The Gray aphid cruciferous Brevicoryne brassicae (Linnaeus, 1758) (Hemiptera: Aphididae) feeds on plants of the Cruciferae family exclusively, causes serious damage to broccoli and cauliflower to contaminate the product with their presence; in addition to feed on the sap of the plant, it transmits more than 20 phytopathogenic virus, and its distribution is cosmopolitan (^{Gill et al., 2013}). ^{Satar et al. (2005}) reported that the optimum temperature for development of B. brassicae is 25 °C and the threshold temperature for cold weather populations is 1.5 °C, while for temperate populations is 4 °C. The increase in the populations of insect pests and their degree of involvement in crops, depends on abiotic and biotic factors; top, temperature, relative humidity and photoperiod are the most important, and as for the latter, are key natural enemies and host plants. In this regard, ^{Hodgson et al. (2011)} mentioned that some climate-related variables directly affect the duration of the life cycles of insects, which increases or reduces its fluctuation over time.

Therefore, we must consider specific information about these factors, to build models that estimate with good approximation the population density of insects (^{Venette et al., 2010}). Models have been constructed using the technique of regression to estimate insect populations of various species, which are precisely predictors climate variables (^{Murphy et al., 2012}; ^{Cuéllar et al., 2012}). Particularly aphids of the species Macrosiphum euphorbiae in growing lettuce, ^{Morales and Fereres (2008)}, won the model defined by Y= - 1.56 - 3.51 T - 0.77 T² + 0.02 T³, to approximate the number of individuals in terms of the temperature through simple nonlinear regression, where Y represents the number of aphids and average temperature T in °C, a coefficient value determination R²= 0.892.

Moreover, one of the main natural enemies of this aphid is Diaeretiella rapae (Mc'Intosh, 1855) (Hymenoptera: Aphidiidae), parasitoid cosmopolitan affect about 60 species of aphids, although only six are the most common guests (^{Basheer et al., 2014}). The host plant influences this wasp parasitism, when B. brassicae Cabbage feeds parasitism is 40.2%, while turnip is 32.6% (^{Ölmez et al., 2007}), for its part ^{Tazerouni et al. (2012)} found that D. rapae parasitize about 37 nymphs of D. noxia in 24 h at 25 °C, so consider it a good choice for augmentative releases. Volatile compounds in cruciferous attract both B. brassicae and D. rapae as the latter responds to the honeydew secreted by aphids to locate more easily (^{Duchovskienė and Raudonis, 2008}).

One of the bases of integrated pest management is to know the variation of a pest population depending on climatic variables and their relationship with their natural enemies, bug so this study was proposed with the objective of estimating the number of individuals B. brassicae depending on the average temperature, and determine the degree of association of the population density of this species of aphid, with its percentage of parasitism caused by D. rapae in growing broccoli, in the region of El Bajio, Guanajuato, Mexico.

This research was performed in the "Loma de las Animas" rancho (20° 58' 29'' north latitude, 101° 28' 15'' west longitude, 1 791 m) in the city of Leon, Guanajuato, the town has a average annual rainfall of 600 mm and an average temperature of 18.4 °C. The work was done in 1 250 with 320 m² broccoli plants Brassica oleraceae var. italica. The transplant took place on November 30, 2009. I was sampled weekly from 5 December 2009 until March 13, 2010, when he was on stage cutoff, taking randomly 50 plants. The entire sheet was reviewed and the number of aphids (B. brassicae) were recorded per plant and parasitized aphids per plant.

Parasitized aphids were placed in jars covered with anti-aphids mesh and kept at 22 °C, in order to await the emergence of wasps, they were stored in 70% methyl alcohol, for identification. The temperature was recorded at the weather station De LaSalle Experimental Agricultural Center. With the information obtained, we proceeded in the first instance to obtain measures of association (correlation coefficients of Pearson), to know the relationship between the aphid population with respect to temperature and percentage of parasitism, in the case of obtaining a strong association between variables, we proceeded to estimate the functional form of the regression model of best fit, using this analysis Statgraphics program (^{Statgraphics Plus Ver. 5.1 Professional, 2001}).

The first individuals of B. brassicae were recorded on 2 January when the average temperature was 13.1 °C; as advanced development of the plant, the aphid populations increased to a maximum of 4.4 individuals aphids plant^-1, with an average temperature of 17.4 °C, which coincides with the cutting step 13 March 2010 (Table 1). To determine the degree of association between the total number of B. brassicae present in 50 plants and the average temperature for the day when each reading was recorded, the Pearson correlation coefficient, which was r= 0.74 was determined, representing a strong association between the two variables, indicating that as the temperature increases, the number of individuals of this species also increases. Then, considering the dependent variable and the number of aphids as an independent variable average temperature, we proceeded to estimate the model of best fit to the observed data, obtaining the functional form of a polynomial of degree five defined by:

Where: Y= number of aphids; and T= the average temperature in °C. The criteria for selecting this function, the values were test F= 14.03 and its corresponding probability p= 0.0005 ** analysis of variance of simple regression and the coefficient of determination R2= 0.89 as a measure of goodness of fit therefore there is enough evidence in the sample to conclude that the obtained model is an appropriate approach and estimating tool. Using the same technique, ^{Morales and Fereres (2008)}, obtained a functional form of a polynomial of degree three with good fit, to get virtually very similar to that obtained in this study R2, only to approximate the population of the species Macrosiphum euphorbiae Thomas, 1878 (Hemiptera: Aphididae) in growing lettuce.

^{Satar et al. (2005)} reported that this aphid nymphal period is 12.5 days at 15 °C and 6 days at 25 °C, which coincides with the results of this work in relation to temperature, but from the standpoint of crop production at the stage of economic cutoff thresholds should be zero individuals per plant. This paper was determined Diaretiella rapae as the only parasitoid associated with B. brassicae, coinciding with ^{Baer et al. (2004)}, who indicated that this expertise is essential in the development of insect diversity; D. rapae when reproduced in other species of aphids, the ability to parasitize B. brassicae decreases, they suggest that the ancestral host of this parasitoid is the ash aphid cruciferous.

The results of this research showed that the highest percentage of parasitism was 35.7% and occurred on January 30, 2010; generally parasitism ranged from 22 to 26% (Table 1). ^{Mussury and Fernandes (2002)} reported an average of 11 aphids parasitized by D. rapae in broccoli with a positive correlation between the towns of Hemiptera and parasitoid populations muestreándolos with striking red, also the population of aphids and parasitism increased in phenological flowering stage; in this study the correlation between the number of aphids and parasitized aphids percentage was also positive (r= 0.64). Meanwhile, ^{Barrios et al. (2004)} found that two weeks after transplantation, the populations of B. brassicae were 49.65 individuals / plant parasitism by D. rapae 14% by the middle of the stage of development of the crop in Texcoco, Mexico.

In another study in the Bajio, ^{Hernández et al. (1990)} reported that the percentage of parasitism of D. rapae in B. brassicae was 70%, while the percentage of parasitism in this study were lower; it is possible that the density of plants with aphids are not enough, as pointed out ^{Mussury and Fernandes (2002)}, who said that when you have more than 50% of infested plants, the activity of natural enemies increases markedly. D. rapae is a natural enemy with great potential in the integrated pest management, it can be used in conjunction with pyrethroids in reducing the incidence of B. Brassica with an additive effect on aphid populations (^{Desneux et al., 2005}). Another feature that may be considered favorable in the presence of D. rapae, is its use in management programs aphids on vegetables, due to its capacity for development in broad temperature ranges, ^{Moayeri et al. (2013)} determined that parasitism of this species is recorded properly in the range of temperatures ranging from 17 to 30 °C, which promotes the establishment of shelters throughout the year for this parasitoid.