Species-Fragmented Area Relationship (SFAR)

Separate the effects of habitat loss (area reduction) from fragmentation (splitting into patches) on species richness. Extends the classic power-law SAR with an explicit fragmentation term.

Usage

sfar(object, patches, model = c("power", "log"), ...)

Arguments

object

A spacc object.

patches

Factor or integer vector assigning each site to a habitat fragment (patch). Must have length equal to the number of sites.

model

Character. SFAR model:

• "power" (default): S = c * A^z * n^(-f)

• "log": log(S) = log(c) + zlog(A) - flog(n)

...

Additional arguments.

Value

An object of class spacc_sfar containing:

fit

Fitted model object

coef

Coefficients: c (intercept), z (area exponent), f (fragmentation exponent)

n_patches

Number of habitat fragments

Details

The SFAR (Hanski et al. 2013) extends the power-law SAR to quantify the additional effect of habitat fragmentation on species richness. The model S = c * A^z * n^(-f) adds a penalty term for fragmentation (n = number of fragments), where f > 0 indicates that fragmentation reduces richness beyond what area loss alone would predict.

References

Hanski, I., Zurita, G.A., Bellocq, M.I. & Rybicki, J. (2013). Species-fragmented area relationship. Proceedings of the National Academy of Sciences, 110, 12715-12720.

Rybicki, J. & Hanski, I. (2013). Species-area relationships and extinctions caused by habitat loss and fragmentation. Ecology Letters, 16, 27-38.

See also

extrapolate(), sesars()

Examples

# \donttest{
coords <- data.frame(x = runif(50), y = runif(50))
species <- matrix(rbinom(50 * 30, 1, 0.3), nrow = 50)
sac <- spacc(species, coords)
patches <- kmeans(coords, centers = 5)$cluster
sfar_result <- sfar(sac, patches)
print(sfar_result)
# }