Accounting for rate instability and spatial patterns in the boundary analysis of cancer mortality maps

Boundary analysis of cancer maps may highlight areas where causative exposures change through geographic space, the presence of local populations with distinct cancer incidences, or the impact of different cancer control methods. Too often, such analysis ignores the spatial pattern of incidence or mortality rates and overlooks the fact that rates computed from sparsely populated geographic entities can be very unreliable. This paper proposes a new methodology that accounts for the uncertainty and spatial correlation of rate data in the detection of significant edges between adjacent entities or polygons. Poisson kriging is first used to estimate the risk value and the associated standard error within each polygon, accounting for the population size and the risk semivariogram computed from raw rates. The boundary statistic is then defined as half the absolute difference between kriged risks. Its reference distribution, under the null hypothesis of no boundary, is derived through the generation of multiple realizations of the spatial distribution of cancer risk values. This paper presents three types of neutral models generated using methods of increasing complexity: the common random shuffle of estimated risk values, a spatial re-ordering of these risks, or p-field simulation that accounts for the population size within each polygon. The approach is illustrated using age-adjusted pancreatic cancer mortality rates for white females in 295 US counties of the Northeast (1970–1994). Simulation studies demonstrate that Poisson kriging yields more accurate estimates of the cancer risk and how its value changes between polygons (i.e., boundary statistic), relatively to the use of raw rates or local empirical Bayes smoother. When used in conjunction with spatial neutral models generated by p-field simulation, the boundary analysis based on Poisson kriging estimates minimizes the proportion of type I errors (i.e., edges wrongly declared significant) while the frequency of these errors is predicted well by the p-value of the statistical test.

Line transect sampling of Karner blue butterflies ( Lycaeides melissa samuelis)

Line transect sampling is an effective survey method for estimating butterfly densities because it provides unbiased estimates of site-density (provided key assumptions are met), and estimates are comparable among sites. For monitoring Karner blue butterflies in Wisconsin, USA, comparable estimates are required because each year a different selection of sites will be monitored. Annual state-wide indices of species abundance can be derived from the site-surveys and compared to previous year's indices to monitor trends. We advocate that line transect sampling is preferable to Pollard-Yates transects as a survey technique for monitoring Karner blue butter- flies. The Pollard-Yates surveys do not adjust for diferences in site detectability. As a consequence, estimates of among-site from Pollard-Yates surveys can be biased. © Rapid Science 1998     

The application of generalized linear mixed models to multi-level sampling for insect population monitoring

Iwao's quadratic regression or Taylor's Power Law (TPL) are commonly used to model the variance as a function of the mean for sample counts of insect populations which exhibit spatial aggregation. The modeled variance and distribution of the mean are typically used in pest management programs to decide if the population is above the action threshold in any management unit (MU) (e.g., orchard, forest compartment). For nested or multi-level sampling the usual two-stage modeling procedure first obtains the sample variance for each MU and sampling level using ANOVA and then fits a regression of variance on the mean for each level using either Iwao or TPL variance models. Here this approach is compared to the single-stage procedure of fitting a generalized linear mixed model (GLMM) directly to the count data with both approaches demonstrated using 2-level sampling. GLMMs and additive GLMMs (AGLMMs) with conditional Poisson variance function as well as the extension to the negative binomial are described. Generalization to more than two sampling levels is outlined. Formulae for calculating optimal relative sample sizes (ORSS) and the operating characteristic curve for the control decision are given for each model. The ORSS are independent of the mean in the case of the AGLMMs. The application described is estimation of the variance of the mean number of leaves per shoot occupied by immature stages of a defoliator of eucalypts, the Tasmanian Eucalyptus leaf beetle, based on a sample of trees within plots from each forest compartment. Historical population monitoring data were fitted using the above approaches.     

Predicting the variation in detection function in line transect sampling through random parameter model

A method for calibrating (localizing) detection function models in line transect sampling is proposed. The method is based on a random parameter model which supplies localized predictions of detection function parameters utilizing a few sample data points from the concerned location(s). The method has the clear advantage of being able to provide density estimates based on very few observations from a location which would be impossible through traditional methods. The method is successfully illustrated using census data on sambar (Cervus unicolor) from a set of wildlife sanctuaries in Kerala, India. The need for further research in this direction is indicated.     

Hunting in unfamiliar space: echolocation in the Indian false vampire bat, Megaderma lyra, when gleaning prey

The literature suggests that in familiar laboratory settings, Indian false vampire bats (Megaderma lyra, family Megadermatidae) locate terrestrial prey with and without emitting echolocation calls in the dark and cease echolocating when simulated moonlit conditions presumably allow the use of vision. More recent laboratory-based research suggests that M. lyra uses echolocation throughout attacks but at emission rates much lower than those of other gleaning bats. We present data from wild-caught bats hunting for and capturing prey in unfamiliar conditions mimicking natural situations. By varying light level and substrate complexity we demonstrated that hunting M. lyra always emit echolocation calls and that emission patterns are the same regardless of light/substrate condition and similar to those of other wild-caught gleaning bats. Therefore, echoic information appears necessary for this species when hunting in unfamiliar situations, while, in the context of past research, echolocation may be supplanted by vision, spatial memory or both in familiar spaces.Communicated by T. Czeschlik     

Spatial pattern and persistence of historical fire boundaries in southern interior British Columbia

Recent ecosystem and fire management research aims to quantify, model and understand historical fire disturbances focusing on their frequency, size and distribution. Less attention, however, has been paid to fire boundaries and their location on the landscape. Our study presents a spatial method to quantify the location, pattern and persistence of historical fire boundaries using tree ring fire scar data in the lower Stein watershed (British Columbia). Data from Pinus ponderosa and Pseudotsuga menziesii collected in 35 one-hectare plots over a 412-hectare study area were analyzed for the period between 1879 and 1947 using local spatial statistics and boundary detection techniques. Results of the analysis using local spatial statistic Moran’s I showed significant clustering of boundaries near topographic breaks. To determine and test whether fire boundaries between plots were persistent, we used boundary detection methods and developed a spatially restricted randomization test. The results revealed that out of 86 possible boundary links, 8 were significantly persistent (P < 0.025) while another 8 were significantly rare (P < 0.025). These spatial methods can help determine the historical spatial configuration of persistent boundaries and can be used to maintain natural forest dynamics.

Estimation of the mean in line intercept sampling

Ratio estimation of the parametric mean for a characteristic measured on plants sampled by a line intercept method is presented and evaluated via simulation using different plant dispersion patterns (Poisson, regular cluster, and Poisson cluster), plant width variances, and numbers of lines. The results indicate that on average the estimates are close to the parametric mean under all three dispersion patterns. Given a fixed number of lines, variability of the estimates is similar across dispersion patterns with variability under the Poisson pattern slightly smaller than varia-bility under the cluster patterns. No variance estimates were negative under the Poisson pattern, but some estimates were negative under the cluster patterns for smaller numbers of lines. Variance estimates become closer to zero similarly for all spatial patterns as the number of lines increases. Ratio estimation of the parametric mean in line intercept sampling works better, from the viewpoint of approximate unbiasedness and variability of estimates, under the Poisson pattern with larger numbers of lines than other combinations of spatial patterns, plant width variances and numbers of lines.     

Importance of biotic and abiotic regulators of abundance of the intertidal amphipod Calliopius laeviusculus (Amphipoda: Gammaridae) and assessment of the accuracy and precision of sampling methods for detecting abundance changes

We examined seasonal patterns of abundance for the intertidal amphipod Calliopius laeviusculus (Amphipoda: Gammaridae). Amphipods were sampled with an epibenthic sled during the daytime high tide period from 18 May to 8 August 1988. Amphipod density increased from May to June and reached maxima in both late June and early August. Amphipod density was unrelated to any abiotic component measured in the intertidal community. These variables included sampling location, wave height, water column height, water temperature, salinity and cloud cover. Changes in abundance were related with sampling date and with the onset of capelin (Mallotus villosus) spawning activity in the intertidal. Capelin eggs are an important food item for amphipods. The accuracy of density estimates obtained with the epibenthic sled was assessed through comparison with densities obtained with a more efficient quadrat sampler. Sled samples consistently sampled ca. 1% of the amphipod population. We found that a large portion of the amphipod population burrowed into the sediment and was not effectively sampled by the sled. Sled sampler precision was roughly equivalent to that of quadrats with D (precision) ranging from 0.26 to 0.42 for sled samples and D=0.29 for quadrat samples. Although sample collection with the epibenthic sled was achieved more quickly and under a wider range of weather conditions than was possible with the quadrat sampler, the serious underestimate of amphipod density based on sled samples alone indicates that both sled and quadrat samples, obtained in concert, are required to obtain accurate measures of daily variation in C. laeviusculus abundance.Contribution to the program of GIROQ (Groupe interuniversitaire de recherches oceanographique du Quebec)     

Determining the optimum number of increments in composite sampling

Composite sampling can be more cost effective than simple random sampling. This paper considers how to determine the optimum number of increments to use in composite sampling. Composite sampling terminology and theory are outlined and a method is developed which accounts for different sources of variation in compositing and data analysis. This method is used to define and understand the process of determining the optimum number of increments that should be used in forming a composite. The blending variance is shown to have a smaller range of possible values than previously reported when estimating the number of increments in a composite sample. Accounting for differing levels of the blending variance significantly affects the estimated number of increments.

Evaluating the Predicted Local Extinction of a Once-Common Mouse

Abstract:  In an earlier paper ( Pergams & Nyberg 2001 ) we found that the proportion of the prairie deer mouse ( Peromyscus maniculatus bairdii ), among all local Peromyscus museum specimens collected in the Chicago region, had significantly declined over time. This proportion changed from about 50% before 1900 to <10% in the last 25 years. Based on this proportion a regression model predicted the local extinction of the prairie deer mouse in 2009. To evaluate that prediction, we estimated current deer mouse abundance by live trapping small mammals at 15 preserves in Cook and Lake counties, Illinois (USA) at which prairie deer mice had previously been caught or that still contained their preferred open habitat. In 1900 trap nights, 477 mammals were caught, including 251 white-footed mice ( P. leucopus ), but only one prairie deer mouse. The observed proportion of Peromyscus that were prairie deer mice, 0.4%, was even lower than the 4.5% predicted for 2000. Here we also introduce a simple, new community proportions model, which for any given geographic region compares the proportions of species recently caught with the proportions of species in museums. We compared proportions of seven species collected in Cook and Lake counties and examined by Hoffmeister (1989) with proportions of these species that we caught. Ten percent of the museum community was prairie deer mice, but only 0.2% of our catch was. The current local scarcity of the prairie deer mouse is consistent with the regression-based prediction of its eminent local extinction. More conservation attention should be paid to changes in relative abundance of once-common species.     

Analysis of composite sampling data using the principle of maximum entropy

A new tool is presented based on the principle of maximum entropy for enhanced hot spot detection based on composite sampling with no (or minimal) requirement for composite breakdown. The methodology presented here is easy to implement and facilitates the use of multiple criteria for evaluating attainment of site remediation objectives. The new methodology provides very simple decision rules that can easily be used by non-statisticians and complements the use of composites for control of residual mean concentrations.     

Quantifying the efficiency of soil sampling designs: A multivariate approach

The objective of this paper is to quantify and compare the loss functions of the standard two-stage design and its composite sample alternative in the context of multivariate soil sampling. The loss function is defined (conceptually) as the ratio of cost over information and measures design inefficiency. The efficiency of the design is the reciprocal of the loss function. The focus of this paper is twofold: (a) we define a measure of multivariate information using the Kullback–Leibler distance, and (b) we derive the variance-covariance structure for two soil sampling designs: a standard two-stage design and its composite sample counterpart. Randomness in the mass of soil samples is taken into account in both designs. A pilot study in Slovenia is used to demonstrate the calculations of the loss function and to compare the efficiency of the two designs. The results show that the composite sample design is more efficient than the two-stage design. The efficiency ratio is 1.3 for pH, 2.0 for C, 2.1 for N, and 2.5 for CEC. The multivariate efficiency ratio is 2.3. These ratios primarily reflect cost ratios; influence of the information is small.     

Rao-Blackwell versions of the Horvitz-Thompson and Hansen-Hurwitz in adaptive cluster sampling

Thompson (1990) introduced the adaptive cluster sampling design and developed two unbiased estimators, the modified Horvitz-Thompson (HT) and Hansen-Hurwitz (HH) estimators, for this sampling design and noticed that these estimators are not a function of the minimal sufficient statistics. He applied the Rao-Blackwell theorem to improve them. Despite having smaller variances, these latter estimators have not received attention because a suitable method or algorithm for computing them was not available. In this paper we obtain closed forms of the Rao-Blackwell versions which can easily be computed. We also show that the variance reduction for the HH estimator is greater than that for the HT estimator using Rao-Blackwell versions. When the condition for extra samples is 0$$ " align="middle" border="0"> , one can expect some Rao-Blackwell improvement in the HH estimator but not in the HT estimator. Two examples are given.     

Evaluating the Success of Conservation Actions in Safeguarding Tropical Forest Biodiversity

Abstract: We reviewed the evidence on the extent and efficacy of conservation of tropical forest biodiversity for each of the classes of conservation action defined by the new International Union for Conservation of Nature (IUCN) classification. Protected areas are the most tested conservation approach, and a number of studies show they are generally effective in slowing deforestation. There is some documentation of the extent of sustainable timber management in tropical forest, but little information on other landscape‐conservation tactics. The extent and effectiveness of ex situ species conservation is quite well known. Forty‐one tropical‐forest species now survive only in captivity. Other single‐species conservation actions are not as well documented. The potential of policy mechanisms, such as international conventions and provision of funds, to slow extinctions in tropical forests is considerable, but the effects of policy are difficult to measure. Finally, interventions to promote tropical conservation by supporting education and livelihoods, providing incentives, and furthering capacity building are all thought to be important, but their extent and effectiveness remain poorly known. For birds, the best studied taxon, the sum of such conservation actions has averted one‐fifth of the extinctions that would otherwise have occurred over the last century. Clearly, tropical forest conservation works, but more is needed, as is critical assessment of what works in what circumstances, if mass extinction is to be averted.     

Evaluating the ability of habitat suitability models to predict species presences

Models predicting species spatial distribution are increasingly applied to wildlife management issues, emphasising the need for reliable methods to evaluate the accuracy of their predictions. As many available datasets (e.g. museums, herbariums, atlas) do not provide reliable information about species absences, several presence-only based analyses have been developed. However, methods to evaluate the accuracy of their predictions are few and have never been validated. The aim of this paper is to compare existing and new presence-only evaluators to usual presence/absence measures.     

Measuring mate choice using correlation: the effect of female sampling behaviour

For intersexual selection to occur, it is necessary that females choose between males. It is now well appreciated that constraints exist, which preclude females sampling all the available males in a population. These constraints are likely to have caused the evolution of sampling rules (such as the “best-of-n” rule) by which females sample males. Here we investigate the impact of female subsampling of the male population, not on the evolution of sampling behaviour, but on the population-level correlation between a male trait and currencies such as reproductive success. This study is important as it illustrates when population-level correlations can be safely used to infer the presence and strength of sexual selection in the field. We find that the correlation between a male trait and a mate choice variable rises steeply as the number of males sampled by each female increases, flattening above seven to ten males sampled. This shape is found to be remarkably robust, and little affected by, for example, the mate choice variable used, by noise in assessment, by sampling behaviour depending on female quality, or by population size. The only variable found to have a large impact is male clumping according to their “quality”. If females are sampling about four males, the maximum correlation that can be found at the population level is in the range 0.4–0.6, perhaps as little as 0.1 if males are strongly clumped. A recent review of the literature suggests that four is the average number of males that females sample. Thus, the absence of a strong correlation cannot by itself be used to infer that sexual selection is weak, as it may be due to females sampling few males. Received: 18 May 1998 / Accepted after revision: 18 July 1998     

Forecasting population trend from the scaling pattern of occupancy

Forecasting the temporal trend of a focal species, its range expansion or retraction, provides crucial information regarding population viability. To this end, we require the accumulation of temporal records which is evidently time consuming. Progress in spatial data capturing has enabled rapid and accurate assessment of species distribution across large scales. Therefore, it would be appealing to infer the temporal trends of populations from the spatial structure of their distributions. Based on a combination of models from the fields of range dynamics, occupancy scaling and spatial autocorrelation, here I present a model for forecasting the population trend solely from its spatial distribution. Numerical tests using cellular automata confirm a positive correlation, as inferred from the model, between the temporal change in species range sizes and the exponent of the power-law scaling pattern of occupancy. The model is thus recommended for rapid estimation of species range dynamics from a single snapshot of its current distribution. Further applications in biodiversity conservation could provide a swift risk assessment, especially, for endangered and invasive species.     

Evaluation of sampling methods for the estimation of structural indices in forest stands

The paper is about the accurate (i.e. unbiased and precise) and efficient estimation of structural indices in forest stands. We present SIAFOR, a computer programme for the calculation of four nearest-neighbour indices, which describe the spatial arrangement of tree positions, the distribution pattern of species, and the size differentiation between trees. The study uses SIAFOR as a sampling simulator in eight completely stem-mapped forest stands of varying area and structural complexity. We statistically evaluate two sample types (distance and plot sampling), comparing sampling error, bias and minimum sample size for index estimation. We introduce the concepts of measurement expansion factor (MEF) and design expansion factor (DEF) for the technical evaluation of sample type efficiency (optimal sample type). Results indicate that sampling error can reach high levels and that minimum sample sizes for index estimation often amply exceed the limit of 20% of tree density or 20 trees per species per hectare, that we set as the highest feasible sample size in normal situations. We found clear feasibility limits (in terms of minimal tree densities and reachable accuracy levels) for the estimation of all investigated indices. Generally, equal or higher sample sizes are needed for plot sampling than for distance sampling to reach equal accuracy levels. Nevertheless, plot sampling resulted more efficient for the estimation of tree size differentiation at low to medium accuracy levels. For all other investigated indices distance sampling resulted more efficient than plot sampling. Minimum sample size increases with accuracy and is negatively correlated with tree density. At a given accuracy level minimum sample size is highest for the estimation of relative mingling and lowest for tree size differentiation; furthermore it is generally lower in large stands than in small ones. Because of the consistency of our conclusions in all of the investigated stands, we think they apply in most stands of similar area (between 1 and 10 ha) and species diversity (not more than four species).     

Evaluating the Quality of Citizen‐Scientist Data on Pollinator Communities

Abstract: Concerns about pollinator declines have grown in recent years, yet the ability to detect changes in abundance, taxonomic richness, and composition of pollinator communities is hampered severely by the lack of data over space and time. Citizen scientists may be able to extend the spatial and temporal extent of pollinator monitoring programs. We developed a citizen‐science monitoring protocol in which we trained 13 citizen scientists to observe and classify floral visitors at the resolution of orders or super families (e.g., bee, wasp, fly) and at finer resolution within bees (superfamily Apoidea) only. We evaluated the protocol by comparing data collected simultaneously at 17 sites by citizen scientists (observational data set) and by professionals (specimen‐based data set). The sites differed with respect to the presence and age of hedgerows planted to improve habitat quality for pollinators. We found significant, positive correlations among the two data sets for higher level taxonomic composition, honey bee (Apis mellifera) abundance, non‐Apis bee abundance, bee richness, and bee community similarity. Results for both data sets also showed similar trends (or lack thereof) in these metrics among sites differing in the presence and age of hedgerows. Nevertheless, citizen scientists did not observe approximately half of the bee groups collected by professional scientists at the same sites. Thus, the utility of citizen‐science observational data may be restricted to detection of community‐level changes in abundance, richness, or similarity over space and time, and citizen‐science observations may not reliably reflect the abundance or frequency of occurrence of specific pollinator species or groups.