Using mathematical models to describe aerial dispersal and silk ball formation of peanut red spider mite, Tetranychus ogmophallos (Acari: Tetranychidae)
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Peanut red spider mite, Tetranychus ogmophallos, exhibits a peculiar dispersal behavior using silk balls, which involves clustering of mites and spinning of webs at the top of plants. Such a dispersal mechanism has not been studied for this species yet. Therefore, this study aimed at using mathematical models to describe aerial dispersal and silk ball formation of peanut red spider mite on peanut plants. The influence of wind speed, generated by a wind tunnel, on the dispersal of mites was studied in two experiments, one with 500 mites per plant and one with 1000 mites per plant, and six wind speeds (5, 10, 15, 20, 25, and 30 km h(-1)) for each mite density. The proportion of displaced mites and the distance they were blown were measured. Another series of experiments considered the formation of silk balls to assess how fast balls were formed as a function of time and the number of mites present on a peanut plant. Data from the wind tunnel experiments were analyzed by logistic regression and multiple regression to assess the proportion of displaced mites and the distance moved, respectively, as functions of wind speed and the initial density of mites on the donor plant. The distribution of dispersal distances from the donor plant was fitted by a mathematical model proposed by Ricker (J Fish Res Board Can 11:559-623, 1954). The number of mites moving upwards on a plant to be involved in silk ball formation was modeled as a function of time based on the initial number of spider mites and their estimated birth, death and movement rates per capita. Logistic regression was used to analyze the presence of balls as a function of time elapsed since a plant was infested with spider mites. Finally, non-linear regression was applied to link ball size to the total number of mites occupying the ball. The data analyses revealed that wind speed had a significant positive effect on take-off probability and distance moved by individual mites, whereas mite density had little influence. Ricker's model adequately described the distribution of dispersal distances. The models describing silk ball formation also described data very well. Ball size was found to increase almost linearly with the number of mites found in the ball. We expect that the knowledge provided by the present study will help to develop efficient management strategies against T. ogmophallos in peanut crops as dispersal seems to be a key factor in the species' capability to become a serious pest.