Model for simulating the impact of predation and trapping of a montane water vole population

The question of the impact of predators on prey populations is very difficult to deal with in ecology because, in the real world, multiple predators whose numbers (movements, reproduction) and food preferences vary nonlinearly and combine, and they can consume multiple prey whose numbers also vary nonlinearly.

Purpose of the model:

The model below, extremely simple, permit to show that the major impact of predation occurs during the phase of low density of voles populations.

Complementarily, it also makes it possible to measure the impact of trapping (with or without predators) on population dynamics.

Examples:

By changing the parameter values (sliders), one can easily see that the impact of predation is very important at low density, but extremely low at high density of voles (for example, increase the initial population density value of voles, at the beginning of the reproduction season, for example at 100 ind./ha and see the effect). One can also see what is the interannual impact of a configuration of parameters by using the vole density value obtained at the end of the simulation as the initial value of the following simulation.

A trapping calendar for voles can also be imported as a text file, delimited by tabs, with two columns, the first giving the trapping day (between 2 and 360 - the numbers of the day in the year counted from March 1st, start of the breeding season, 2 = March 2^nd, 360 = 360^th day after March 1^st), and the second the total number of voles trapped each day. The file below contains 4 sample files, and a zeroing file. Once downloaded and unzipped, you can import each table with the "Browse" button.

Samples of trapping timetable (to unzip)

The model (clic on the image):

The system is simplified as follows:

 the number of predators is constant;
 the functional response is of the Holling II type (in short, the variation in the proportion of voles in the diet saturates at 100% with high densities of voles);

 the intrinsic rate of voles population growth (r₀) is set up assuming that one vole female produces, by embeding generations, potentially 100 voles (50 females) during a breeding season;
 the growth is logistic, and the biotic capacity is fixed to the maximum number of voles that the habitat can support;
 the breeding season begins on March 1 and lasts 8 months, then for 4 months the breeding stops (no mortality other than that due to predation and trapping is taken into account during this period).

Caveats :

 attention to the y-axis scale, it varies to optimize the display, maximizing the apparent distance between the minimum and maximum values ​​of y; when the initial density is close to K, small differences then appear very magnified graphically (but only graphically).
 accounting for trapping alone: ​​simply set the predator density or their daily consumption to zero.
 be careful with the results obtained by this type of model when the initial density of voles exceeds K; there, because of logistic growth, the population growth rate becomes negative when N>K, and the model is no longer relevant (the decline is intrinsic, even without predators). Here, the input value is automatically corrected so that the initial density value cannot exceed K.

Contact and code:

• Patrick Giraudoux
• Model code on Github