Applications of the Bootstrap to Insect Physiology
Abstract
The effect of temperature on development and the effect of photoperiod on diapause incidence of insects are common topics in insect physiology. Related to these topics, are 3 important concepts: the lower and upper developmental thresholds, which represent the lower and upper limits of thermal range for insects to develop, and the critical photoperiod, which causes diapause in 50% of a population. To compare lower or upper developmental thresholds of 2 different developmental stages or of 2 populations at the same developmental stage is difficult because of the lack of a suitable statistical method. Shi et al. (2010) proposed 2 methods for testing whether there is a significant difference between 2 lower developmental thresholds. However, these 2 methods are only applicable to the linear relationship between developmental rate and temperature. There are also many studies on the geographic variation in the critical photoperiods for different populations of an insect species. Also, a method is lacking for testing whether there is a significant difference between 2 critical photoperiods. In this study, we test bootstrap to determine if there is a significant difference between different parameters. Bootstrap can then be used to compare any 2 lower or upper developmental thresholds, or to compare 2 critical photoperiods. It can also provide the confidence interval of a critical photoperiod.El efecto de la temperatura sobre el desarrollo y el efecto del fotoperíodo sobre la incidencia de la diapausa de insectos son temas comunes en la fisiología de insectos. En relación a estos temas, hay tres conceptos importantes: los umbrales inferiores y superiores de desarrollo, que representan los límites inferiores y superiores del rango térmico de los insectos a desarrollar, y el fotoperiodo crítico, lo que causa la diapausa en el 50% de la población. Para comparar los umbrales inferiores y superiores de desarrollo de dos etapas diferentes de desarrollo de dos poblaciones en el mismo estado de desarrollo es difícil debido a la falta de un método estadístico adecuado. Shi et al. (2010) propusieron dos métodos para comprobar si existe una diferencia significativa entre los dos umbrales más bajos de desarrollo. Sin embargo, estos dos métodos sólo son aplicables a la relación lineal entre la tasa de desarrollo y de la temperatura. También hay muchos estudios sobre la variación geográfica en el fotoperiodo crítico para las diferentes poblaciones de una especie de insecto. Además, también hace falta un método para comprobar si existe una diferencia significativa entre los dos fotoperíodos críticos. En este estudio, se utilizó el método de “bootstrap” para determinar si existe una diferencia significativa entre los diferentes parámetros. Se puede usar este método para comparar cualquier dos umbrales de desarrollo inferiores o superiores, o para comparar dos fotoperíodos críticos. También puede proveer un intervalo de confianza de un fotoperíodo crítico.
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