  It has been a century since the species-area relationship (SAR) was first
proposed as a power law to explain how species richness scales with area. There
have been many attempts to explain the origin of this predominant form. Apart
from the power law, numerous empirical studies also report a semi-log form of
the SAR, but very few have addressed its incidence. In this work, we test
whether these relationships could emerge from the assembly of large random
communities on island-like systems. We reformulate the generalized
Lotka-Volterra model by introducing an area parameter that determines the
species richness of the assembled communities. Our analysis demonstrates that
the two most widely reported relationship forms can emerge due to differences
in immigration rates and skewness towards weak interactions. We particularly
highlight the incidence of the semi-log SAR for low immigration rates from a
source pool, which is consistent with several previous empirical studies. The
two SAR forms might show good fits to data over a large span of areas but a
power-law overestimates species richness on smaller islands in remote
archipelagoes.
