Equation 5: Allocate breeding females to sink habitat (B.fk)

This function allocates breeding (B.) females (f) to to sink habitat (k).

eq05_Bfk(W2, K.bc, K.bk)

Arguments

W2

Population vector produced by eq02buildW1Mat()
K.bc

Carrying capacity (K) during breeding season (b) of source (c) habitat
K.bk

Carrying capacity (K) during breeding season (b) of sink (k) habitat

Value

B.fk, the total number of females allocated to sink

Details

This function compares total number of females (fg + fp) against K.bc, the carrying capacity ("K.") of the breeding-ground (".b.") source habiat (".c")

Notes:

  1. If fg + fp < K.bc, then ALL birds were allocated to the source ("c"; via the previous function) and 0 birds end up going to the breeding sink (k).

  2. If K.bc < fg + fp, then the total female population is larger than source carrying capacity (K.bc) and all females birds cannot go to source. (That is, the number of females is in excess of the amount of source habitat) Therefore, some birds will go to source and some to sink, with birds wintering in high quality habitat having preference.

So, if K.bc < (fg + fp) AND fg + fp < (K.bc+K.bk) (total female population is less than combined source and sinkk) THEN the number that go to the sink is fg + fp - K.bc. That is, the number going to the sink is anything left after allocation to the source K.bc.

  1. If fg + fp >= (K.bc+K.bk) (total female population is greater than or equal to the combined combined carrying capacity of both habitats) THEN both the source and the sink get completely filled up and any remaining female birds, from the perspective of the model functionally die.

The death of excess females is explained by the authors: "density dependence is implicit in EQUATION (5): females displaced from sink habitat are presumed to die. This is a 'ceiling' form of dd - no effect is evident until the number of arriving females exceeds the combined carrying capacity of the source and sink habitats" (Runge and Marra 2004, pg 378)

References

Runge, MC and PP Marra. 2004. Modeling seasonal interactions in the population dynamics of migratory birds. In Greenberg, R and PP Marra, eds. Birds of two worlds. Johns Hopkins University Press, Baltimore.

Examples

# Set parameters:
## Create named population W2 vector using the eq01buildW0vect()
W2 <- eq01buildW0vect(100,10,100,10)

W2
#>  mg  mp  fg  fp 
#> 100  10 100  10 

#Breeding source habitat carrying capacity
K.bc.110 <- 110
K.bc.100 <- 100
K.bc.10  <- 10

#Breeding sink habitat carrying capacity
K.bk <- 1000

# Total population is 110 and source habitat size is 110, so 0 go to sink
eq05_Bfk(W2 = W2, K.bc = K.bc.110, K.bk = K.bk)
#> fg 
#>  0 

# Reduce source habitat size down to 100 so 10 go to sink
eq05_Bfk(W2 = W2, K.bc = K.bc.100, K.bk = K.bk)
#> fg 
#> 10 

# Redeuce source habitat size down to 10, so 100 go to sink
eq05_Bfk(W2 = W2, K.bc = K.bc.10, K.bk = K.bk)
#>  fg 
#> 100