grazing: Grazing model

In caspr: Cellular Automata for Spatial Pressure in R

Description

A spatially-explicit model of grazing pressure in drylands.

Usage

ca(l, grazing)

Arguments

del	local seed dispersal
b	environmental quality
c_	global competition
m0	intrinsic mortality
g	grazing pressure
r	regeneration rate of degraded cells
f	local facilitation
d	intrinsic degradation rate
p	associational resistance against grazing

Format

List of 6
 $ name  : chr "Spatial Grazing Model"
 $ ref   : chr "Schneider and Kefi 2015, in review"
 $ states: chr [1:3] "+" "0" "-"
 $ cols  : chr [1:3] "#000000" "#7F7F7F" "#FFFFFF"
 $ parms :List of 9
  ..$ del: num 0.9
  ..$ b  : num 0.5
  ..$ c_ : num 0.2
  ..$ m0 : num 0.05
  ..$ g  : num 0.2
  ..$ r  : num 0.01
  ..$ f  : num 0.9
  ..$ d  : num 0.1
  ..$ p  : num 1
 $ update:function (x_old, parms_temp, subs = 10, timestep = NA)  
  ..- attr(*, "srcref")=Class 'srcref'  atomic [1:8] 85 19 136 1 19 1 85 136
  .. .. ..- attr(*, "srcfile")=Classes 'srcfilecopy', 'srcfile' <environment: 0x4455490> 
 - attr(*, "class")= chr "ca_model"

Details

The model builds upon a published model by Kefi et al. 2007. Spatial models of vegetation cover so far have considered grazing mortality a rather constant pressure, affecting all plants equally, regardless of their position in space. In the known models it usually adds as a constant to the individual plant risk (Kefi et al 2007 TPB). However, grazing has a strong spatial component: Many plants in rangelands invest in protective structures such as thorns or spines, or develop growth forms that reduce their vulnerability to grazing. Therefore, plants growing next to each other benefit from the protection of their neighbors.

Such associational resistance is widely acknowledged in vegetation ecology but hardly integrated in models as a cause for spatially heterogenous grazing pressure. It also renders the plant mortality density dependent, which has important impacts on the bistability of the system.

The model investigates how the assumption of spatially heterogeneous pressure alters the bistability properties and the response of spatial indicators of catastrophic shifts.

The model knows three different cell states: occupied by vegetation "+", empty but fertile "0" and degraded "-". Transitions between cell states are only possible between vegetated and empty (by the processes of plant 'death' and 'recolonization') and between empty and degraded (by 'degradation' and 'regeneration').

To account for the spatially heterogeneous impacts of grazing due to associational resistance, we assumed that a plant's vulnerability to grazers decreases with the proportion of occupied neighbors, $q_+|+$. The individual probability of dying is therefore defined as

w_{ ≤ft\{ +,0 \right\} } = m_0 + g_0 ≤ft( 1 - q_{+|+} \right)

where the additional mortality due to grazing is maximized to g_0 if a plant has no vegetated neighbor (i.e., q_{+|+} = 0) and gradually reduces to 0 with an increasing fraction of occupied neighbors, q_{+|+}.

Author(s)

Florian D. Schneider and Sonia Kefi (2015, in revision)

See Also

project on GitHub

Other models: forestgap; life; livestock; musselbed; predprey

Examples

l <- init_landscape(c("+","0","-"), c(0.6,0.2,0.2), width = 50) # create initial landscape
p <- list(del = 0.9, b = 0.4, c_ = 0.2, m0 = 0.05, g = 0.25, r = 0.01, f = 0.9, d = 0.1, p = 1)   # set parameters
r <- ca(l, model = grazing, parms = p, t_max = 100)    # run simulation

caspr documentation built on May 2, 2019, 5:25 p.m.