Ecosystem services are strongly responsive to changes in land use intensity, especially water purification, which is highly sensitive to water pollutant emission. Increased nitrogen (N) application to cropland has potential impacts on the supply and demand for water purification through changes in land use intensity. However, there has been a lack of research focusing on the impacts of cropland N application on population exposure to water purification deficits and their cross-regional delivery network. Taking the Dongting Lake (DTL) Basin as an example, this study explored the spatial pattern of N exposure in the DTL Basin from 1990 to 2015 by integrating water purification deficit and population density. Changes in potential N exposure in 2050 were simulated based on population projection data from the Shared Socioeconomic Pathways (SSP1-5). N export pathways in the DTL Basin were clarified by constructing the N delivery network. The results showed that (1) N exposure increased significantly with increasing N application in DTL Basin. (2) The DTL surrounding area and lower reaches of the Xiangjiang River Basin had high increases of N exposure (50.2 % and 71.6 %) and high increases in N exposure due to increases in N application per unit (N influence coefficients exceeding 0.5). (3) The lower reaches of the Xiangjiang River Basin with the highest population density had the smallest decrease in N exposure (1.4 %-11.1 %) in the SSP1-5 scenarios. (4) During 1990-2015, the increase of N export to the DTL surrounding area was higher in the lower reaches sub-basins of DTL Basin. N application had a stronger impact on N delivery processes in the lower reaches of DTL Basin. Managers should distribute N applications to basins with high N retention and whose N export to the DTL surrounding area is weak. This study confirmed the strong response of water purification deficits and their population exposures to N application, and provided decision-making guidelines for water quality enhancement programs in DTL Basin from a spatial planning perspective.

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.

Spinner dolphins (Stenella longirostris subsp.) occupy the nearshore waters of several Hawaiian Islands. Due to their constrained behavioral pattern and genetic isolation, they are vulnerable to anthropogenic threats. Their occurrence and behavior are well-described, yet a lack of data on their abundance and survival rates hinders optimal conservation action. Using design-based photo-identification surveys, this study estimated the abundance, apparent survival, and emigration of spinner dolphins off the Wai\'anae Coast of O\'ahu through multi-state open robust design (MSORD) and POPAN modelling. Eight seasonal field seasons, (two winter, spring, summer, and autumn) each comprised of six surveys of the study area, were completed during two consecutive years. Seasonal abundance estimates derived from the best fitting model ranged from 140 (± 36.8 SE, 95% CI 84-232) to 373 (± 60.0, 95% CI 273-509) individuals and were lowest during winter seasons. The MSORD estimated a survival rate of 0.95 (± 0.02 SE) and a Markovian pattern of temporary emigration. POPAN modelling estimated a super-population size of 633 (± 78 SE, 95% CI 492-798), reflecting the total number of individual dolphins that used the study area during the entire study period. Additional research on circum- and inter-island dolphin movements around and between O\'ahu and the Maui Nui region may shed light on both seasonal movement patterns and overall abundance for the O\'ahu/4-Islands stock. This work represents the first systematic mark-recapture effort to assess the abundance and survival rates of these highly exposed dolphins, providing valuable insights for conservation and management.

The dispersal strategies of a species can affect its invasion success. Investigations into the dispersal strategies of invasive species in relation to different factors help improve our understanding of invasion mechanisms and provide knowledge for population management and invasion evaluation. Tetranychus ludeni Zacher (Acari: Tetranychidae) is an invasive species which is native to Europe but is now cosmopolitan. Here, we examined the effects of age and density on dispersal in mated females. Our results show that older females that are capable of producing more eggs within 24 h were more likely to disperse and moved longer distances than younger ones with fewer eggs. Older females spread most of their eggs out of their natal habitats and over longer distances, which reduced competition and increased offspring fitness. Females exhibited significantly increased dispersal probability and distances with an increase in population density to avoid crowding. The synchronization of dispersal and reproduction, along with the positive density-dependent dispersal strategy, may facilitate the habitat colonization and invasion speed of T. ludeni.

The component Allee effect (AE) is the positive correlation between an organism\'s fitness component and population density. Depending on the population spatial structure, which determines the interactions between organisms, a component AE might lead to positive density dependence in the population per-capita growth rate and establish a demographic AE. However, existing spatial models impose a fixed population spatial structure, which limits the understanding of how a component AE and spatial dynamics jointly determine the existence of demographic AEs. We introduce a spatially explicit theoretical framework where spatial structure and population dynamics are emergent properties of the individual-level demographic and movement rates. This framework predicts various spatial patterns depending on its specific parametrization, including evenly spaced aggregates of organisms, which determine the demographic-level by-products of the component AE. We find that aggregation increases population abundance and allows population survival in harsher environments and at lower global population densities when compared with uniformly distributed organisms. Moreover, aggregation can prevent the component AE from manifesting at the population level or restrict it to the level of each independent aggregate. These results provide a mechanistic understanding of how component AEs might operate for different spatial structures and manifest at larger scales.

In the study of biological populations, the Allee effect detects a critical density below which the population is severely endangered and at risk of extinction. This effect supersedes the classical logistic model, in which low densities are favorable due to lack of competition, and includes situations related to deficit of genetic pools, inbreeding depression, mate limitations, unavailability of collaborative strategies due to lack of conspecifics, etc. The goal of this paper is to provide a detailed mathematical analysis of the Allee effect. After recalling the ordinary differential equation related to the Allee effect, we will consider the situation of a diffusive population. The dispersal of this population is quite general and can include the classical Brownian motion, as well as a Lévy flight pattern, and also a \"mixed\" situation in which some individuals perform classical random walks and others adopt Lévy flights (which is also a case observed in nature). We study the existence and nonexistence of stationary solutions, which are an indication of the survival chance of a population at the equilibrium. We also analyze the associated evolution problem, in view of monotonicity in time of the total population, energy consideration, and long-time asymptotics. Furthermore, we also consider the case of an \"inverse\" Allee effect, in which low density populations may access additional benefits.

Negative density dependence (NDD) in biotic interactions of interference such as plant-plant competition, granivory and herbivory are well-documented mechanisms that promote species\' coexistence in diverse plant communities worldwide. Here, we investigated the generality of a novel type of NDD mechanism that operates through the mutualistic interactions of frugivory and seed dispersal among fruit-eating birds and plants. By sampling community-wide frugivory interactions at high spatial and temporal resolution in Pennsylvania, Puerto Rico, Peru, Brazil and Argentina, we evaluated whether interaction frequencies between birds and fruit resources occurred more often (selection), as expected, or below expectations (under-utilization) set by the relative fruit abundance of the fruit resources of each plant species. Our models considered the influence of temporal scales of fruit availability and bird phylogeny and diets, revealing that NDD characterizes frugivory across communities. Irrespective of taxa or dietary guild, birds tended to select fruits of plant species that were proportionally rare in their communities, or that became rare following phenological fluctuations, while they mostly under-utilized abundant fruit resources. Our results demonstrate that negative density-dependence in frugivore-plant interactions provides a strong equalizing mechanism for the dispersal processes of fleshy-fruited plant species in temperate and tropical communities, likely contributing to building and sustaining plant diversity. This article is part of the theme issue \'Diversitydependence of dispersal: interspecific interactions determine spatial dynamics\'.

Intergroup aggression often results in the production of public goods, such as a safe and stable social environment and a home range containing the resources required to survive and reproduce. We investigate temporal variation in intergroup aggression in a growing population of colobus monkeys (Colobus vellerosus) to ask a novel question: \"Who stepped-up to produce these public goods when doing so became more difficult?\". Both whole-group encounters and male incursions occurred more frequently as the population grew. Males and females were both more likely to participate in whole-group encounters when monopolizable food resources were available, indicating both sexes engaged in food defence. However, only females increasingly did so as the population grew, suggesting that it was females who increasingly produced the public good of home range defence as intergroup competition intensified. Females were also more active in male incursions at high population densities, suggesting they increasingly produced the public good of a safe and stable social environment. This is not to say that males were chronic free-riders when it came to maintaining public goods. Males consistently participated in the majority of intergroup interactions throughout the study period, indicating they may have lacked the capacity to invest more time and effort.

The Living Planet Index (LPI) measures the average change in population size of vertebrate species over recent decades and has been repeatedly used to assess the changing state of nature. The LPI indicates that vertebrate populations have decreased by almost 70% over the last 50 years. This is in striking contrast with current studies based on the same population time series data that show that increasing and decreasing populations are balanced on average. Here, we examine the methodological pipeline of calculating the LPI to search for the source of this discrepancy. We find that the calculation of the LPI is biased by several mathematical issues which impose an imbalance between detected increasing and decreasing trends and overestimate population declines. Rather than indicating that vertebrate populations do not substantially change, our findings imply that we need better measures for providing a balanced picture of current biodiversity changes. We also show some modifications to improve the reliability of the LPI.

Communities in resource-poor areas face health, food production, sustainability, and overall survival challenges. Consequently, they are commonly featured in global debates surrounding societal collapse. Rapa Nui (Easter Island) is often used as an example of how overexploitation of limited resources resulted in a catastrophic population collapse. A vital component of this narrative is that the rapid rise and fall of pre-contact Rapanui population growth rates was driven by the construction and overexploitation of once extensive rock gardens. However, the extent of island-wide rock gardening, while key for understanding food systems and demography, must be better understood. Here, we use shortwave infrared (SWIR) satellite imagery and machine learning to generate an island-wide estimate of rock gardening and reevaluate previous population size models for Rapa Nui. We show that the extent of this agricultural infrastructure is substantially less than previously claimed and likely could not have supported the large population sizes that have been assumed.