  Species distribution modeling plays an important role in estimating the
habitat suitability of species using environmental variables. For this purpose,
Maxent and the Poisson point process are popular and powerful methods
extensively employed across various ecological and biological sciences.
However, the computational speed becomes prohibitively slow when using huge
background datasets, which is often the case with fine-resolution data or
global-scale estimations. To address this problem, we propose a computationally
efficient species distribution model using a cumulant-based approximation (CBA)
applied to the loss function of $\gamma$-divergence. Additionally, we introduce
a sequential estimating algorithm with an $L_1$ penalty to select important
environmental variables closely associated with species distribution. The
regularized geometric-mean method, derived from the CBA, demonstrates high
computational efficiency and estimation accuracy. Moreover, by applying CBA to
Maxent, we establish that Maxent and Fisher linear discriminant analysis are
equivalent under a normality assumption. This equivalence leads to an highly
efficient computational method for estimating species distribution. The
effectiveness of our proposed methods is illustrated through simulation studies
and by analyzing data on 226 species from the National Centre for Ecological
Analysis and Synthesis and 709 Japanese vascular plant species. The
computational efficiency of the proposed methods is significantly improved
compared to Maxent, while maintaining comparable estimation accuracy. A R
package {\tt CBA} is also prepared to provide all programming codes used in
simulation studies and real data analysis.
