Estimation of abundance from presence–absence maps using cluster models

A presence–absence map consists of indicators of the occurrence or nonoccurrence of a given species in each cell over a grid, without counting the number of individuals in a cell once it is known it is occupied. They are commonly used to estimate the distribution of a species, but our interest is in using these data to estimate the abundance of the species. In practice, certain types of species (in particular flora types) may be spatially clustered. For example, some plant communities will naturally group together according to similar environmental characteristics within a given area. To estimate abundance, we develop an approach based on clustered negative binomial models with unknown cluster sizes. Our approach uses working clusters of cells to construct an estimator which we show is consistent. We also introduce a new concept called super-clustering used to estimate components of the standard errors and interval estimators. A simulation study is conducted to examine the performance of the estimators and they are applied to real data.     

Estimates from a consumer demand system: implications for the incidence of environmental taxes

Most studies suggest that environmental taxes are regressive, making them less attractive policy options. We consider the distributional effects of a gasoline tax increase using four incidence measures and under three scenarios for gas tax revenue use. To incorporate behavioral responses we use Consumer Expenditure Survey data to estimate a consumer demand system that includes gasoline, other goods, and leisure. Our estimates confirm that when revenues are not recycled, a gasoline tax is regressive. Use of incidence measures that ignore demand responses, however, will substantially overstate this regressivity. In contrast, the differences between the equivalent variation and easier-to-implement consumer surplus measures are relatively small. In addition, our results suggest that using the additional gas tax revenue to fund labor tax cuts makes the policy substantially less regressive while using the revenue to fund lump-sum transfers actually makes it progressive.     

Use of Integrated Modeling to Enhance Estimates of Population Dynamics Obtained from Limited Data

Abstract:  Demographic data of rare and endangered species are often too sparse to estimate vital rates and population size with sufficient precision for understanding population growth and decline. Yet, the combination of different sources of demographic data into one statistical model holds promise. We applied Bayesian integrated population modeling to demographic data from a colony of the endangered greater horseshoe bats (Rhinolophus ferrumequinum) . Available data were the number of subadults and adults emerging from the colony roost at dusk, the number of newborns from 1991 to 2005, and recapture data of subadults and adults from 2004 and 2005. Survival rates did not differ between sexes, and demographic rates remained constant across time. The greater horseshoe bat is a long-lived species with high survival rates (first year: 0.49 [SD 0.06]; adults: 0.91 [SD 0.02]) and low fecundity (0.74 [SD 0.12]). The yearly average population growth was 4.4% (SD 0.1%) and there were 92 (SD 10) adults in the colony in year 2005. Had we analyzed each data set separately, we would not have been able to estimate fecundity, the estimates of survival would have been less precise, and the estimate of population growth biased. Our results demonstrate that integrated models are suitable for obtaining crucial demographic information from limited data.     

Space-time stick-breaking processes for small area disease cluster estimation

We propose a space-time stick-breaking process for the disease cluster estimation. The dependencies for spatial and temporal effects are introduced by using space-time covariate dependent kernel stick-breaking processes. We compared this model with the space-time standard random effect model by checking each model’s ability in terms of cluster detection of various shapes and sizes. This comparison was made for simulated data where the true risks were known. For the simulated data, we have observed that space-time stick-breaking process performs better in detecting medium- and high-risk clusters. For the real data, county specific low birth weight incidences for the state of South Carolina for the years 1997–2007, we have illustrated how the proposed model can be used to find grouping of counties of higher incidence rate.     

The effect of outdoor air pollutants and greenness on allergic rhinitis incidence rates: a cross-sectional study in Seoul,Korea

Air pollution poses a serious threat to human health in Asia. This study analyzes the association of air pollutants and greenness with incidence rates of allergic rhinitis in Seoul at the administrative district level to gain insight into district-level urban policies to improve public health. A spatial regression model is constructed to investigate the correlation between allergic rhinitis incidence rates and five air pollutants measured at 128 air pollution monitoring stations around Seoul: sulfur dioxide (SO₂), particulate matter less than 10 μm (PM₁₀), ozone (O₃), nitrogen dioxide (NO₂), and carbon monoxide (CO). The allergic rhinitis incidence data are derived from the National Health Insurance Service’s database that includes the number of allergic rhinitis-related clinic visits by the patients over 20 years of age and living in Seoul. A kriging geostatistical interpolation was used to estimate average air pollution level of 423 administrative districts. To assess pollen concentrations that can affect allergic rhinitis, the average normalized difference vegetation index (NDVI) is measured based on the urban greenness. The model, controlling for built environment and socio-economic attributes, identifies the possibility of a weak association between allergic rhinitis incidence rates and carbon monoxide levels. The NDVI value is negatively correlated with allergic rhinitis incidence rates, implying a complicated aspect in relation to the effect of urban greenness.     

Epiphyte metapopulation dynamics are explained by species traits, connectivity, and patch dynamics

The colonization-extinction dynamics of many species are affected by the dynamics of their patches. For increasing our understanding of the metapopulation dynamics of sessile species confined to dynamic patches, we fitted a Bayesian incidence function model extended for dynamic landscapes to snapshot data on five epiphytic lichens among 2083 mapped oaks (dynamic patches). We estimate the age at which trees become suitable patches for different species, which defines their niche breadth (number of suitable trees). We show that the colonization rates were generally low, but increased with increasing connectivity in accordance with metapopulation theory. The rates were related to species traits, and we show, for the first time, that they are higher for species with wide niches and small dispersal propagules than for species with narrow niches or large propagules. We also show frequent long-distance dispersal in epiphytes by quantifying the relative importance of local dispersal and background deposition of dispersal propagules. Local stochastic extinctions from intact trees were negligible in all study species, and thus, the extinction rate is set by the rate of patch destruction (tree fall). These findings mean that epiphyte metapopulations may have slow colonization-extinction dynamics that are explained by connectivity, species traits, and patch dynamics.     

Estimating survival rates with time series of standing age-structure data

It has long been recognized that age-structure data contain useful information for assessing the status and dynamics of wildlife populations. For example, age-specific survival rates can be estimated with just a single sample from the age distribution of a stable, stationary population. For a population that is not stable, age-specific survival rates can be estimated using techniques such as inverse methods that combine time series of age-structure data with other demographic data. However, estimation of survival rates using these methods typically requires numerical optimization, a relatively long time series of data, and smoothing or other constraints to provide useful estimates. We developed general models for possibly unstable populations that combine time series of age-structure data with other demographic data to provide explicit maximum likelihood estimators of age-specific survival rates with as few as two years of data. As an example, we applied these methods to estimate survival rates for female bison (Bison bison) in Yellowstone National Park, USA. This approach provides a simple tool for monitoring survival rates based on age-structure data.     

A simulation study of the medium-term effects of field patterns on cross-pollination rates in oilseed rape (Brassica napus L.)

Gene flow between cultivars within a landscape may lead to impurities that reduce harvest value. In OSR, as for most crops, impurity rates are expected to depend on the spatial distribution of crops over the landscape. However, in contrast to other well-studied crops such as maize, OSR crops generate seed banks in European agro-ecosystems. Gene flow is thus a spatio-temporal process which depends on cropping systems. We therefore aimed at identifying spatial variables that have an effect on regional or local harvest impurities, taking account of the time since the introduction of OSR crops in the regions and of cropping system. Gene flow was simulated over 36 field patterns cultivated with either 15% or 30% of OSR fields, among which 10% or 50% were GM, for three contrasted cropping systems, with the GeneSys software already used for EU co-existence studies. Through regression analyses, we determined spatial and agronomic factors that most affected harvest impurity rates of non-GM OSR after one or seven years of OSR cultivation. The cropping system was the main factor explaining regional harvest impurity rates. Its importance increased after six years of OSR cultivation. For a given cropping system, the regional impurity rate after one year increased linearly with the current proportion of GM crop. In contrast, impurity rates after six years largely depended on the proportions of OSR crop (GM or not) in the two preceding years. During the first year of OSR cultivation, local impurity rates were mostly explained by the distance to the closest GM field. After six years, these rates were mostly explained by the density of GM volunteers in the analysed field and, to a lesser degree, to that of volunteers in neighbour non-OSR fields. Cropping systems were most important in determining impurity rates and the way impurity rates related to regional or local factors. Determination of isolation distances to ensure harvest purity should thus consider past history of OSR cultivation in the area and, in particular, how current or future cropping systems will manage volunteers. Regression quantiles were fitted to the simulated data to determine regional rules (i.e. the maximum regional area of GM OSR and isolation distances between GM and non-GM crops) as a function of the risk accepted by the decision-maker (i.e. the % of situations exceeding harvest impurity thresholds), the cropping system and the volunteer infestation.     

Modeling regional impacts of climate teleconnections using functional data analysis

Teleconnections are quasi-periodic changes in atmospheric circulation that oscillate over long periods of time and impact climate over large regions. These patterns are often linked to long-term variations in climate and extreme weather events and may explain regional differences in climate vulnerability. We apply methods of functional data analysis to examine regional impacts of teleconnections on climate in British Columbia, Canada, between 1951 and 2000. We focus on monthly mean temperature as an overall determinant of crop growth and apply functional principal components analysis (FPCA) to study variations in the impacts of four major teleconnection indices affecting the Northern Hemisphere (the Southern Oscillation Index, the Pacific North American (PNA), Pacific Decadal Oscillation, and the North American Oscillation indices). Two challenges we consider are that the impacts of teleconnections cannot be observed directly and that fine scale data required to study regional variations may come from different sources with highly varied records. We first fit thin-plate regression splines to the raw data to construct complete series of pseudo-data at fixed grid points. Regression models incorporating Bayesian P-splines were then fit to the pseudo-data to estimate the impacts of the four teleconnections over time. Finally, FPCA was then applied to study regional variations in these effects. Our analysis identified strong variations in mean temperature associated with the PNA. The resulting spatial patterns also reveal areas of increased/decreased temperature variability that may have higher climate risk or be suitable for expansion of agricultural activity.     

Power evaluation of focused cluster tests

Many statistical tests have been developed to assess the significance of clusters of disease located around known sources of environmental contaminants, also known as focused disease clusters. The majority of focused-cluster tests were designed to detect a particular spatial pattern of clustering, one in which the disease cluster centers around the pollution source and declines in a radial fashion with distance. However, other spatial patterns of environmentally related disease clusters are likely given that the spatial dispersion patterns of environmental contaminants, and thus human exposure, depend on a number of factors (i.e., meteorology and topography). For this study, data were simulated with five different spatial patterns of disease clusters, reflecting potential pollutant dispersion scenarios: (1) a radial effect decreasing with increasing distance, (2) a radial effect with a defined peak and decreasing with distance, (3) a simple angular effect, (4) an angular effect decreasing with increasing distance and (5) an angular effect with a defined peak and decreasing with distance. The power to detect each type of spatially distributed disease cluster was evaluated using Stone’s Maximum Likelihood Ratio Test, Tango’s Focused Test, Bithell’s Linear Risk Score Test, and variations of the Lawson–Waller Score Test. Study findings underscore the importance of considering environmental contaminant dispersion patterns, particularly directional effects, with respect to focused-cluster test selection in cluster investigations. The effect of extra variation in risk also is considered, although its effect is not substantial in terms of the power of tests.     

Drivers of carbon dioxide emissions: an empirical investigation using hierarchical and non-hierarchical clustering methods

The mitigation of CO2 emissions requires a global effort with common but differentiated responsibilities. In this paper, we identify clusters of CO2 emissions across 72 countries. First, using the stochastic version of the IPAT and employing the dynamic common correlated effects technique, we identify three key determinants affecting CO2 emissions (non-renewables, population, and real GDP). In the second step, both hierarchical and non-hierarchical clustering methods are considered to identify the optimal number of clusters. We identify two to four clusters with different member countries, and in particular establish that in most cases, a 2-cluster solution appears to be optimal. The contents of clusters vary slightly according to the clustering methods for each period. The clustering results from using only the overall CO2 emissions indicate that the countries we consider form three clusters, with China and the USA each within a single member cluster. The remaining 70 countries form the third cluster. Our findings reflect the prominent roles of China and the USA in overall CO2 emissions. Analyses with sub-period and largest emitters reflect a different clustering structure. Some policy recommendations in setting emission reductions are made, considering different clusters across countries.     

Long-term drivers of persistence and colonization dynamics in spatially structured amphibian populations

Many organisms live in networks of local populations connected by dispersing individuals, called spatially structured populations (SSPs), where the long-term persistence of the entire network is determined by the balance between 2 processes acting at the scale of local populations: extinction and colonization. When multiple threats act on an SSP, a comparison of the different factors determining local extinctions and colonizations is essential to plan sound conservation actions. We assessed the drivers of long-term population dynamics of multiple amphibian species at the regional scale. We used dynamic occupancy models within a Bayesian framework to identify the factors determining persistence and colonization of local populations. Because connectivity among patches is fundamental to SSPs dynamics, we considered 2 measures of connectivity acting on each focal patch: incidence of the focal species and incidence of invasive crayfish. We used meta-analysis to summarize the effect of different drivers at the community level. Persistence and colonization of local populations were jointly determined by factors acting at different scales. Persistence probability was positively related to the area and the permanence of wetlands, whereas it was negatively related to occurrence of fish. Colonization probability was highest in semipermanent wetlands and in sites with a high incidence of the focal species in nearby sites, whereas it showed a negative relationship with the incidence of invasive crayfish in the landscape. By analyzing long-term data on amphibian population dynamics, we found a strong effect of some classic features commonly used in SSP studies, such as patch area and focal species incidence. The presence of an invasive non-native species at the landscape scale emerged as one of the strongest drivers of colonization dynamics, suggesting that studies on SSPs should consider different connectivity measures more frequently, such as the incidence of predators, especially when dealing with biological invasions.     

A new procedure to optimize the selection of groups in a classification tree: Applications for ecological data

Agglomerative cluster analyses encompass many techniques, which have been widely used in various fields of science. In biology, and specifically ecology, datasets are generally highly variable and may contain outliers, which increase the difficulty to identify the number of clusters. Here we present a new criterion to determine statistically the optimal level of partition in a classification tree. The criterion robustness is tested against perturbated data (outliers) using an observation or variable with values randomly generated. The technique, called Random Simulation Test (RST), is tested on (1) the well-known Iris dataset [Fisher, R.A., 1936. The use of multiple measurements in taxonomic problems. Ann. Eugenic. 7, 179–188], (2) simulated data with predetermined numbers of clusters following Milligan and Cooper [Milligan, G.W., Cooper, M.C., 1985. An examination of procedures for determining the number of clusters in a data set. Psychometrika 50, 159–179] and finally (3) is applied on real copepod communities data previously analyzed in Beaugrand et al. [Beaugrand, G., Ibanez, F., Lindley, J.A., Reid, P.C., 2002. Diversity of calanoid copepods in the North Atlantic and adjacent seas: species associations and biogeography. Mar. Ecol. Prog. Ser. 232, 179–195]. The technique is compared to several standard techniques. RST performed generally better than existing algorithms on simulated data and proved to be especially efficient with highly variable datasets.     

Photographic mark-recapture analysis of clustered mammal-eating killer whales around the Aleutian Islands and Gulf of Alaska

We used photographic mark-recapture methods to estimate the number of mammal-eating “transient” killer whales using the coastal waters from the central Gulf of Alaska to the central Aleutian Islands, around breeding rookeries of endangered Steller sea lions. We identified 154 individual killer whales from 6,489 photographs collected between July 2001 and August 2003. A Bayesian mixture model estimated seven distinct clusters (95% probability interval = 7–10) of individuals that were differentially covered by 14 boat-based surveys exhibiting varying degrees of association in space and time. Markov Chain Monte Carlo methods were used to sample identification probabilities across the distribution of clusters to estimate a total of 345 identified and undetected whales (95% probability interval = 255–487). Estimates of covariance between surveys, in terms of their coverage of these clusters, indicated spatial population structure and seasonal movements from these near-shore waters, suggesting spatial and temporal variation in the predation pressure on coastal marine mammals.     

Survey methods for assessing land cover map accuracy

The increasing availability of digital photographic materials has fueled efforts by agencies and organizations to generate land cover maps for states, regions, and the United States as a whole. Regardless of the information sources and classification methods used, land cover maps are subject to numerous sources of error. In order to understand the quality of the information contained in these maps, it is desirable to generate statistically valid estimates of accuracy rates describing misclassification errors. We explored a full sample survey framework for creating accuracy assessment study designs that balance statistical and operational considerations in relation to study objectives for a regional assessment of GAP land cover maps. We focused not only on appropriate sample designs and estimation approaches, but on aspects of the data collection process, such as gaining cooperation of land owners and using pixel clusters as an observation unit. The approach was tested in a pilot study to assess the accuracy of Iowa GAP land cover maps. A stratified two-stage cluster sampling design addressed sample size requirements for land covers and the need for geographic spread while minimizing operational effort. Recruitment methods used for private land owners yielded high response rates, minimizing a source of nonresponse error. Collecting data for a 9-pixel cluster centered on the sampled pixel was simple to implement, and provided better information on rarer vegetation classes as well as substantial gains in precision relative to observing data at a single-pixel.     

A general model for tagging on multiple component fisheries: an integration of age-dependent reporting rates and mortality estimation

A major objective of analyzing multiple year tag return data in fisheries is to estimate fishing and natural mortality rates which may vary by age class and calendar year. To do this one needs to be able to estimate the reporting rates for the tags recovered. Some fisheries such as that for Southern Bluefin Tuna (Thunnus maccoyii) have multiple components with potentially different reporting rates for the tag returns. In this paper we develop a general model for multi-cohort, multi-year tag return analyses where there are multiple components to the fishery with potentially different reporting rates. We require the assumption that one component has a reporting rate of 100% (i.e., this could be the component of a boat based fishery where scientific observers are present). We show further how it is possible to partition the overall likelihood developed into two conditionally independent components. The first component of the likelihood is the standard multinomial likelihood that allows estimation of fishing and natural mortality rates. It uses the tag return matrix summed over all the components of the fishery. It requires an average reporting rate for the tag returns (where the average reporting rate is a weighted average of the individual reporting rates of the different components). The second component is also multinomial for the individual component tag returns and allows us to estimate individual component reporting rates. However, this requires that we augment our second component tag return likelihood with a catch data likelihood for the corresponding components. The methodology is illustrated on some Southern Bluefin Tuna tagging and catch data. We also discuss important model assumptions and give suggestions for future research including the integration of tag-return and catch at age data analyses.     

A regional approach to estimating recreation benefits of improved water quality

Recreation demand and value are estimated with the travel-cost method for fishing, camping, boating, and swimming on a site-specific regional basis. The model regional in that 179 sites are defined for the Pacific Northwest. A gravity model is employed to estimate the number of trips from each origin to its destination in the region, and these data are the basic input in the travel-cost demand curves. The model is illustrated by estimating the recreation benefits that would result from meeting the national environmental goal of “fishable and swimmable” rivers. The main finding is that potential recreation benefits are concentrated in a few select areas, which are accessible to large population centers.     

Incorporating Collateral Data in Conservation Biology

Abstract:  Conservation biologists often need to set ecological modeling assumptions or estimate parameters from sparse data. In some cases this problem can be addressed by incorporating data from closely related species or from the same species at different sites (i.e., collateral data). Currently no structured methods exist for incorporating such information. An analogous problem in Actuarial science is to set premium rates in situations with little direct data on claim frequency or size. The rates are estimated using actuarial credibility theory, which incorporates collateral data with the direct data. actuarial credibility theory combined with the actuarial control cycle financial management process also provides an adaptive mechanism for updating assumptions. This theory may have some utility for ecologists wanting to incorporate collateral data in an adaptive management framework, a companion to approaches such as Bayesian updating. We describe the historical development of actuarial credibility theory from early ad hoc methods to empirical Bayes approaches. We explore some of the theory's strengths, such as relative simple formulae for incorporation collateral data, and we explore some of the theory's weaknesses, such as the use of the best linear approximation to the Bayes estimate. We illustrate potential applications of the theory using an example on the mortality rate of the Powerful Owl (  Ninox strenua ).     

An incidence-based richness estimator for quadrats sampled without replacement

Most richness estimators currently in use are derived from models that consider sampling with replacement or from the assumption of infinite populations. Neither of the assumptions is suitable for sampling sessile organisms such as plants where quadrats are often sampled without replacement and the area of study is always limited. In this paper, we propose an incidence-based parametric richness estimator that considers quadrat sampling without replacement in a fixed area. The estimator is derived from a zero-truncated binomial distribution for the number of quadrats containing a given species (e.g., species i) and a modified beta distribution for the probability of presence-absence of a species in a quadrat. The maximum likelihood estimate of richness is explicitly given and can be easily solved. The variance of the estimate is also obtained. The performance of the estimator is tested against nine other existing incidence-based estimators using two tree data sets where the true numbers of species are known. Results show that the new estimator is insensitive to sample size and outperforms the other methods as judged by the root mean squared errors. The superiority of the new method is particularly noticeable when large quadrat size is used, suggesting that a few large quadrats are preferred over many small ones when sampling diversity.     

A new approach to the "apparent survival" problem: estimating true survival rates from mark-recapture studies

Survival estimates generated from live capture-mark-recapture studies may be negatively biased due to the permanent emigration of marked individuals from the study area. In the absence of a robust analytical solution, researchers typically sidestep this problem by simply reporting estimates using the term "apparent survival." Here, we present a hierarchical Bayesian multistate model designed to estimate true survival by accounting for predicted rates of permanent emigration. Initially we use dispersal kernels to generate spatial projections of dispersal probability around each capture location. From these projections, we estimate emigration probability for each marked individual and use the resulting values to generate bias-adjusted survival estimates from individual capture histories. When tested using simulated data sets featuring variable detection probabilities, survival rates, and dispersal patterns, the model consistently eliminated negative biases shown by apparent survival estimates from standard models. When applied to a case study concerning juvenile survival in the endangered Cape Sable Seaside Sparrow (Ammodramus maritimus mirabilis), bias-adjusted survival estimates increased more than twofold above apparent survival estimates. Our approach is applicable to any capture-mark-recapture study design and should be particularly valuable for organisms with dispersive juvenile life stages.