Modelling the spiders ballooning effect on the vineyard ecology

Abstract

Abstract. We consider an ecosystem in which spiders may be transported by the wind from vineyards into the surrounding woods and vice versa. The model takes into account this tranport phenomenon without building space explicitly into the governing equations. The equilibria of the dynamical system are analyzed together with their stability, showing that bifurcations may occur. Then the effects of indiscriminated spraying to keep pests under control is also investigated via suitable simulations.

Spiders as biological controllers in the agroecosystem

“…That is, in the absence of the spiders it will never happen that one or two prey populations alone remain in the system. We observe the same result in [3,19,20,21]. On the other hand, all the three insects populations survive in the ecosystem in absence of spiders, if the death rate of the latter is higher than a certain critical value.…”

“…Thus it may remain within the agroecosystem or move to the woods and vice versa. The probability of changing the habitat is assumed to be proportional to the surface of the two patches [19], which in turn is measured by their respective carrying capacities. This migration effect is expressed by the last two terms of F 4 and F 5 in (1), while the first three terms respectively express the gain of predation on insects and prey, when the latter can occur, with conversion rates α ′ and γ ′ of agroecosystem webweavers on the insects in the agroecosystems and on the pest, and spiders mortalities δ a and δ w respectively.…”

“…Note that the wind transport effect on insects is disregarded, as we assume that they are able to fly and therefore willingly move toward the environment place that they prefer, i.e. eventually return to it, [19]. Finally, in the last equation we consider the wandering spiders, which are assumed to move and live anywhere among the two environments.…”

“…This model is used to examine the crucial role of spiders in controlling pest outbreaks, taking into account the adverse effect of pesticides and the role of spider ballooning as a key factor for spider population survival and related biological control. As such then, this model merges into a larger one several other simpler models, [3,19,20,21], which we investigated separately. The aim is the preparation of a more comprehensive simulation tool.…”

“…A four dimensional predator-prey model is studied in [19], with insects living in woods and vineyards as the prey and the webweavers living in the woods and the vineyards as their predator populations. The system accounts for ballooning, this transport phenomenon being modeled without explicitly using space in the governing equations, a feature we retain in the present model as mentioned.…”