New distributional records for ants and the evaluation of ant species richness and endemism patterns in Mexico

Ants (Formicidae) in Mexico have usually been undersampled despite their ecological significance and their utility as environmental service providers and bioindicators. This study estimates the species richness and the narrow endemic species number of ants across Mexico. It also documents the presence of one species newly recorded in Mexico and 19 new state-based records of 14 species from central and north Mexico. No surveys have been performed in most of the localities where we report those records, suggesting the need for a higher sampling effort across the country. We present an ant species richness estimation and a narrow endemic ant species estimation in a grid of 0.5 degrees in Mexico. Stenamma schmitii is recorded for the first time from Mexico. Additionally, new state-based records of Azteca velox, Dorymyrmex insanus, Camponotus coruscus, Camponotus striatus, Formica propatula, Lasius latipes, Neivamyrmex melanocephalus, Neivamyrmex rugulosus, Syscia augustae, Atta texana, Cephalotes scutulatus, Crematogaster crinosa and Temnothorax andrei are recorded.

A Truncation Model for Estimating Species Richness

We propose a truncation model for the abundance distribution in species richness estimation. This model is inherently semiparametric and incorporates an unknown truncation threshold between rare and abundant observations. Using the conditional likelihood, we derive a class of estimators for the parameters in this model by stepwise maximization. The species richness estimator is given by the integer maximizing the binomial likelihood, given all other parameters in the model. Under regularity conditions, we show that our estimators of the model parameters are asymptotically efficient. We recover Chaos lower bound estimator of species richness when the parametric part of the model is single-component Poisson. Thus our class of estimators strictly generalized the latter. We illustrate the performance of the proposed method in a simulation study, and compare it favorably to other widely-used estimators. We also give an application to estimating the number of distinct vocabulary words in French playwright Molière’s Tartuffe.