### Species-fragmented area relationship

• relationship between increasing number of species and increasing area of habitat
• (so I suppose inverse is true, e.g. climate change reduce area of habitat, reduce number of species?)
• predict number of extinctions due to loss of habitat
• the issue is fragmentation
• habitat loss generally results in a fragmented (sub) habitat
• SAR assumes contiguous regions (think a circle getting smaller)
• fragmentation is when holes appear (think a doughnut)
• (meta) population capacity is essentially the carrying capacity of the habitat
• fragmentation causes this to decline
• e.g. due to disconnect between fragments
• SFAR (species-fragmented area relationship) fits better than SAR in simulations
• Figure 1
• the authors suggest the SAR does not fit the number of species well, but it looks like it does to me? The lines are pretty close to the points?
• I think perhaps the figure legend is not described well — the lines are not SARs but just general fitted lines?
• Species traits
• when including the fragmentation part, the authors suggest a large amount of variation in the ratio of extinction and colonisation
• this has an effect on their $b$ parameter
• how are the models fit? stupid pnas, need to check in supplementary material
• Case study uses only 14 points
• they suggest that species number is reduced due to fragmentation
• a better visualisation would be to use points proportional to $\lambda$ in Figure 4A
• They suggest hat SFAR is better than SAR, due to a difference in AICc of 2.44 (!)
• furthermore, the least-squares value of the area coefficient is negative, meaning that conditional on $\lambda$, the number of species $S$ is increasing as area $A$ decreases
• what!?
• this same thing happens in eqn 3, where if $z < 0$, if $A_{\text{new}} < A$, \$S~new~/S >1 \$!
• they do discuss what they term hidden parameters: those used for estimating $\lambda$
• perhaps these should be estimated in a hierarchical model?