musselbed: Musselbed Disturbance Model
In caspr: Cellular Automata for Spatial Pressure in R

Description Usage Arguments Format Details Author(s) References See Also Examples

Model for spatial pattern of intertidal mussel beds with wave disturbance. With three cell states: occupied by mussels ("+"), empty sites ("0" and disturbed sites ("-").

1	ca(l, musselbed, parms = p)

`r`	A numerical value. recolonisation of empty sites dependent on local density.
`d`	A numerical value. probability of disturbance of occupied sites if at least one disturbed site is in the direct 4-cell neighborhood.
`delta`	A numerical value. intrinsic disturbance rate.

List of 6
 $ name  : chr "Musselbed Disturbance Model"
 $ ref   : chr "Guichard, F., Halpin, P.M., Allison, G.W., Lubchenco, J. & Menge, B.A. (2003). Mussel disturbance dynamics: signatures of ocean"| __truncated__
 $ states: chr [1:3] "+" "0" "-"
 $ cols  : chr [1:3] "#000000" "#7F7F7F" "#FFFFFF"
 $ parms :List of 3
  ..$ r    : num 0.4
  ..$ d    : num 0.9
  ..$ delta: num 0.01
 $ update:function (x_old, parms_temp, delta = 0.2, subs = 10, timestep = NA)  
  ..- attr(*, "srcref")=Class 'srcref'  atomic [1:8] 74 21 121 1 21 1 74 121
  .. .. ..- attr(*, "srcfile")=Classes 'srcfilecopy', 'srcfile' <environment: 0x4e5c7b8> 
 - attr(*, "class")= chr "ca_model"

The model represents the spatial dynamics in mussel cover of rock substrate in intertidal systems. The stochastic wave disturbances will most likely remove mussels that are located next to a gap because of the losened byssal threads in their proximity. This causes a dynamic gap growth.

The model describes the process by simplifying the system into three potential cell states: occupied by mussel ("+"), empty but undisturbed ("0"), and disturbed, bare rock with loose byssal threads ("-").

Mussel growth on empty cells is defined by parameter r multiplied by the local density of mussels in the direct 4-cell neighborhood.

Any cell occupied by mussels has an intrinsic chance of delta to become disturbed from intrinsic cause, e.g. natural death or predation. Additionally, wave disturbance will remove mussels and leave only bare rock, i.e. disturbed sites, with probability d if at least one disturbed cell is in the direct 4-cell neighborhood. This causes disturbances to cascade through colonies of mussels.

Disturbed sites will recover into empty sites with a constant rate of 1 per year, i.e. on average a disturbed site becomes recolonisable within one year after the disturbance happened.

Guichard, Halpin, et al. (2003)

Guichard, F., Halpin, P.M., Allison, G.W., Lubchenco, J. & Menge, B.A. (2003). Mussel disturbance dynamics: signatures of oceanographic forcing from local interactions. The American Naturalist, 161, 889<e2><80><93>904.

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

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l <- init_landscape(c("+","0","-"), c(0.6,0.2,0.2), width = 50) # create initial landscape
p <- list(delta = 0.01, d = 09, r = 0.4)   # set parameters
r <- ca(l, musselbed, p, t_max = 100)    # run simulation