Biological control of the chestnut gall wasp with \emph{T. sinensis}: a mathematical model

The Asian chestnut gall wasp \emph{Dryocosmus kuriphilus}, native of China, has become a pest when it appeared in Japan, Korea, and the United States. In Europe it was first found in Italy, in 2002. In 1982 the host-specific parasitoid \emph{Torymus sinensis} was introduced in Japan, in an attempt to achieve a biological control of the pest. After an apparent initial success, the two species seem to have locked in predator-prey cycles of decadal length. We have developed a spatially explicit mathematical model that describes the seasonal time evolution of the adult insect populations, and the competition for finding egg deposition sites. In a spatially homogeneous situation the model reduces to an iterated map for the egg density of the two species. While the map would suggest, for realistic parameters, that both species should become locally extinct (somewhat corroborating the hypothesis of biological control), the full model, for the same parameters, shows that the introduction of \emph{T. sinensis} sparks a traveling wave of the parasitoid population that destroys the pest on its passage. Depending on the value of the diffusion coefficients of the two species, the pest can later be able to re-colonize the empty area left behind the wave. When this occurs the two populations do not seem to attain a state of spatial homogeneity, but produce an ever-changing pattern of traveling waves

A Mathematical Model of Flavescence Dor\'ee Epidemiology

Flavescence dor\'ee (FD) is a disease of grapevine transmitted by an insect vector, $Scaphoideus$ $titanus$ Ball. At present, no prophylaxis exists, so mandatory control procedures (e.g. removal of infected plants, and insecticidal sprays to avoid transmission) are in place in Italy and other European countries. We propose a model of the epidemiology of FD by taking into account the different aspects involved into the transmission process (acquisition of the disease, latency and expression of symptoms, recovery rate, removal and replacement of infected plants, insecticidal treatments, and the effect of hotbeds). The model was constructed as a system of first order nonlinear ODEs in four compartment variables. We perform a bifurcation analysis of the equilibria of the model using the severity of the hotbeds as the control parameter. Depending on the non-dimensional grapevine density of the vineyard we find either a single family of equilibria in which the health of the vineyard gradually deteriorates for progressively more severe hotbeds, or multiple equilibria that give rise to sudden transitions from a nearly healthy vineyard to a severely deteriorated one when the severity of the hotbeds crosses a critical value. These results suggest some lines of intervention for limiting the spread of the disease

Seasonal and Daily Movement of Scaphoideus titanus Ball (Homoptera: Cicadellidae)

Seasonal and daily flight patterns of Scaphoideus titanus Ball were investigated in northern Italy, throughout a 3-yr period, using yellow sticky traps placed in an experimental vineyard. Capture data were also analyzed in relation to temperature and relative humidity values. The leafhopper was found to be more active from 1800 to 0800 hours, whereas little movement occurred during high light intensity hours. Although the sex ratio was always male biased, no difference in flight periodicity was found between genders. The seasonal flight peak occurred each year in different periods, ranging from the end of June to the beginning of July, depending on mean temperature values. Daily capture increases were correlated with daily minimum and maximum temperatures and were negatively correlated with maximum values of relative humidity. As a result, this species could be crepuscular or nocturnal, and a bimodal flight periodicity is likely

Hoverflies in organic apple orchards in north-western Italy

A list is given of hoverflies collected by means of Malaise and white sticky traps in two organic apple orchards in north-western Italy. The total number of collected species was 17 and it was compared with literature, in order to discuss differences due to sampling methods. The predominant species collected were Sphaerophoria scripta (L.) (73% of the total sample) and Eupeodes corollae (F.) (14%). The trend of adult captures of this species is drawn and discussed. Data on wild plant species in the orchards are also given