Estimating population abundance and growth

We designed a procedure for deriving meaningful parameters to characterise the population growth of Popillia japonica. These parameters were derived from adult trap catch data collected by the Phytosanitary Service of the Lombardy Region between 2015 and 2021. The Regional Phytosanitary Service has overlaid a hexagonal grid onto the infested area to track the movement and expansion of the pest. Each hexagon, referred to as a "cell", covers an area of 5.42 square kilometers and serves as the fundamental spatial unit in our research. The whole cell was considered infested if at least one individual was detected in it during the monitoring activities. The adult population abundance was monitored during the species' flight period using traps baited with a combination of a floral attractant and a synthetic pheromone lure (specifically, Japonilure pheromone along with a blend of 3:7:3 phenyl propionate, eugenol, and geraniol). The traps were Trécé traps from USDA-APHIS.

We developed and applied an ad-hoc estimation procedure based on fitting a continuous function on trap catch data. This method was structured around five key steps:

1. We omitted traps that were set up after the peak of adult presence, specifically those that exhibited a monotonic decline in catches.

2. We computed the average adult trap catch values for each sampling date per cell to address challenges arising from variations in sampling efforts (stemming from differences in the number of traps per cell) and varying trap deployment times within each i-th cell. This yielded a time-series depicting the sampled adult population abundance for the i-th cell per year. We intentionally excluded missing data from the mean calculation to overcome the issues related to damage and removal of traps.

3. We formed a weighted aggregate of observed data for the i-th sampled cell by assigning a weight of 50% to the time-series data of the adult population in the i-th cell and another 50% to the available time-series data of the adult population in the six neighboring cells.

4. We employed the Erlang probability density function to model the i-th weighted dataset, which is a suitable choice for representing the stochastic development time distribution data (as suggested by Curry and Feldman in 1987). To estimate the parameters of the Erlang probability density function, we utilised the lsqcurvefit function in MATLAB (version R2021b).

5. We computed the sum of the weighted pool of observed data for the i-th cell. Subsequently, we defined the total adult population abundance in the cell as the ratio of the sum of the weighted pool of observed data to the integral of the fitted Erlang function over the sampling period. To determine the mean daily adult abundance on the k-th day, we multiplied the total adult population abundance by the integral value of the fitted Erlang probability density function for that specific day. The distribution of mean daily adult abundance was computed exclusively during the flight period, which was defined as the range encompassed by the 1st and 99th percentiles of the fitted Erlang function.

We examined the adult population's growth in relation to the age of infestation. Age-specific abundance was defined as the average daily trap catches calculated over the entire flight period in cells with the same age of infestation. Since the year of the species' entry and establishment in Italy remains unknown, we excluded cells that became infested during the first year of monitoring (i.e., in 2015), as it was not possible to know the year of the initial infestation (i.e., when the presence of P. japonica was first confirmed in the cell). We determined the age of infestation for every infested cell by subtracting the year of the initial infestation from the sampling year and then adding 1. This calculation can yield a range between 1 (when the sampled cell was first identified as infested during the same year as the sampling) and 6 (in cases where a cell first became infested in 2016 and was subsequently sampled in 2021). To depict the growth pattern of P. japonica, we relied on changes in the mean daily adult abundance across different infestation ages in all the infested cells. The population growth of P. japonica is described by the discrete-time Beverton-Holt model (Liang et al. 2016)