Equivalence of truncated count mixture distributions and mixtures of truncated count distributions

This article is about modeling count data with zero truncation. A parametric count density family is considered. The truncated mixture of densities from this family is different from the mixture of truncated densities from the same family. Whereas the former model is more natural to formulate and to interpret, the latter model is theoretically easier to treat. It is shown that for any mixing distribution leading to a truncated mixture, a (usually different) mixing distribution can be found so. that the associated mixture of truncated densities equals the truncated mixture, and vice versa. This implies that the likelihood surfaces for both situations agree, and in this sense both models are equivalent. Zero-truncated count data models are used frequently in the capture-recapture setting to estimate population size, and it can be shown that the two Horvitz-Thompson estimators, associated with the two models, agree. In particular, it is possible to achieve strong results for mixtures of truncated Poisson densities, including reliable, global construction of the unique NPMLE (nonparametric maximum likelihood estimator) of the mixing distribution, implying a unique estimator for the population size. The benefit of these results lies in the fact that it is valid to work with the mixture of truncated count densities, which is less appealing for the practitioner but theoretically easier. Mixtures of truncated count densities form a convex linear model, for which a developed theory exists, including global maximum likelihood theory as well as algorithmic approaches. Once the problem has been solved in this class, it might readily be transformed back to the original problem by means of an explicitly given mapping. Applications of these ideas are given, particularly in the case of the truncated Poisson family.

Nest spacing and breeding performance in Short-toed Eagle Circaetus gallicus in northeast Greece

Aims: To describe the phenology and breeding success of one of the densest populations of Short-toed Eagle in Europe. Methods All nests in the Dadia-Lefkimi-Soufli forest in northeast Greece were located and visited regularly throughout the 1996-98 breeding seasons. Data on every stage of the breeding cycle were collected and related to among-year variation in the weather conditions during March to June. Results: A total of 58 pairs were located during the three-year study spread across 22 territories (the same territories are usually occupied each year). The nests were evenly spaced (mean of 2.7 km between nests). Adults arrived between mid-March and mid-April. Only one egg per nest was laid. Nestlings fledged on average after 68.9 days. Eagles departed between 8 September and 2 October. Conclusions: Arrival date determines laying date. The population size appears to be stable but the species has a relatively low reproductive rate and takes three to four years to mature, consequently it may be susceptible to stochastic or human-mediated factors.

On the regulation of populations of mammals, birds, fish, and insects

A key unresolved question in population ecology concerns the relationship between a population's size and its growth rate. We estimated this relationship for 1780 time series of mammals, birds, fish, and insects. We found that rates of population growth are high at low population densities but, contrary to previous predictions, decline rapidly with increasing population size and then flatten out, for all four taxa. This produces a strongly concave relationship between a population's growth rate and its size. These findings have fundamental implications for our understanding of animals' lives, suggesting in particular that many animals in these taxa will be found living at densities above the carrying capacity of their environments.

Conserving marginal populations of the foodplant (Impatiens noli-tangere) of an endangered moth (Eustroma reticulatum) in a changing climate

Impatiens noli-tangere is scarce in the UK and probably only native to the Lake District and Wales. It is the sole food plant for the endangered moth Eustroma reticulattum. Significant annual fluctuations in the size of I. noli-tangere populations endanger the continued presence of E. reticulatum in the UK. In this study, variation in population size was monitored across native populations of L noli-tangere in the English Lake District and Wales. In 1998, there was a crash in the population size of all metapopulations in the Lake District but not of those found in Wales. A molecular survey of the genetic affinities of samples in 1999 from both regions and a reference population from Switzerland was performed using AFLP and ISSR analyses. The consensus UPGMA dendrogram and a PCO scatter plot revealed clear differentiation between the populations of L noli-tangere in Wales and those in the Lake District. Most of the genetic variation in the UK (H-T= 0.064) was partitioned between (G(ST) = 0.455) rather than within (H-S = 0.034) regions, inferring little gene flow occurs between regions. There was similar bias towards differentiation between metapopulations in Wales, again consistent with low levels of interpopulation gene flow. This contrasts with far lower levels of differentiation in the Lake District which suggests modest rates of gene flow may occur between populations. It is concluded that in the event of local extinction of sites or populations, reintroductions should be restricted to samples collected from the same region. We then surveyed climatic variables to identify those most likely to cause local extinctions. Climatic correlates of population size were sought from two Lake District metapopulations situated close to a meteorological station. A combination of three climatic variables common to both sites explained 81-84% of the variation in plant number between 1990 and 2001. Projected trends for these climatic variables were used in a Monte Carlo simulation which suggested an increased risk of I. noli-tangere population crashes by 2050 at Coniston Water. but not at Derwentwater. Implications of these findings for practical conservation strategies are explored. (C) 2003 Elsevier Ltd. All rights reserved.

Dynamics and foraging behaviour of adult hornet robberflies, Asilus crabroniformis: implications for conservation strategy

Mark resighting studies of the hornet robberfly, Asilus crabroniformis, were carried out during the flight seasons of 1999 and 2000 on agricultural land on the Chilterns in Oxfordshire, UK. Six patches of land were identified which contained characteristics thought to be attractive to hornet robberflies. One hundred and twenty eight adults were marked in 1999 and 257 in 2000. Marking was carried out on one of the patches, but resighting observations were collected from all six sites. The daily population sizes were estimated using the Jolly-Seber method. The daily population size peaked between 50 and 72 from 23 August until 13 September in 2000. This was very similar to the peak population size of between 50 and 74 estimated for 1999. Adults were found to be capable of living for nearly 5 weeks. The maximum linear distance from the point of marking that any individual moved across the study site was 625 m, but some individuals moved over 400 m in a single day. Unsuitable habitat (suburban gardens and a main road) did not present a barrier to dispersal. Males were more likely than females to loiter in sites peripheral to the breeding site, whilst females seemed to be more tied to the breeding site. Most adults were caught from dung piles, but insects avoided fresh dung and preferred instead dung that was well into the process of drying out. A variety of insect species were taken as prey, including many beetles and flies. The findings of the study are discussed in relation to the management of the landscape to enhance the long-term prospects of the hornet robberfly in the UK, and to achieve the UK Biodiversity Action Plan target for this species.

CAMCR: Computer-Assisted Mixture model analysis for Capture–Recapture count data

Population size estimation with discrete or nonparametric mixture models is considered, and reliable ways of construction of the nonparametric mixture model estimator are reviewed and set into perspective. Construction of the maximum likelihood estimator of the mixing distribution is done for any number of components up to the global nonparametric maximum likelihood bound using the EM algorithm. In addition, the estimators of Chao and Zelterman are considered with some generalisations of Zelterman’s estimator. All computations are done with CAMCR, a special software developed for population size estimation with mixture models. Several examples and data sets are discussed and the estimators illustrated. Problems using the mixture model-based estimators are highlighted.

Use of the ratio plot in capture-recapture estimation

Statistical graphics are a fundamental, yet often overlooked, set of components in the repertoire of data analytic tools. Graphs are quick and efficient, yet simple instruments of preliminary exploration of a dataset to understand its structure and to provide insight into influential aspects of inference such as departures from assumptions and latent patterns. In this paper, we present and assess a graphical device for choosing a method for estimating population size in capture-recapture studies of closed populations. The basic concept is derived from a homogeneous Poisson distribution where the ratios of neighboring Poisson probabilities multiplied by the value of the larger neighbor count are constant. This property extends to the zero-truncated Poisson distribution which is of fundamental importance in capture–recapture studies. In practice however, this distributional property is often violated. The graphical device developed here, the ratio plot, can be used for assessing specific departures from a Poisson distribution. For example, simple contaminations of an otherwise homogeneous Poisson model can be easily detected and a robust estimator for the population size can be suggested. Several robust estimators are developed and a simulation study is provided to give some guidance on which should be used in practice. More systematic departures can also easily be detected using the ratio plot. In this paper, the focus is on Gamma mixtures of the Poisson distribution which leads to a linear pattern (called structured heterogeneity) in the ratio plot. More generally, the paper shows that the ratio plot is monotone for arbitrary mixtures of power series densities.

Physical interpretation of the spectral radiative signature in the transition zone between cloud-free and cloudy regions

One-second-resolution zenith radiance measure- ments from the Atmospheric Radiation Measurement pro- gram’s new shortwave spectrometer (SWS) provide a unique opportunity to analyze the transition zone between cloudy and cloud-free air, which has considerable bearing on the aerosol indirect effect. In the transition zone, we find a re- markable linear relationship between the sum and difference of radiances at 870 and 1640 nm wavelengths. The intercept of the relationship is determined primarily by aerosol prop- erties, and the slope by cloud properties. We then show that this linearity can be predicted from simple theoretical con- siderations and furthermore that it supports the hypothesis of inhomogeneous mixing, whereby optical depth increases as a cloud is approached but the effective drop size remains un- changed.

Extending the Lincoln–Petersen estimator for multiple identifications in one source

The Lincoln–Petersen estimator is one of the most popular estimators used in capture–recapture studies. It was developed for a sampling situation in which two sources independently identify members of a target population. For each of the two sources, it is determined if a unit of the target population is identified or not. This leads to a 2 × 2 table with frequencies f11, f10, f01, f00 indicating the number of units identified by both sources, by the first but not the second source, by the second but not the first source and not identified by any of the two sources, respectively. However, f00 is unobserved so that the 2 × 2 table is incomplete and the Lincoln–Petersen estimator provides an estimate for f00. In this paper, we consider a generalization of this situation for which one source provides not only a binary identification outcome but also a count outcome of how many times a unit has been identified. Using a truncated Poisson count model, truncating multiple identifications larger than two, we propose a maximum likelihood estimator of the Poisson parameter and, ultimately, of the population size. This estimator shows benefits, in comparison with Lincoln–Petersen’s, in terms of bias and efficiency. It is possible to test the homogeneity assumption that is not testable in the Lincoln–Petersen framework. The approach is applied to surveillance data on syphilis from Izmir, Turkey.

Achieving production and conservation simultaneously in tropicalagricultural landscapes

Increasing population size and demand for food in the developing world is driving the intensification ofagriculture, often threatening the biodiversity within the farmland itself and in the surrounding land-scape. This paper quantifies bird and tree species richness, tree carbon and farmer’s gross income, andinteractions between these four variables, across an agricultural gradient in central Uganda. We showedthat higher cultivation intensities in farmed landscapes resulted in increased income but also a declinein species richness of birds and trees, and reductions in tree carbon storage. These declines were particu-larly marked with a shift from high intensity smallholder mixed cropping to plantation style agriculture.This was especially evident for birds where significant declines only occurred in plantations. Small scalefarming will likely continue to be a key source of cash income for the rural populations, and ensuring‘sustained agricultural growth’ within such systems while minimising negative impacts on biodiversityand other key ecosystem services will be a major future challenge.

Conservation assessments and Red Listing of the endemic Moroccan flora (monocotyledons)

Morocco constitutes an important centre of plant diversity and speciation in the Mediterranean Basin. However, numerous species are threatened by issues ranging from human activities to global climatic change. In this study, we present the conservation assessments and Red Listing of the endemic Moroccan monocotyledons according to International Union for Conservation of Nature (IUCN) criteria and categories. For each species, we include basic taxonomic information, local names and synonyms, uses, a distribution map, extent of occurrence, area of occupancy, population size and trend, a description of habitats and ecological requirements, and a discussion of the threats affecting the species and habitats. We assessed the threatened status of the endemic Moroccan monocotyledons at the species level (59 species) using the IUCN Red List criteria and categories (Version 3.1). This study shows the high extinction risk to the Moroccan monocotyledon flora, with 95% of threatened species (20% Critically Endangered, 50% Endangered, 25% Vulnerable) and only 5% not threatened (2% Near Threatened and 3% Least Concern). The flora is thus of conservation concern, which is poorly recognized, both nationally and internationally. The study presents the first part and so far the only national IUCN Red Data List for a large group of Moroccan plants, and thus provides an overview of the threatened Moroccan flora. This IUCN Red List is an important first step towards the recognition of the danger to Moroccan biodiversity hotspots, conservation of threatened species and the raising of public awareness at national and international levels.

Can site and landscape-scale environmental attributes buffer bird populations against weather events?

Projected impacts of climate change on the populations and distributions of species pose a challenge for conservationists. In response, a number of adaptation strategies to enable species to persist in a changing climate have been proposed. Management to maximise the quality of habitat at existing sites may reduce the magnitude or frequency of climate-driven population declines. In addition large-scale management of landscapes could potentially improve the resilience of populations by facilitating inter-population movements. A reduction in the obstacles to species’ range expansion, may also allow species to track changing conditions better through shifts to new locations, either regionally or locally. However, despite a strong theoretical base, there is limited empirical evidence to support these management interventions. This makes it difficult for conservationists to decide on the most appropriate strategy for different circumstances. Here extensive data from long-term monitoring of woodland birds at individual sites are used to examine the two-way interactions between habitat and both weather and population count in the previous year. This tests the extent to which site-scale and landscape-scale habitat attributes may buffer populations against variation in winter weather (a key driver of woodland bird population size) and facilitate subsequent population growth. Our results provide some support for the prediction that landscape-scale attributes (patch isolation and area of woodland habitat) may influence the ability of some woodland bird species to withstand weather-mediated population declines. These effects were most apparent among generalist woodland species. There was also evidence that several, primarily specialist, woodland species are more likely to increase following population decline where there is more woodland at both site and landscape scales. These results provide empirical support for the concept that landscape-scale conservation efforts may make the populations of some woodland bird species more resilient to climate change. However in isolation, management is unlikely to provide a universal benefit to all species.

Interactions between climate change and land use change on biodiversity: attribution problems, risks, and opportunities

Global change drivers are known to interact in their effects on biodiversity, but much research to date ignores this complexity. As a consequence, there are problems in the attribution of biodiversity change to different drivers and, therefore, our ability to manage habitats and landscapes appropriately. Few studies explicitly acknowledge and account for interactive (i.e., nonadditive) effects of land use and climate change on biodiversity. One reason is that the mechanisms by which drivers interact are poorly understood. We evaluate such mechanisms, including interactions between demographic parameters, evolutionary trade-offs and synergies and threshold effects of population size and patch occupancy on population persistence. Other reasons for the lack of appropriate research are limited data availability and analytical issues in addressing interaction effects. We highlight the influence that attribution errors can have on biodiversity projections and discuss experimental designs and analytical tools suited to this challenge. Finally, we summarize the risks and opportunities provided by the existence of interaction effects. Risks include ineffective conservation management; but opportunities also arise, whereby the negative impacts of climate change on biodiversity can be reduced through appropriate land management as an adaptation measure. We hope that increasing the understanding of key mechanisms underlying interaction effects and discussing appropriate experimental and analytical designs for attribution will help researchers, policy makers, and conservation practitioners to better minimize risks and exploit opportunities provided by land use-climate change interactions.

Pre-Columbian ring ditch construction and land use on a “chocolate forest island” in the Bolivian Amazon

We present a palaeoecological investigation of pre-Columbian land use in the savannah “forest island” landscape of north-east Bolivian Amazonia. A 5700 year sediment core from La Luna Lake, located adjacent to the La Luna forest island site, was analysed for fossil pollen and charcoal. We aimed to determine the palaeoenvironmental context of pre-Columbian occupation on the site and assess the environmental impact of land use in the forest island region. Evidence for anthropogenic burning and Zea mays L. cultivation began ~2000 cal a BP, at a time when the island was covered by savannah, under drier-than-present climatic conditions. After ~1240 cal a BP burning declined and afforestation occurred. We show that construction of the ring ditch, which encircles the island, did not involve substantial deforestation. Previous estimates of pre-Columbian population size in this region, based upon labour required for forest clearance, should therefore be reconsidered. Despite the high density of economically useful plants, such as Theobroma cacao, in the modern forest, no direct pollen evidence for agroforestry was found. However, human occupation is shown to pre-date and span forest expansion on this site, suggesting that here, and in the wider forest island region, there is no truly pre-anthropogenic ‘pristine’ forest.

Density and survival rate of Culex quinquefasciatus at Parque Ecologico do Tiete, Sao Paulo, Brazil

Parity rate, gonotrophic cycle length, and density of a Culex quinquefasciatus female population was estimated at the Parque Ecologico do Tiete (PET), Sao Paulo, Brazil. Adult Cx. quinquefasciatus females were collected from vegetation along the edges of a polluted drainage canal with the use of a battery-powered backpack aspirator from September to November 2005 and from February to April 2006. We examined 255 Cx. quinquefasciatus ovaries to establish the parity rate of 0.22 and determined the gonotrophic cycle length under laboratory conditions to be 3 and 4 days. From these data, we calculated the Cx. quinquefasciatus survival rate to be 0.60 and 0.68 per day. Density of the Cx. quinquefasciatus female (5.71 females per m(2)) was estimated based on a population size of 28,810 individuals divided by the sampled area of 5,040 m(2). Results of all experiments indicate medium survivorship and high density of the Cx. quinquefasciatus female population. This species is epidemiologically relevant in the PET area and should be a target of the vector control program of Sao Paulo municipality.