Decision rules
The simplest decision rule, whereby hunters select farms at random.
Hunters select the closest farms to their home locations, within the model area. A couple of studies had indicated that distances to hunting locations were an important consideration for hunters. Preferred hunting locations were more likely to be chosen if they were relatively close to a hunter’s residence, population centers or easily reached due to their centrality (Hussain, Munn, Hudson & West, 2010; Lundhede, Jacobsen & Thorsen, 2015).
This decision rule is used as a proxy for a hunter’s knowledge of goose behavior and the suitability of a farm for geese to forage on. It was based on field observations monitoring the impact of disturbances on pink-footed geese in Jutland, Denmark. This study showed that geese, being wary, tend to utilize fields of a size that have a minimum visible diameter, if geese stand in the middle of the field. In this context field openness was a measure of perceived predator threat and the study concluded that fields with no hindrances in more than one direction e.g. roads, communications masts, trees, houses and/or boundary markers. etc. must exceed 500 m to be acceptable to flocks of pink-footed geese in autumn (Madsen, 1985). For our purposes, field openness was adapted to be a radius value, ranging between 50-250 meters, from a field’s center and where there were no obstructions and within potential shooting range for hunters e.g. a minimum radius of unhindered view in a field in which the geese might forage and be within shooting distance. If not explicitly set, then openness was assumed to be 1 (i.e. have not effect).
The assumption was that hunters would avoid ‘crowding’ and select farms based on the number of goose hunters already using it. Analysis of unpublished hunter survey data indicated that there was a limit to how many companions a goose hunter hunted with or had access to a hunting location. In addition, results from a published Norwegian grouse hunter study showed that the effect of crowding (relationship between hunter densities and hunter encounters) reduced hunter willingness-to-pay for hunting (Wam, Pedersen & Hjeljord, 2012). Accordingly, this decision rule was expressed in terms of hunters per hectare, whereby hunters would only select a farm below a maximum density of hunters per hectare of ‘open fields’. Therefore, the density decision rule was also dependent on the openness parameter value. Density values were varied between 0.5 and 999 e.g. restrictive or unlimited. With ‘density’ set at 0.5 a hunter would not select a farm with 10 hectares of open fields, if 5 hunters had already been allocated to it, conversely set at 999 the same 10 hectares could take all hunters in the model.
The original assumption was that hunters would opt to select the closest farm to their home location. However, after initial model runs, it was clear the closest farm decision rule needed to be relaxed. It was supposed that some hunters, out of necessity, would be willing to accept farms that were not necessarily the closest when selecting goose hunting locations e.g. a few additional kilometers would not matter to hunters living a long way outside the model area. A probability function was created to determine a hunter’s acceptance based on the distance between home and farm locations, controlling the selection of hunting locations by making it more or less likely for hunters to select the closest farm.
For each hunting location a farm was chosen at random from the possible list of farms. The distance to the farm was calculated and a probability of acceptance (ap) calculated by ap = exp(sl*d), where sl was a slope parameter, and d was the distance in meters. Using this curve ap dramatically increased with distance. If a randomly generated, uniformly distributed number between 0 and 1.0 was higher than ap then this farm was accepted. If not accepted another farm was picked and the procedure repeated until a farm was selected. This gave a skewed distribution of acceptance with distance that could be adjusted by altering the parameter sl.
This decision rule was added to represent another aspect of hunter knowledge about goose behavior. This probability function was created to determine hunter acceptance of hunting locations based on distances between farms and goose roost locations within the model. It was postulated that hunters would prefer to select hunting locations nearer to known goose roost sites, within the model, as these would have a higher propensity for geese to frequent and forage at these locations. To test this and simulate it in the model a probability function was created to determine a hunter’s acceptance based on the distance between roost locations and farms, controlling the selection of hunting locations by making it more, or less likely for hunters to select farms closest to a roost site. This probability function was calculated as for the closest farm probability function.
