  Models for accurately predicting species distributions have become essential
tools for many ecological and conservation problems. For many species,
presence-background (presence-only) data is the most commonly available type of
spatial data. A number of important methods have been proposed to model
presence-background (PB) data, and there have been debates on the connection
between these seemingly disparate methods. The paper begins by studying the
close relationship between the LI (Lancaster & Imbens, 1996) and LK (Lele &
Keim, 2006) models, which were among the first developed methods for analysing
PB data. The second part of the paper identifies close connections between the
LK and point process models, as well as the equivalence between the Scaled
Binomial (SB), Expectation-Maximization (EM), partial likelihood based Lele
(2009) and LI methods, many of which have not been noted in the literature. We
clarify that all these methods are the same in their ability to estimate the
relative probability (or intensity) of presence from PB data; and the absolute
probability of presence, when extra information of the species' prevalence is
known. A new unified constrained LK (CLK) method is also proposed as a
generalisation of the better known existing approaches, with less theory
involved and greater ease of implementation.
