This R package includes code for a paper on spatial indicators of land degradation authored by Florian Schneider and Sonia Kéfi. The repository of the study can be found at: https://github.com/cascade-wp6/resilience_rangelands
The livestock model is a pair-approximation model of spatial vegetation dynamics. This model approximates the dynamics that can be observed in cellular automata, but instead of defining individual cell states and transitions by neighborhood conditions, it defines transition probabilities of neighboring pairs of cells/localities in a grid/landscape.
The model assumes that each locality can either be empty of vegetation (0) or occupied (1). Pairs of localities can be either both empty (00), mixed (01) or both occupied (11). The pair-approximation model defines the population dynamics of those pairs in ordinary differential equations.
The package further includes a function ini_rho() to define the initial conditions of a system in dual state space of total cover and local cover. It takes two variables and returns an object of class cover which includes two list entries: total vegetation cover on the landscape scale (rho_1) and total cover of 11-pairs (rho_11).
The package provides individual-level model definitions in the functions colonization() and death() which take an object of class cover. Those are defined as non-linear functions of total vegetation cover on the landscape scale (rho_1) and average local cover q_11.
The dual state can be translated into average local vegetation cover with q_11().
The model specifications are provided within the model object livestock. This includes default parameters, and different simplifications of the model. The function livestock$pair() describes the differential equations for the pair-approximation and is called by default within the function ode_run() (making use of package deSolve).
A single model run is returned by calling
out <- run_ode(ini_rho(0.5), func = livestock$pair, parms = p)
par(mfrow = c(1,2); plot(out)
Parameters can be updated using the function set_parms().
out <- run_ode(ini_rho(0.5), func = livestock$pair,
parms = set_parms(livestock$parms, set = list(b = 0.2, f = 0.9, p = 0.99, v = 0.9))
)
Several simulation/plotting functions exist to provide analytical graphs of the models.
MIT License
Copyright (c) 2016 Florian D. Schneider ([email protected])
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