Quantitative description and simulation of stochastic behaviour in dragonflies (Aeschna cyanea, odonata)

Abstract

1. A dynamic description model of the flight path a dragonfly takes is required in order to derive the encounter frequency of the dragonfly males visiting a pond. It is considered as the first part of a realistic description of the regulation of dragonfly density at the pond by behavioural interaction. 2. Since the dragonfly males fly strictly along the shoreline of the pond, their displacement may be perceived as a quasi linear movement. The flight paths of dragonflies were recorded in field by registering at regular time intervals (1.5 seconds) the number of the shoreline section. (1 m length) in which the dragonfly was staying at that moment. 3. The recorded flight paths show a wide variety from circling around the pond or flying widely to and fro to remaining in a narrow sector of the shoreline (figs. 2–4). 4. The records were classified into 9 flight style groups. The flight style is temperature dependent, but there are also individual differences between the dragonflies. 5. The strategy adopted for model building is to start with the most simple assumptions and parameters. The dynamic performance of each model is assessed by simulations. The model has to be extended until the simulated flight path patterns resemble the observed patterns. 6. In a model with one parameter the displacement for every time interval is given by a stochastic decision using the probabilities evaluated from the observed frequencies of step length (fig. 5). 7. This model was run with different sets of data. The simulated patterns using the data from all records together slightly resemble some observed patterns. They represent, however, only a small range of the variability observed. With data from the different style groups or the single records the simulated patterns are much more variable, but they are too irregular and contain too many turns (figs. 7–9). 8. Therefore the description model was extended by a second parameter determining the direction of each step. The probability of turning is dependent on the number of steps already taken in the same direction (fig. 10). The probabilities are evaluated from the observed frequencies of step series. 9. With the data from all records together, this model yields patterns more similar to the observed flight paths but they still represent only a restricted range of the observed variability. The patterns obtained using the data from the different style groups or from the single records cover the full range of the observed variability and they resemble closely the observed patterns even in minute details (figs. 12–14). Thus this description model together with the data from the flight style groups is accepted as fully sufficient for the present purpose. 10. The simulations allow the assessment of the range of chance variability (fig. 15). 11. The assumptions implied in the description model were corroborated by statistical tests. 12. The approach developed here for the quantification of the behaviour of dragonflies is generally applicable to stochastic behaviour.