin et al. (1995) (from 0.9485 to 0.9997, and from 0.8961 to 0.9997 for males and females, respectively) (Table 6) indicate good adjustment of these models for data of developmental rate of P. nigrispinus.

Females of P. nigrispinus showed great tolerance to high temperature, which is represented by high value of H_H for the immature stage (Table 5) obtained with the model of Sharpe & DeMichele (1977).

The parameter T_H of the model of Sharpe & DeMichele (1977) represents the temperature (°K) in which the enzyme that controls developmental rate of the insect is partially inactivated. The values of the parameter T_H were similar in all developmental stages of the P. nigrispinus. The values of T_H for P. nigrispinus males and females were of 306.3°K and 306.4°K (Table 5). Therefore, this species will experience thermal stress at 33.3°C. This indicates that the estimate of the maximum thermal action for the model of Sharpe & DeMichele (1977) was quite realistic.

The parameter T_L of the model of Lactin et al. (1995) represents the temperature (°C) at which life can no longer be sustained. The value of this parameter is expressed in degree Celsius. The values of T_L were similar in all developmental stages of the predator. The estimated values of T_L for males and females of P. nigrispinus were 37.80 and 35.38°C, respectively (Table 6). The model of Lactin et al. (1995) showed that males of P. nigrispinus are more tolerant to high temperatures than females of this species. Values of l were lower than zero, indicating that it can estimate the threshold for all developmental stages of P. nigrispinus. Therefore, relationship between developmental rate and temperature for males and females of P. nigrispinus was appropriately described by the models of Sharpe & DeMichele (1977) and of Lactin et al. (1995) (Figs. 1 and 2).

Discussion

Medeiros et al. (1998) reported that P. nigrispinus maintained its population in the cotton crop in the State of Paraíba, Brazil, during all cotton season in conditions of prey scarcity (after outbreaks of A. argillacea) and at temperatures that can reach 35°C. However, these authors reported that P. nigrispinus presented low survival at 33°C in laboratory conditions and no development at 35°C. It is probable that high mortality at extreme constant temperatures may be the result from different mortality agents and inactivation of enzymes (Sharpe & DeMichele 1977). Similar results were obtained by Didonet et al. (1995). It is possible that the development of P. nigrispinus in areas where maximum temperatures exceed the lethal one can be explained by oscillations of temperature during the day and to the microclimate produced by the agroecossistem of cotton plants. High mortality in experiments with insect maintained at extreme and constant temperatures may not reflect its real response to natural conditions of temperature fluctuation (Logan et al. 1985, Torres et al. 1998) because the insect can receive strong radiation during the day and mild temperatures at night (Worner 1992). Besides, the lethal effect of extreme temperatures depends on length of the period of maintainance of the insect in those temperatures (Howe 1967).

The non linear logistic model of Davidson (1942, 1944) and the sigmoid model of Stinner et al. (1974) have not appropriately described the relationship between developmental rates of different stages of P. nigrispinus and the temperature. Wagner et al. (1984) stated that the models to describe the relationship between developmental rate and temperature of different species of insects have the followings problems: (1) the model of Stinner et al. (1974) assumes symmetrical form on both sides of the optimal temperature and for this reason does not describe, appropriately, the development of insects at high temperatures; and (2) the model of Davidson (1942, 1944) has low descriptive precision at both final of the curves of the relationship between developmental rate and temperature. Harari et al. (1998) have pointed out that the model of Davidson (1942, 1944) do not appropriately estimate the optimal temperature for development of Maladera matrida Argaman (Coleoptera: Scarabaeidae) because it estimated longer developmental rates at higher than at optimal temperatures.

The biophysical model of Sharpe & DeMichele (1977) describes a non linear response between developmental rates at low and high temperatures, as well as a linear response at intermediate temperatures. For this reason, Wagner et al. (1984) and Fan et al. (1992) consider that this non linear model better describes the effect of constant temperatures on insects development. This model was applied and evaluated by Gould & Elkinton (1990), Orr & Obrycki (1990), Fan et al. (1992), Morales-Ramos & Cate (1993), Judd & McBrien (1994) and Harari et al. (1998) and it was appropriate for determination of developmental rates studied.

Lactin et al. (1995), modified the non linear model of Logan et al. (1976), by eliminating the parameter Y and introducing the parameter l (intercept), which allowed to estimate developmental threshold of insects. This model was applied and evaluated by Briere & Pracros (1998) and it is appropriate to describe relationship between developmental rate of different stages of Lobesia botrana Dennis & Schiffermüller (Lepidoptera: Tortricidae) and temperature.

The models of Sharpe & DeMichele (1977) and of Lactin et al. (1995) described, appropriately, the relationship between developmental rates of different stages of males and females of P. nigrispinus and the temperature (Figs. 1 and 2) because both described an asymmetrical form around high temperature. Briere & Pracros (1998) stated that the relationship between developmental rate and temperature in insects is not linear, and it presents asymmetrical form being composed by three sections: the first is represented by low temperatures, where the increase on developmental rate is not linear from the point of development zero; second section is where the developmental rate becomes proportional to temperature increase; and the third begin from optimal until lethal temperature. Our results suggest that the models of Sharpe & DeMichele (1977) and of Lactin et al. (1995) are appropriate to describe relationship between developmental rates of different instars and stages of P. nigrispinus and temperature.

Acknowledgments

To the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), to the Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG), to the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) and to the staff of the Biological Control Unit/Embrapa Algodão.

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Received 25/03/03.

Accepted 05/02/04.

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Publication Dates

• Publication in this collection
  14 July 2004
• Date of issue
  Apr 2004

History

• Accepted
  05 Feb 2004
• Received
  25 Mar 2003