Detecting spatial aggregation from distance sampling: a probability distribution model of nearest neighbor distance

Spatial point pattern is an important tool for describing the spatial distribution of species in ecology. Negative binomial distribution (NBD) is widely used to model spatial aggregation. In this paper, we derive the probability distribution model of event-to-event nearest neighbor distance (distance from a focal individual to its n-th nearest individual). Compared with the probability distribution model of point-to-event nearest neighbor distance (distance from a randomly distributed sampling point to the n-th nearest individual), the new probability distribution model is more flexible. We propose that spatial aggregation can be detected by fitting this probability distribution model to event-to-event nearest neighbor distances. The performance is evaluated using both simulated and empirical spatial point patterns.     

Predicting species distributions from checklist data using site‐occupancy models

Aim (1) To increase awareness of the challenges induced by imperfect detection, which is a fundamental issue in species distribution modelling; (2) to emphasize the value of replicate observations for species distribution modelling; and (3) to show how ‘cheap’ checklist data in faunal/floral databases may be used for the rigorous modelling of distributions by site‐occupancy models. Location Switzerland. Methods We used checklist data collected by volunteers during 1999 and 2000 to analyse the distribution of the blue hawker, Aeshna cyanea (Odonata, Aeshnidae), a common dragonfly in Switzerland. We used data from repeated visits to 1‐ha pixels to derive ‘detection histories’ and apply site‐occupancy models to estimate the ‘true’ species distribution, i.e. corrected for imperfect detection. We modelled blue hawker distribution as a function of elevation and year and its detection probability of elevation, year and season. Results The best model contained cubic polynomial elevation effects for distribution and quadratic effects of elevation and season for detectability. We compared the site‐occupancy model with a conventional distribution model based on a generalized linear model, which assumes perfect detectability (p = 1). The conventional distribution map looked very different from the distribution map obtained using site‐occupancy models that accounted for the imperfect detection. The conventional model underestimated the species distribution by 60%, and the slope parameters of the occurrence–elevation relationship were also underestimated when assuming p = 1. Elevation was not only an important predictor of blue hawker occurrence, but also of the detection probability, with a bell‐shaped relationship. Furthermore, detectability increased over the season. The average detection probability was estimated at only 0.19 per survey. Main conclusions Conventional species distribution models do not model species distributions per se but rather the apparent distribution, i.e. an unknown proportion of species distributions. That unknown proportion is equivalent to detectability. Imperfect detection in conventional species distribution models yields underestimates of the extent of distributions and covariate effects that are biased towards zero. In addition, patterns in detectability will erroneously be ascribed to species distributions. In contrast, site‐occupancy models applied to replicated detection/non‐detection data offer a powerful framework for making inferences about species distributions corrected for imperfect detection. The use of ‘cheap’ checklist data greatly enhances the scope of applications of this useful class of models.     

A Pragmatic Approach for Determining Otter Distribution from Disparate Occurrence Records

Opportunistic records of animal occurrence may be problematic for inferring species distribution and habitat requirements because of unknown and uncontrolled sources of sampling variance. In this study, we used occurrence records for river otters (Lontra canadensis) derived from sign surveys, road kills, trapper bycatch, and opportunistic sightings (n = 185 records collected 2001–2012) to assess the potential distribution and habitat relationships of otters across central and western New York, USA. To mitigate for obvious observation biases, we standardized observation intensity across regions a priori and restricted inference to readily accessible areas (i.e., ≤700 m from the nearest road). Model selection, and the direction of covariate effects, proved robust to these sampling biases although effect sizes varied −7.1% to +48.0% after bias correction, with the coefficient for the proportion of available shoreline being the most unstable. Ultimately, the top bias-corrected model proved a reliable index for otter probability of occurrence given a strong, positive, and linear relationship with a withheld set of standardized survey records for otters collected in winter 2016–2017 (n = 57; R² = 0.90). This model indicated that approximately 20% of the study area represented high probability of otter occurrence. We demonstrated that reliable inference on wildlife habitat requirements can be obtained from disparate records of animal occurrence provided that data biases are known and effectively mitigated. © 2020 The Wildlife Society.     

Occurrence and dominance of six Pacific Northwest conifer species

Questions: Can probability of occurrence and dominance be accurately estimated for six important conifer species with varying range sizes? Does range size impact the accuracy of species probability of occurrence models? Is species predicted probability of occurrence significantly related to observed dominance? Location: Pacific Northwest region, North America (60°–40°N, 140°–110°W). Methods: This study develops near range‐wide predictive distribution maps for six important conifer species (Pseudotsuga menziesii, Tsuga heterophylla, Pinus contorta, Thuja plicata, Larix occidentalis, and Picea glauca) using forest inventory data collected across the United States and Canada. Species model accuracies are compared with range size using a rank scoring system. A suite of climate and topographic predictor variables are used to investigate environmental constraints that limit species range and quantify relationships between species predicted probability of occurrence and dominance at both plot and landscape scales. Results: Evaluation statistics revealed significant and accurate probability of occurrence models were developed for all six species. Based on ranked evaluation statistics, Tsuga heterophylla had highest overall model accuracy (statistic rank score=5) and Pinus contorta the lowest (statistic rank score=17). Across species, ranked evaluation statistics also revealed a pattern of decreasing model accuracy with increasing range size. At plot level, correlations between dominance and probability of occurrence were weakly positive for all species with only half of the species having statistically significant correlations. Pseudotsuga menziesii had the highest correlation (r=0.36, P<0.001) and Thuja plicata lowest (r=0.038, P=0.799). At the 50‐km scale, correlations between dominance and probability of occurrence improved for all species except Pinus contorta. Pseudotsuga menziesii displayed the highest correlation (r=0.68, P<0.001) and Thuja plicata the lowest (r=0.07, P>0.709). Conclusions: Species probability of occurrence model accuracy decreased with increasing range size. The strength and significance of correlations between probability of occurrence and dominance varied considerably by species and across spatial scales. Apart from Pseudotsuga menziesii and L. occidentalis, the results suggest that probability of occurrence is not a consistently reliable surrogate for species dominance in Pacific Northwest forests. We demonstrate how the degree of correlation between species occurrence and dominance can be used as an indicator of how well predictions of occurrence characterize the optimal niche of a species.     

Climate change reduces resilience to fire in subalpine rainforests

Climate change is affecting the distribution of species and the functioning of ecosystems. For species that are slow growing and poorly dispersed, climate change can force a lag between the distributions of species and the geographic distributions of their climatic envelopes, exposing species to the risk of extinction. Climate also governs the resilience of species and ecosystems to disturbance, such as wildfire. Here we use species distribution modelling and palaeoecology to assess and test the impact of vegetation–climate disequilibrium on the resilience of an endangered fire‐sensitive rainforest community to fires. First, we modelled the probability of occurrence of Athrotaxis spp. and Nothofagus gunnii rainforest in Tasmania (hereon “montane rainforest”) as a function of climate. We then analysed three pollen and charcoal records spanning the last 7,500 cal year BP from within both high (n = 1) and low (n = 2) probability of occurrence areas. Our study indicates that climatic change between 3,000 and 4,000 cal year bp induced a disequilibrium between montane rainforests and climate that drove a loss of resilience of these communities. Current and future climate change are likely to shift the geographic distribution of the climatic envelopes of this plant community further, suggesting that current high‐resilience locations will face a reduction in resilience. Coupled with the forecast of increasing fire activity in southern temperate regions, this heralds a significant threat to this and other slow growing, poorly dispersed and fire sensitive forest systems that are common in the southern mid to high latitudes.     

Models of large-scale breeding-bird distribution as a function of macro-climate in Ontario, Canada

Aim We modelled the relationship of breeding evidence for five species of forest songbirds (ruby-crowned kinglet (Regulus calendula) Blackburnian warbler (Dendroica fusca), black-throated blue warbler (Dendroica caerulescens), bay-breasted warbler (Dendrioca castanea) and Connecticut warbler (Oporornis agilis)) and a variety of macro-climate variables to examine the importance of climate as a factor determining distribution of breeding in these species and to assess the usefulness of spatial predictions generated from these models. Location Modelling was conducted over the entire province of Ontario, Canada, an area of ≈900,000 km². Methods Data on the distribution of breeding in the province was derived from the Breeding Bird Atlas of Ontario. We used logistic regression to model the relationship between the probability of breeding (assessed in 10 km×10 km blocks) and estimates of a variety of climate variables at the same scale. Models were selected that had the least number of explanatory variables while at the same time having close to the best possible classification accuracy. Results The final models for these five species had from one to six explanatory variables and an overall concordance of 70.4% to 86.3% indicating a good classification accuracy. Results from subsampling 50% of the original data ten times indicate that (1) the classification accuracy of the model for data used to generate the model is not very sensitive to the specific observations used to generate the model (2) the classification accuracy of test data is close to the classification accuracy of the model data and (3) the classification accuracy of the test data is not dependent on the specific observations used to generate the model. We generated a spatial prediction of the probability of occurrence of each species for Ontario using the relationships defined by the logistic regression models and using 1 km gridded estimates of the necessary climate variables. These probability maps closely matched the maps of observed evidence of breeding from the Atlas. Main conclusions Although mechanisms controlling breeding distribution cannot be determined using this method, we can conclude that (1) macro-climate is an important factor directly and/or indirectly determining distribution of breeding in these species and (2) spatial predictions of probability of breeding are accurate enough to be useful in predicting probability of breeding in unsampled areas.     

Extinction dynamics in mainland-island metapopulations: an N-patch stochastic model

A generalization of the well-known Levins’ model of metapopulations is studied. The generalization consists of (i) the introduction of immigration from a mainland, and (ii) assuming the dynamics is stochastic, rather than deterministic. A master equation, for the probability that n of the patches are occupied, is derived and the stationary probability P _s (n), together with the mean and higher moments in the stationary state, determined. The time-dependence of the probability distribution is also studied: through a Gaussian approximation for general n when the boundary at n = 0 has little effect, and by calculating P(0, t), the probability that no patches are occupied at time t, by using a linearization procedure. These analytic calculations are supplemented by carrying out numerical solutions of the master equation and simulations of the stochastic process. The various approaches are in very good agreement with each other. This allows us to use the forms for P _s 0) and P(0, t) in the linearization approximation as a basis for calculating the mean time for a metapopulation to become extinct. We give an analytical expression for the mean time to extinction derived within a mean field approach. We devise a simple method to apply our mean field approach even to complex patch networks in realistic model metapopulations. After studying two spatially extended versions of this nonspatial metapopulation model—a lattice metapopulation model and a spatially realistic model—we conclude that our analytical formula for the mean extinction time is generally applicable to those metapopulations which are really endangered, where extinction dynamics dominates over local colonization processes. The time evolution and, in particular, the scope of our analytical results, are studied by comparing these different models with the analytical approach for various values of the parameters: the rates of immigration from the mainland, the rates of colonization and extinction, and the number of patches making up the metapopulation.     

Predictive model of distribution of Atta robusta Borgmeier 1939 (Hymenoptera: Formicidae): subsidies for conservation of a Brazilian leaf-cutting ant endangered species

The aim of this work was to create a predictive model of the potential geographical distribution of the leaf-cutting ant Atta robusta Borgmeier 1939 (Hymenoptera: Formicidae) using ecological niche modeling. We used previous collection records available in the literature together with our database. This is the first study in Brazil using ecological niche modeling as a tool for predicting ant species distribution. Besides the already known distribution, the model generated results showing a medium to low probability of occurrence in the coastal regions of Paraná and São Paulo states, and a very high probability of occurrence in southern Bahia State, in environments popularly known as muçunungas. These environments are characterized by a lower density of trees and the dominance of herbaceous-shrub vegetation. Moreover, we discuss how geographic barriers and anthropogenic pressure in restinga environments may be the determining factors in the current distribution of this species. According to the predictive model used in this study, there is strong evidence that this species occurs only in these states and deserves special attention from government conservation agencies in the restingas where it is located.     

Neutral Models with Generalised Speciation

Hubbell’s neutral theory claims that ecological patterns such as species abundance distributions can be explained by a stochastic model based on simple assumptions. One of these assumptions, the point mutation assumption, states that every individual has the same probability to speciate. Etienne et al. have argued that other assumptions on the speciation process could be more realistic, for example, that every species has the same probability to speciate (Etienne, et al. in Oikos 116:241–258, 2007). They introduced a number of neutral community models with a different speciation process, and conjectured formulas for their stationary species abundance distribution. Here we study a generalised neutral community model, encompassing these modified models, and derive its stationary distribution, thus proving the conjectured formulas.     

植物空间分布格局中邻体距离的概率分布模型及参数估计

最近邻体法是一类有效的植物空间分布格局分析方法,邻体距离的概率分布模型用于描述邻体距离的统计特征,属于常用的最近邻体法之一。然而,聚集分布格局中邻体距离(个体到个体)的概率分布模型表达式复杂,参数估计的计算量大。根据该模型期望和方差的特性,提出了一种简化的参数估计方法,并利用遗传算法来实现参数优化,结果表明遗传算法可以有效地估计的该模型的两个参数。同时,利用该模型拟合了加拿大南温哥华岛3个寒温带树种的空间分布数据,结果显示:该概率分布模型可以很好地拟合美国花旗松(P.menziesii)和西部铁杉(T.heterophylla)的邻体距离分布,但由于西北红柏(T.plicata)存在高度聚集的团簇分布,拟合结果不理想;美国花旗松在样地中近似随机分布,空间聚集参数对空间尺度的依赖性不强,但西北红柏和西部铁杉空间聚集参数具有尺度依赖性,随邻体距离阶数增加而变大。最后,讨论了该模型以及参数估计方法的优势和限制。     

Equilibrium distribution of species among vessels of a gradostat

The distribution of concentrations of two competing microbial species among the vessels of an n-vessel gradostat at equilibrium is studied for the standard mathematical model of the gradostat. As the equilibrium concentrations cannot be explicitly computed, a continuum limit, as the number of vessels becomes large, is considered which yields a singularly perturbed boundary value problem. Standard singular perturbation techniques yield information on equilibrium species concentration distributions which agree well with numerical calculations for even moderate values of n.Research supported by NSF Grant DMS 8922654     

The biogeography of invasive alien plants in California: an application of GIS and spatial regression analysis

The spatial distribution of invasive alien plants has been poorly documented in California. However, with the increased availability of GIS software and spatially explicit data, the distribution of invasive alien plants can be explored. Using bioregions as defined in Hickman (1993 ), I compared the distribution of invasive alien plants (n = 78) and noninvasive alien plants (n = 1097). The distribution of both categories of alien plants was similar with the exception of a higher concentration of invasive alien plants in the North Coast bioregion. Spatial autocorrelation analysis using Moran's I indicated significant spatial dependence for both invasive and noninvasive alien plant species. I used both ordinary least squares (OLS) and spatial autoregressive (SAR) models to assess the relationship between alien plant species distribution and native plant species richness, road density, population density, elevation, area of sample unit, and precipitation. The OLS model for invasive alien plants included two significant effects; native plant species richness and elevation. The SAR model for invasive alien plants included three significant effects; elevation, road density, and native plant species richness. The SAR model for noninvasive alien plants resulted in the same significant effects as invasive alien plants. Both invasive and noninvasive alien plants are found in regions with low elevation, high road density, and high native‐plant species richness. This is in congruity with previous spatial pattern studies of alien plant species. However, the similarity in effects for both categories of alien plants alludes to the importance of autecological attributes, such as pollination system, dispersal system and differing responses to disturbance in the distribution of invasive plant species. In addition, this study emphasizes the critical importance of testing for spatial autocorrelation in spatial pattern studies and using SAR models when appropriate.     

Leaf wax <Emphasis Type="Italic">n</Emphasis>-alkane chemotaxonomy of bamboo from a tropical rain forest in Southwest China

The leaf waxes of 23 woody bamboo species of three subgenera, Dendrocalamus, Bambusa and Dendrocalamopsis, from the Xishuangbanna tropical rain forest in Southwest China were analyzed by gas chromatography and coupled gas chromatography–mass spectrometry. The waxes of the Dendrocalamus species are dominated by C₂₇ and C₂₉ n-alkanes and their average chain length (ACL) has an average of 28.3. In marked contrast to the Dendrocalamus species, the wax composition of the Bambusa species is characterized by a broad distribution of major n-alkanes from C₂₇ to C₃₅, greater ACL values (>29) and an enhanced relative abundance (>30%) of n-alkanes with a carbon number greater than 30. Unlike the Dendrocalamus species and the Bambusa species, the Dendrocalamopsis species do not have a distinct n-alkane distribution; in some species the n-alkane distribution is comparable to that in the Bambusa species and in others to that in the Dendrocalamus species. The lipid data suggest that it might be reasonable to classify the controversial Dendrocalamopsis group as an independent genus separate from the Bambusa genus. On the basis of their smaller diversity of the dominant n-alkanes and their lower ACL values, the Dendrocalamus species might be more evolutionarily advanced than the Bambusa species, with the Dendrocalamopsis species being at an intermediate stage. The evolution and classification of the woody bamboos inferred from leaf wax n-alkanes are consistent with morphological investigations reported previously.     

Neurotransmitter release statistics: Moment estimates for inhomogeneous Bernoulli trials

Summary Evoked release of quanta of neurotransmitter is generally treated as a set of homogeneous, stationary Bernoulli trials, hence governed by the binomial distribution. Relaxing the assumptions of uniformity and stationarity leads to a more realistic physiological model of transmitter release but also introduces systematic biases in the moment estimates of the binomial parameters. We derive probability generating functions for quantal release and expressions for the moment estimates of ¯n and ¯p for a generalized model that incorporates temporal variation and nonuniformity in individual release probabilities and in numbers of release sites.     

A stochastic model of seed dispersal pattern to assess seed predation by ants in annual dry grasslands

A combined field experiment and modelling approach has been used to provide evidence that ants may be responsible for an observed lower patchiness and higher plant diversity in the neighbourhood of ant nests, within Mediterranean dry grasslands belonging to the phytosociological class Tuberarietea guttatae. The hypothesis was that seeds occurring in clumps may have a higher probability to be harvested than seeds having a scattered distribution. In order to test this hypothesis, four analysis steps were performed. First, pattern of seed production and dispersal of four species was recorded; two of them were more abundant next to ant nests (Tuberaria guttata, Euphorbia exigua), whereas the other two were more abundant away from ant nests (Bromus scoparius and Plantago bellardi). Second, a stochastic model was developed to simulate the observed dispersal patterns of each studied species. Third, 10 seed spatial arrangements in accordance to the distribution patterns created by the model were offered to ants and the location of predated seeds was recorded. Finally, the observed pattern of seed predation was matched to models performed by different distributions of probability. Results showed that the probability of being predated decreased as distance among seeds increased. This preference of ants for high concentration of food items holds down the dominant species sufficiently to allow the subordinates to survive, thus increasing diversity near nests. The observed higher frequency of small-seeded, small-sized, or creeping therophytes close to the ant nests can be therefore seen as an example of indirect myrmecophily.     

Stochastic models for the Trojan Y-Chromosome eradication strategy of an invasive species

The Trojan Y-Chromosome (TYC) strategy, an autocidal genetic biocontrol method, has been proposed to eliminate invasive alien species. In this work, we develop a Markov jump process model for this strategy, and we verify that there is a positive probability for wild-type females going extinct within a finite time. Moreover, when sex-reversed Trojan females are introduced at a constant population size, we formulate a stochastic differential equation (SDE) model as an approximation to the proposed Markov jump process model. Using the SDE model, we investigate the probability distribution and expectation of the extinction time of wild-type females by solving Kolmogorov equations associated with these statistics. The results indicate how the probability distribution and expectation of the extinction time are shaped by the initial conditions and the model parameters.     

The time sequence of the relation between mean crowding and mean density with some population processes

Summary The theories of the stochastic processes are applied to construct mathematical models for describing the processes of population change as an ever changing the distribution of individuals in a space. These models consist of two mathematical expressions which are named the spatial distribution probability function (Q _n (t)) and the transition probability function (P _i,n (t)), respectively. The former gives the spatial distribution at any future time. Given an actual spatial distribution at any time, the latter function converts it to the spatial distribution at any future time. According to these models, we discussed the time sequence of the mean crowding-mean density relation (Iwao andKuno, 1971) in some population processes such as mortality, birth, immigration, growth, and their combined processes.     

Understanding regional species diversity through the log series distribution of occurrences

The distribution of benthic foraminifera around the continental margins of North America is extensively documented. Data from 2673 localities consists of a synonomized list of 2329 species (S) and 61 369 occurrences (n). Here, the margins are divided into five geographical regions: Pacific (PA), S=965, n=19 014; Arctic (AR), S=458, n=7342; Atlantic (AT), S=878, n=10 034; Gulf of Mexico (GM), S=849, n=18 011; Caribbean (CR), S=1188, N=6968. As for many other organisms, species richness is lowest in the Arctic and highest in the Caribbean. In each region, the distribution of species richness and occurrences is a log series. Consequently, the entire series of species occurrences is predicted by the single proportionality constant, α. After log series rarefaction, differences in species richness among areas are nearly all accounted for by species occurring ≤10 times. Most of the differences are accounted for by species occurring once, less by twice, and so on. For example, species occurring once account for 81% of the difference in species richness between the Atlantic and Caribbean, and those occurring once and twice account for 87% of the difference. Most rare species have no fossil record and most endemic species are rare. Probably most of these species evolved recently indicating more origination in species-rich areas. High origination might also be coupled with less extinction. Although each of the five regions can easily be distinguished by differences in composition, in all regions the 10 most abundantly occurring species exhibit nearly equal proportions of occurrences. No region is dominated by only one or two species. All regions exhibit the log series distribution, have nearly equal proportions for abundant species, and differ only in the number of rare species that coexist. Thus, from the point of view of the distribution of occurrences, the most striking aspect is the similarity among regions.     

A New Estimator of the Discovery Probability

Summary Species sampling problems have a long history in ecological and biological studies and a number of issues, including the evaluation of species richness, the design of sampling experiments, and the estimation of rare species variety, are to be addressed. Such inferential problems have recently emerged also in genomic applications, however, exhibiting some peculiar features that make them more challenging: specifically, one has to deal with very large populations (genomic libraries) containing a huge number of distinct species (genes) and only a small portion of the library has been sampled (sequenced). These aspects motivate the Bayesian nonparametric approach we undertake, since it allows to achieve the degree of flexibility typically needed in this framework. Based on an observed sample of size n , focus will be on prediction of a key aspect of the outcome from an additional sample of size m , namely, the so‐called discovery probability. In particular, conditionally on an observed basic sample of size n , we derive a novel estimator of the probability of detecting, at the (n+m+1) th observation, species that have been observed with any given frequency in the enlarged sample of size n+m . Such an estimator admits a closed‐form expression that can be exactly evaluated. The result we obtain allows us to quantify both the rate at which rare species are detected and the achieved sample coverage of abundant species, as m increases. Natural applications are represented by the estimation of the probability of discovering rare genes within genomic libraries and the results are illustrated by means of two expressed sequence tags datasets.     

Predicting the distribution of a rare species of moss: The case of Buxbaumia viridis (Bryopsida,Buxbaumiaceae)

Buxbaumia viridis is a rare policy species restricted to decaying woods in forests. Although Member States of EU are required to monitor its conservation status, specific models able to predict species distribution are still lacking. However, the availability of such models would strongly improve the efficiency in collection additional data and consequently lead to a better knowledge of its ecology. Aims of this work were (i) to provide a model for species distribution assessing the importance of different environmental variables thought to be important in setting the occurrence of Buxbaumia viridis and (ii) to test the effect of imperfect detection in defining the environmental space where the species occur. With this work, records of B. viridis increased twofold in the Alpine region of Italy, passing from 13 records to 26. We showed that on the Alps, occurrence of Buxbaumia viridis was best predicted by northness, rainfall, canopy closure and necromass. Necromass was the single most important variable. A volume of 48–61 m³/ha of necromass was identified as the threshold value determining the high probability of species occurrence. The imperfect detection probability of the species (p = 0.25), biased towards zero the importance of the environmental variables.