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## Acta zoológica mexicana

*versión On-line* ISSN 2448-8445*versión impresa* ISSN 0065-1737

#### Resumen

HERNANDEZ-REGALADO, Evelia et al. **Prediction of the population fluctuation of the Chrysanthemum leaf miner Liriomyza huidobrensis Blanchard (Diptera: Agromyzidae), using time series models**.

*Acta Zool. Mex*[online]. 2009, vol.25, n.1, pp.21-32. ISSN 2448-8445.

The present study had the objective of modelling population fluctuation of chrysanthemum leaf miner *(Liriomyza huidobrensis *Blanchard), using the Box & Jenkins method, in order to find prediction models, which could represent and adequately predict population density of the insect at its larval stage. The work was carried out in two four-month crop cycles. The number of insects was recorded periodically every two days, resulting in 61 observations for each crop cycle. The number of live larvae was registered by reading date, obtaining two time series. The first 55 observations of each series were analyzed to set the model according to the Box & Jenkins' method, and the six final observations helped to validate the prediction capacity of the model found. In the process of identifying the model for the representation of each of the observed series, their transformation was tested, finding for series 1 that the transformation with square root had the most adequate fit, and for series 2, the transformation of Box-Cox with power (0.387455) was the most adequate. In both series, the autocorrelations (FAC) showed stationarity, and partial autocorrelations (FACP) were interrupted in autocorrelation 1. The estimated model for series 1 was Yt=0.246842 + 0.978041 Yt-1 , and for series 2, it was Yt= 0.283874 + 0.985939 Yt-1. The testing of the model fitted the data well, obtaining white noise in the residuals of FAC and FACP of the estimated models. Two stationary models of autoregressive time series of the AR (1) type were generated, representing the observed series of *L. huidobrensis, *well fitting the true behaviour of their populations and achieving to satisfactorily forecast future values of the insect population fluctuation.

**Palabras clave
:
***Liriomyza huidobrensis*; mathematical models; ARIMA; pest prediction.