Mathematics and Statistics Journal

IWNES PUBLIHER Mathematics and Statistics Journal (ISSN: 2077-4591) Journal home page: http://www.iwnest.com/msj/ Expecting the Coming Changes in the Population Density of Male Flies of Peach Fruit Fly, Bactrocera Zonata Based on Actual Data Figures and Corresponding Meteorological Factors El-Gendy, I.R. Plant Protection Research Institute, Agricultural Research Center, Giza, Egypt. A R I C L E I N F O Article history: Received 22 February 2015 Accepted 20 March 2015 Keywords: Peach fruit fly, Bactrocera zonata, population density, Actual data figures, meteorological factors. A B S R A C Expected of the coming changes in the population density of peach fruit fly males (PFF), Bactrocera zonata were completed through advanced statistical trials based on field trials data represented as numbers of captured male flies (Y) and the corresponding meteorological factors (x). he weekly mean temperature and relative humidity (X) for two successive years; 2010 and 2011 growing seasons were first estimated and adopted along with the actual data figures representatives for B. zonata population density of male flies. he results revealed that the regression exponential model gives the best results followed by natural logarithm for predicting the coming number males of PFF (Y) when carried out the mean- temperature, -relative humidity and -degrees-day with high population density of PFF. While, the natural logarithm is the most suitable model for predicting the coming number males of PFF (Y) with lower population density of PFF. 2015 IWNES Publisher All rights reserved. o Cite his Article: El-Gendy, I.R.., Expecting the Coming Changes in the Population Density of Male Flies of Peach Fruit Fly, Bactrocera Zonata Based on Actual Data Figures and Corresponding Meteorological Factors. Math. Stat. J., 1(1), 6-11, 2015 INRODUCION Peach fruit fly (PFF), Bactrocera zonata (Saunders) (Diptera: ephritidae) is a key insect-pest of horticulture in Egypt [5]. PFF is an active insect-pest throughout the year in Egypt exception of cooler months, especially January month [4] and [5]. Presence of this insect-pest threatens foreign trade, domestic fruit and vegetable crops. emperature is an important abiotic factor affecting on survival and developmental rates of fruit flies [1,2,8] also, temperature and relative humidity is related to activity and population density PFF. herefore, it was thought of interest that temperature is the most important factor governing the changes in the population activity and accordingly population density of PFF inhabited Kom-Hamda, El-Beheira governorate behave as the same route. he basic population levels and its corresponding weekly fluctuations were determined by simply adopting the following equations based on both weekly-air temperature and relative humidity for El-Dalangate weather station for 2010 and 2011 seasons [5]. he population abundance of PFF is partially depended on environmental temperature and corresponding of the accumulated degrees-day (ADD's), so, monitoring the ADD's is a valuable tool for predicting insect-pest activity and timing pest management practices [5]. Predicting the annual generations of peach fruit fly, Bactrocera zonata (saunders) (diptera: tephritidae) using heat units accumulation in Egypt was estimated [7,9] as well as, the predicting of the annual generations of insects in the future under climate change [9,11]. he accuracy of prediction - that depends on DD s and population of B. zonata - enabling growers and pest control advisors to reduce monitoring periods to make a true decision for pest control in the proper time, which minimize costs and the hazard of chemical control [7], while the predicting of the population density of PFF under field conditions wasn't determine yet, so the present study aims to explain the variation in the coming changes in the population density of PFF (Y) through advanced statistical models of regression based on field trials with corresponding meteorological factors. Corresponding Author: Ismail Ragab El-Gendy, Plant Protection Research Institute, Agricultural Research Center, Giza, Egypt. E-mail: somaa_gendy@yahoo.com, Cell phone: 01279109437

7 Ismail Ragab El-Gendy, 2015 MAERIAL AND MEHODS Field trials: he new calculated figures are depended on the weekly basic population levels of PFF, B. zonata for two years of observations of these insects inhabiting the trapping area. Population density of PFF males: Jackson trap provided with cotton wick (5 cm long and 1 cm diameter) baited with liquid sex attractant (Methyl Eugenol 98%) with Killing agent, Malathion, with a ratio 8:2 (vol:vol) and the cotton wick retained for one month at most. he experiment was conducted for two calendar years from first January, 2010 to last December, 2011. Four Jackson traps were set up separately in mango and Citrus orchards at Kom-Hamadah district, N 30 30, E 30 49. raps were hanged at a height of 1.5 to 2 m above the ground. Weekly serviced of traps was done and captured male flies of PFF were expressed as a number of male flies catch /trap /week (CW) [5]. Meteorological factors: Meteorological parameters like maximum-, minimum- temperature, and relative humidity were collected from El-Dalangat weather station. he collected data of above meteorological parameters were expressed as weekly mean for every standard week, as well as degrees-day for every standard week along study according to El-Gendy and El-Saadany [5]. Statistical trails: he present obtained data were subjected to advanced models of regression; Polynomial, multiple, exponential and logarithmic regression by CoStat Software, 1990, which were made between weekly mean of trap catches of PFF males (y) and mean weather parameters of temperature, relative humidity and the estimated degrees-day for every standard week along the study owing to determine the actual effect for (x) on (Y). Results: Polynomial, multiple, exponential and logarithmic regressions were subjected to show the relationship between the weekly mean numbers of capture PFF males (Y) and both weekly mean-temperature and -relative humidity as well as degrees-day (X) as the actual effect for (x) on (Y), which was demonstrated by the following data figures: Actual data figures through 2010 season: A. Regression models of the actual weekly number of male flies (Y) and weekly figures of weekly mean temperature (X): he obtained results (able, 1) of Polynomial, Natural logarithm and Exponential regressions of the actual weekly number of male flies (Y) and weekly figures of weekly mean temperature (X) explained 54, 56 and 60 % of the total variations in the population density (PD) of PFF males according to the estimating of determination coefficients; R 2 values were 0.536, 0.559 and 0.60 for Polynomial, Natural logarithm and Exponential regressions, respectively. While, 46, 44 and 40 % of variances are referred to other factors did not include in these present analyses, respectively. According to the estimated Polynomial regression value, the following equation is recommended: Ŷ = - 15.479 + 1.211 x a (1), i.e. every unit effect (1ºC) around the general average gives an increase in population density equal to 1.2 flies/week. While, the recommended equations for both Natural logarithm and Exponential regressions are y = -71.118+26.815*ln(x) (2) and y = 0.43478183985*e^(0.13674728887*x). (3), respectively. B. Regression models of actual weekly number of male flies (Y) and weekly figures of weekly mean of relative humidity % (X): Data in able (1) of Polynomial, Natural logarithm and Exponential regressions of the actual weekly number of male flies (Y) and weekly figures of weekly mean of relative humidity % (X) appeared that 25, 24 and 23 % of the total variations in PD regard to weekly mean relative humidity %, while 75, 76 and 77 % variance in PD is referred to other factors not included in the present analysis. he equation of Polynomial regression is recommended: Ŷ = 82.37-1.345 x (4), i.e. every unit effect (RH %) around the general average gives a decrease in PD equal to 1.3 flies /week. While, it was y = 294.92+-71.53*ln(x) (5) and y = 13019.276806*e^(-0.1374737004*x) (6) for Natural logarithm and Exponential regressions, respectively.

8 Ismail Ragab El-Gendy, 2015 able 1: Regression models analysis between weekly mean numbers of capture male flies of PFF and meteorological parameters through 2010 season. Model X 1 Regression Coefficients values R 2 2 b 3 a 4 value P 5 value P 6 Poly-nominal 0.536 0.245 0.518 1.24±0.16-1.35±0.33 0.17±0.02-15.47±3.63 82.37±17.56-0.875±1.85 0.63 ns Natural log. 0.559 0.243 0.541 26.81±3.36-70.76±17.65 10.77±1.40 0.002 *** -71.12±10.41 294.92±69.96-33.38±5.66 Exponential 0.60 0.23 0.58 0.136±0.37-0.13±0.04 0.019±0.002 1; metrological factors, 2; determination coefficient, 3; constant 4; intercept, 5; probability level of constant, 6; probability level of intercept. 0.005 *** -0.83±0.02 9.47±1.92 0.82±0.19 0.03 * C. Regression models of actual weekly number of Males (Y) and weekly mean of degree-days (X): he estimated of determination coefficient of Polynomial, Natural logarithm and Exponential regressions of the actual weekly number of male flies (Y) and weekly mean of degree-days (X) (able, 1) explained variance about 52, 54 and 58 % of the total variance (100%) in PD, respectively. Where, he equation of Polynomial regression is recommended Y = -0.875 + 0.170* DD's (7) and this means that every unit increase by 1ºC gives an increase in population density by 0.17 males/week on the other hand, the recommended equations for Natural logarithm and Exponential regressions are y = -32.09+10.64*ln(x) (8) and y = 2.27783825463*e^(0.01912905686*x) (9). Generally, Its appear from the equations 1-9 that the regression exponential model gives the best result than model of either natural logarithm or polynomial model of regression for predicting the coming number males of PFF against mean-temperature, -relative humidity and -degrees day. Actual data figures through 2011 season: A. Regression models of the actual weekly number of male flies (Y) and weekly figures of weekly mean temperature (X) throughout 2011 season: Data in able (1) showed that the estimated coefficient of determination of Polynomial, Natural logarithm and Exponential regressions of the actual weekly number of male flies (Y) and weekly figures of weekly mean temperature (X) were 0.199, 0.216 and 0.04, respectively. It appears that the estimated determination coefficient value explained 20, 22 and 4 % of the total variations in PD of PFF by estimating Polynomial, Natural logarithm and Exponential regressions, respectively, i.e. 80, 78 and 96 % of variances are referred to other factors not included in these present analyses of Polynomial, Natural logarithm and Exponential regressions, respectively. he estimated of Polynomial regression equation takes the following pattern: Ŷ = -9.023 + 0.822* a. (1) From the above equation every unit effect (1ºC) around the general average gives an increase in PD equal to 0.82 flies/week. On the other hand, the recommended equations for Natural logarithm and Exponential regressions are y = - 40.99+16.26*ln(x) (2) and y = 4.18813055*e^(0.03377022855*x) (3), respectively. B. Regression models of the actual weekly number of male flies (Y) and weekly figures of daily mean relative humidity % (X): Present values in able (2) showed that the determination coefficient values of Polynomial, Natural logarithm and Exponential regressions of the actual weekly number of male flies and weekly figures of daily mean relative humidity % (X) were 0.022, 0.023 and 8.75 e-6, respectively. It appears that the estimated determination coefficient value explained 2.5, 2.3 and 8.75 e-6 % of the total variations in PD for Polynomial, Natural logarithm and Exponential regressions of the actual weekly number of male flies and weekly figures of daily mean relative humidity % (X). According to the estimated regression values, the following equation is recommended: Ŷ = 20.71-0.27* (4) it means that every unit effect (RH %) around the general average gives a decrease in population density equal to 0.27 flies/week. On the other hand, the recommended equations for Natural logarithm and Exponential regressions are y = 62.98+-14.344*ln(x) (5) y = 8.64399255194*e^(-4.334407e-4*x) (6)

9 Ismail Ragab El-Gendy, 2015 able 2: Regression models analysis between weekly mean numbers of capture male flies of PFF and meteorological parameters through 2011 season. Model X 1 Regression Coefficients values R 2 2 b 3 a 4 value P 5 value P 6 Poly-nominal 0.199 0.022 0.205 0.822±0.23-0.28±0.26 0.115±0.03 0.28 ns 0.00 7*** -9.023±4.50 20.71±13.04-0.875±1.85 0.05 ns 0.12 ns 0.63 ns Natural log. 0.216 0.023 0.24 16.62±4.34-14.43±13.02 5.17±1.28 0.004 *** 0.275 ns 0.002 *** -40.99±12.74 62.98±51.40-12.68±4.89 0.00 ** 0.22 ns 0.02 * Expotenial 0.035 8.75 e-6 0.058 0.033±0.03-4.33 e-4 ±0.25 0.006±0.004 1; metrological factors, 2; determination coefficient, 3; constant 4; intercept, 5; probability level of constant, 6; probability level of intercept. 0.27 ns 0.98 ns 1.43±0.64 2.16 ±1.25 1.78±0.27 0.032 *** 0.94 ns 0.18 ns C. Regression models of the actual weekly number of male flies (Y) and weekly mean of degree-days (X): he estimated coefficient of determination of Polynomial, Natural logarithm and Exponential regressions of the actual weekly number of male flies and weekly mean of degree-days (X) explained variance 21, 24 and 5.2 % of the total variances (100%) in PD when Polynomial, Natural logarithm and Exponential regressions of the actual weekly number of male flies and weekly mean of degree-days (X) were conducted, respectively. According to regression analysis values of polynomial regression the equation takes the form: Ŷ = 0.875 + 0.115x deg. Days (7) his means that every unit increase of 1ºC gives an increase in population density by 0.12 males /week. While, it was y = -12.68+5.17*ln(x) (8) and y = 5.93637863469*e^(0.00567844711*x) (9), for equations of Natural logarithm and Exponential regressions, respectively. It's appear from equations 1-9 that the regression analysis by model of the natural logarithm give the best result than the model of polynomial for predicting the coming number males of PFF when carried out meantemperature, -relative humidity and -degrees day. Overall, the multiple regression procedure between PD of PFF and tested factors on mango orchard (ables, 3and 4) explained 52.0 and 41.0 % variance in PD of PFF of total variance (100 %), according to Adj. R 2 between PD of PFF and tested factors through both of 2010 (Adj. R^2-0.517) and 2011(Adj. R^2-0.405) seasons, respectively. On the other hand, the estimated liner regression equation for 2010 season was: [No] = -16.344915983 +0.0139746321*[RH mean] +1.21780418669*[ mean], while it was [No] = - 128.97556037+2.36117493273*[ mean] +1.78814556233*[RH] for 2011 season. able 3: Multiple regression analysis between weekly mean captured flies of PFF, B. zonata and tested meteorological factors through 2010 season. Source SS df MS F P Regression 1594.19 2 797.09 28.31 0.0000 *** [RH mean] 731.38 1 731.38 25.98 0.0000 *** [ mean] 862.80 1 862.80 30.648 0.0000 *** Error 1379.43 49 28.15 otal 2973.62 51 R 2-0.517, R 2 : Determination coefficient, PFF: Peach fruit fly, *Low significant, ***High significant, ns: non-significant. able 4: Multiple regression analysis between weekly mean captured flies of PFF, B. zonata and tested meteorological factors through 2011 season. Source SS df MS F P Regression 1030.09 2 515.04 18.76 0.0000 *** [RH mean] 551.52 1 551.52 20.09 0.0000 *** [ mean] 478.56 1 478.56 17.43 0.0001 *** Error 1372.20 50 27.44 otal 2402.30 52 R 2-0.405, R 2 : Determination coefficient, PFF: Peach fruit fly, *Low significant, ***High significant, ns: non-significant Discussion: So far, no references are available about the actual data figures, so it is may be regards as the first article about application the mathematic models for predicting the coming flies of PFF under field condition. emperature, however, is the most important weather factor governing the life span of an insect survivor. emperature influences on the rate of development, mobility activity, etc he growth rate pattern (Sigmoid, J-

10 Ismail Ragab El-Gendy, 2015 shaped and stable shape) which, in turn, depends on temperature, where the Development times for all stages of PFF, B. zonata were inversely related to temperature [10]. By using the actual data figures in this paper, we can estimate the changing of the coming PFF males with climatic change throughout the year. he obtained results of forecasting the coming changes and early warning methods are considered for the indirect monitoring of population activity of PFF, B. zonata. his was in the same trend with Farag et al. [7] who mentioned that the accuracy of prediction - that depends on DD s and population of B. zonata - enabling growers and pest control advisors to reduce monitoring periods to make a true decision for pest control in the proper time, which minimize costs and the hazard of chemical control. he present results indicated that the Physical environmental factors govern the changes in the population density of PFF. his was resemble to Khalil et al. [9] evaluated how temperature expected to influence the annual generation numbers in three governorates of Egypt using the climate change data output from the HadCM3 model for A1 scenarios proposed by the Intergovernmental Panel on Climate Change. his was extended to other insects, where Estay et al., [6] predict a change in the equilibrium density of the confused flour beetle, ribolium confusum Jacquelin (Coloeoptera: enebrionidae) from 10 to 14% under the moderate B2 scenario and 12 to 22% under the extreme A2 scenario for the period, 2071 2100. he relative humidity comes next in this respect; i.e. one of the most important physical factors in environment. High relative humidity usually reduces reproduction of the insect. Forecasting the spatial distribution, seasonal (monthly and perhaps weekly) fluctuations in the population density outbreaks of pests have to be considered when the principal aims in studying on an economic basis. In staple habitats such as forests, deserts and similar areas where only steady or periodic changes in the natural cultivations occur, insect populations maintain, more or less, definite levels. Any variations in these levels would largely be due to environmental changes. Conclusion: It concludes that the expecting of the coming weekly catch would have to be occurring in the trap, and in case of high population density of PFF the exponential model gives the best results than both natural logarithm and polynomial models for predicting the coming number males of PFF (Y) against temperature, relative humidity and degrees day. While, the natural logarithm is the most suitable model for expecting the coming male flies in case of lower population density of PFF using Jackson traps baited with methyl eugenol. ACKNOWLEDGMEN We thank to all staff members of El-Dalangat weather station at El-Beheira (Damanhur) Governorate for their assistance. REFERENCES [1] Afia, Y.E., 2007. Comparative studies on the biology and ecology of the two fruit flies, in Egypt Bactrocera zonata (Saunders) and Ceratitis capitata (Wiedemann). Ph.D. hesis, Faculty of Agriculture, Cairo University, Egypt. [2] Amin, A.A., 2008. Ecological and biological studies on the peach and Mediterranean fruit flies in Fayoum governorate. Ph. D. hesis, Fac.Agric., Fayoum University, 225 pp. [3] CoStat Sowftware, 1990. Microcomputer program analysis. Version 4.20, CoHort software, Berkeley, CA. [4] Draz, K.A.A., A.G. Hashem, M.A. El-Aw, I.R. El-Gendy, 2002. Monitoring the changes in the population activity of peach fruit fly, Bactrocera zonata (Saunders) at certain agro-ecosystem in Egypt. 2 nd International Conference, Plant Protection Research Institute, Cairo, Egypt, 21-24 December, 1: 570-575. [5] El-Gendy, I.R., G.B. El-Saadany, 2012. (1) Monitoring the changes in the population dynamics of field generations of peach fruit fly, Bactrocera zonata and some factors affecting them under field conditions. Cairo International Conference for clean pest Management, Egypt, 12-13 November, 90(2): 777-798. [6] Estay, S.A., M. Lima and F.A. Labra, 2009. Predicting insect pest status under climate change scenarios: combining experimental data and population dynamics modeling. J. Appl. Entomol., Blackwell Verlag, GmbH, 1-9. [7] Farag, M.M.A., A.A.A. Sharaf El-Din and E.A. EL-Shazly, 2009. (1) Predicting the annual generation peaks of peach fruit fly, Bactrocera zonata (saunders) (diptera: tephritidae) using heat units accumulation at Giza governorate, Egypt. 4 Conference on Recent echnologies in Agriculture, 1-6. [8] Ghanim, N.M., 2009. Studies on the peach fruit fly, Bactrocera zonata (Saunders) (ephritidae, Diptera). Ph. D. hesis, Fac. Agric. Mansoura Univ., pp: 33: 40, 121. [9] Khalil, A.A., S.M. Abolmaaty, M.K. Hassanein, M.M. ElMtewally and S.A. Moustafa, 2010. Degree-days units and expected generation numbers of peach fruit fly Bactrocera zonata (Saunders) (Diptera: ephritidae) under climate change in Egypt. Egypt. Acad. J. biolog. Sci., 3(1): 11-19.

11 Ismail Ragab El-Gendy, 2015 [10] Qureshi, Z.,. Hussain, J.R. Carey and R.V. Dowell, 1993. Effects of temperature on development of Bactrocera zonata (Saunders) (Diptera: ephritidae.pan- Pasific Entomol., 69(1): 71-76. [11] Yamamura, K. and K. Kiritani, 1998. A simple method to estimate the potential increase in the number of generations under global warming in temperate zones. Appl. Entomol. Zool., 33(2): 289-298.