We introduce a model that can be used for the description of the distribution of species when there is scarcity of data, based on our previous work (Ballesteros et al. J Math Biol 85(4):31, 2022). We address challenges in modeling species that are seldom observed in nature, for example species included in The International Union for Conservation of Nature\'s Red List of Threatened Species (IUCN 2023). We introduce a general method and test it using a case study of a near threatened species of amphibians called Plectrohyla Guatemalensis (see IUCN 2023) in a region of the UNESCO natural reserve \"Tacaná Volcano\", in the border between Mexico and Guatemala. Since threatened species are difficult to find in nature, collected data can be extremely reduced. This produces a mathematical problem in the sense that the usual modeling in terms of Markov random fields representing individuals associated to locations in a grid generates artificial clusters around the observations, which are unreasonable. We propose a different approach in which our random variables describe yearly averages of expectation values of the number of individuals instead of individuals (and they take values on a compact interval). Our approach takes advantage of intuitive insights from environmental properties: in nature individuals are attracted or repulsed by specific features (Ballesteros et al. J Math Biol 85(4):31, 2022). Drawing inspiration from quantum mechanics, we incorporate quantum Hamiltonians into classical statistical mechanics (i.e. Gibbs measures or Markov random fields). The equilibrium between spreading and attractive/repulsive forces governs the behavior of the species, expressed through a global control problem involving an energy operator.

In this study, we describe and illustrate two new species and the female of Metriogryllacris (Metriogryllacris) obscurata Zhang, Pang & Bian, 2022 based on the specimens from Fujian Province. The new erected Homogryllacris foveolis sp. nov. (Chinese name: ) is very similar to Homogryllacris rufovaria Liu, 2007 in appearance, but the two can distinguished by the spines of male tenth abdominal tergite and shapes of male subgenital plate. All the specimens are deposited in Guangxi Normal University.

Based on new collections, we described one new species from Yunnan Province, i.e. Homogryllacris xishanensis sp. nov. (Chinese name: ). Meanwhile, we first describe and illustrate the male sex of Homogryllacris biloba (Bey-Bienko, 1957). After the study, these species of Homogryllacris with reduced wings could be formed into one morphological group for classical taxonomy, but they with other species of the genus (with long wings) actually lost and regained wings during evolution.

A new species of Gnorimoschemini (Gelechiidae), Klimeschiopsis arnoldfransorum sp. nov., is described from specimens collected in Spain. The species is most closely related to Klimeschiopsis terroris (Hartig, 1938), with which it was hitherto mixed, but differs particularly by its small size with reduced yellowish-white forewing markings, the characters of the male and female genitalia, and the highly divergent DNA barcode (cytochrome c-oxidase subunit 1). Adult and genitalia of both sexes are figured. Finally, a checklist of the genus is provided.

Based on the former studies and new material, Anelytra (Euanelytra) eunigrifrons Ingrisch, 1998 is reported in China for the first time. In addition, the female sex of Anelytra (Euanelytra) spinia Shi & Qiu, 2009 is described. We also confirmed that Anelytra (Euanelytra) spinia Shi & Qiu, 2009 is mainly distributed in Southern China. The examined specimens are deposited in Guangxi Normal University.

In this work, the results of a survey for species of Fluda Peckham & Peckham, 1892 in primary forest in five Bolivian forest ecoregions are reported. Fluda dauca sp. nov. is described from Southwest Amazon forest and F. thuruampara sp. nov. from Bolivian Yungas forest. Fluda perdita (Peckham & Peckham, 1892) is reported from Bolivia for the first time. Both new species exhibited polymorphic mimicry; dark females of both species resembled the turtle ant Cephalotes pusillus (Klug, 1824) and dark males of F. thuruampara sp. nov. the carpenter ant Camponotus sanctaefidei Dalla Torre, 1892. Orange males and females of F. dauca sp. nov. are likely mimics of Camponotus latangulus Roger, 1863. Males of Fluda may compensate lower mimetic accuracy by the broadened femora I, resembling an ant head in lateral view and ant mandibles when moving the face towards a potential threat. As in other Simonellini, the turnover of Fluda species between the South American superregions suggests that significant shifts in seasonality and related conditions are major factors triggering speciation in the tribe Simonellini.

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This paper deals with three species of Capnogryllacris from Yunnan, China. One new species, one new recorded species and the female sex of Capnogryllacris rufonotata (Li, Liu Li, 2014) are described. All the examined specimens deposited in the Guangxi Normal University and Institute of Entomoceutics, Research, Dali University.

Cubiceps baxteri McCulloch 1923 was described based on a single, imperfect (devoid of a tail) stranded specimen collected from a beach in Lord Howe Island, Tasman Sea. Though C. baxteri was reported as a widely distributed tropical species (Butler 1979), it was mainly a result of its incorrect identification (see Agafonova 1994; Stewart and Last 2015). The distribution of C. baxteri is reported to be restricted to the Pacific Ocean, from Japan and eastwards to Baja California (Mexico), southwards to the Hawaiian Islands, New South Wales (Australia), and Lord Howe Island (Tasman Sea) to the Southern parts of Chile (Eschmeyer et al. 2017; Mundy 2005; Agafonova 1994).

Ecological niche models (ENMs) aim to recreate the relationships between species and the environments where they occur and allow us to identify unexplored areas in geography where these species might be present. These models have been successfully used in terrestrial organisms but their application in aquatic organisms is still scarce. Recent advances in the availability of species occurrences and environmental information particular to aquatic systems allow the evaluation of these models. This study aims to characterize the niche of the Sabaleta Brycon henni Eigenmann 1913, an endemic fish of the Colombian Andes, using ENMs to predict its geographical distribution across the Magdalena Basin. For this purpose, we used a set of environmental variables specific to freshwater systems in addition to the customary bioclimatic variables, and species\' occurrence data to model its potential distribution using the Maximum Entropy algorithm (MaxEnt). We evaluate the relative importance between these two sets of variables, the model\'s performance, and its geographic overlap with the IUCN map. Both on-site (annual precipitation, minimum temperature of coldest month) and upstream variables (open waters, average minimum temperature of the coldest month and average precipitation seasonality) were included in the models with the highest predictive accuracy. With an area under the curve of 90%, 99% of the species occurrences and 68% of absences correctly predicted, our results support the good performance of ENMs to predict the potential distribution of the Sabaleta and the utility of this tool in conservation and decision-making at the national level.