Network inclusion probabilities and Horvitz-Thompson estimation for adaptive simple Latin square sampling

Consider a survey of a plant or animal species in which abundance or presence/absence will be recorded. Further assume that the presence of the plant or animal is rare and tends to cluster. A sampling design will be implemented to determine which units to sample within the study region. Adaptive cluster sampling designs Thompson (1990) are sampling designs that are implemented by first selecting a sample of units according to some conventional probability sampling design. Then, whenever a specified criterion is satisfied upon measuring the variable of interest, additional units are adaptively sampled in neighborhoods of those units satisfying the criterion. The success of these adaptive designs depends on the probabilities of finding the rare clustered events, called networks. This research uses combinatorial generating functions to calculate network inclusion probabilities associated with a simple Latin square sample. It will be shown that, in general, adaptive simple Latin square sampling when compared to adaptive simple random sampling will (i) yield higher network inclusion probabilities and (ii) provide Horvitz-Thompson estimators with smaller variability.     

Halton iterative partitioning: spatially balanced sampling via partitioning

A new spatially balanced sampling design for environmental surveys is introduced, called Halton iterative partitioning (HIP). The design draws sample locations that are well spread over the study area. Spatially balanced designs are known to be efficient when surveying natural resources because nearby locations tend to be similar. The HIP design uses structural properties of the Halton sequence to partition a resource into nested boxes. Sample locations are then drawn from specific boxes in the partition to ensure spatial diversity. The method is conceptually simple and computationally efficient, draws spatially balanced samples in two or more dimensions and uses standard design-based estimators. Furthermore, HIP samples have an implicit ordering that can be used to define spatially balanced over-samples. This feature is particularly useful when sampling natural resources because we can dynamically add spatially balanced units from the over-sample to the sample as non-target or inaccessible units are discovered. We use several populations to show that HIP sampling draws spatially balanced samples and gives precise estimates of population totals.     

Two-stage estimation of ungulate abundance in Mediterranean areas using pellet group count

A design-based strategy for estimating wildlife ungulate abundance in a Mediterranean protected area (Maremma Regional Park) is considered. The estimation is based on pellet group count (clearance count technique) in a set of plots, whose size and number is established on the basis of practical considerations and available resources. The sampling scheme involves a preliminary stratification and subsequent two-stage sampling. In the first stage, large strata (defined through habitat features) are partitioned into spatial units and a sample of units is selected by means of a sampling scheme ensuring inclusion probabilities proportional to unit size, but avoiding the selection of contiguous units. Then, the abundances of the selected units are estimated in a second stage, in which plots are located using a random scheme ensuring an even coverage of the units. In small strata, only the second stage is performed. Unbiased estimators of abundance and conservative estimators of their variances are derived for each strata and for the whole study area. The proposed strategy has been applied since the Summer of 2006 and the estimation results reveal substantial improvement with respect to the previous results obtained by means of an alternative strategy.     

A framework for adapting survey design through time for wildlife population assessment

Sampling strategies for monitoring the status and trends in wildlife populations are often determined before the first survey is undertaken. However, there may be little information about the distribution of the population and so the sample design may be inefficient. Through time, as data are collected, more information about the distribution of animals in the survey region is obtained but it can be difficult to incorporate this information in the survey design. This paper introduces a framework for monitoring motile wildlife populations within which the design of future surveys can be adapted using data from past surveys whilst ensuring consistency in design-based estimates of status and trends through time. In each survey, part of the sample is selected from the previous survey sample using simple random sampling. The rest is selected with inclusion probability proportional to predicted abundance. Abundance is predicted using a model constructed from previous survey data and covariates for the whole survey region. Unbiased design-based estimators of status and trends and their variances are derived from two-phase sampling theory. Simulations over the short and long-term indicate that in general more precise estimates of status and trends are obtained using this mixed strategy than a strategy in which all of the sample is retained or all selected with probability proportional to predicted abundance. Furthermore the mixed strategy is robust to poor predictions of abundance. Estimates of status are more precise than those obtained from a rotating panel design.     

Nest selection by snow petrels Pagodroma nivea in East Antarctica: Validating predictive habitat selection models at the continental scale

Little is known on the factors controlling distribution and abundance of snow petrels in Antarctica. Studying habitat selection through modeling may provide useful information on the relationships between this species and its environment, especially relevant in a climate change context, where habitat availability may change. Validating the predictive capability of habitat selection models with independent data is a vital step in assessing the performance of such models and their potential for predicting species’ distribution in poorly documented areas.From the results of ground surveys conducted in the Casey region (2002–2003, Wilkes Land, East Antarctica), habitat selection models based on a dataset of 4000 nests were created to predict the nesting distribution of snow petrels as a function of topography and substrate. In this study, the Casey models were tested at Mawson, 3800 km away from Casey. The location and characteristics of approximately 7700 snow petrel nests were collected during ground surveys (Summer 2004–2005). Using GIS, predictive maps of nest distribution were produced for the Mawson region with the models derived from the Casey datasets and predictions were compared to the observed data. Models performance was assessed using classification matrixes and Receiver operating characteristic (ROC) curves. Overall correct classification rates for the Casey models varied from 57% to 90%. However, two geomorphologically different sub-regions (coastal islands and inland mountains) were clearly distinguished in terms of habitat selection by Casey model predictions but also by the specific variations in coefficients of terms in new models, derived from the Mawson data sets. Observed variations in the snow petrel aggregations were found to be related to local habitat availability.We discuss the applicability of various types of models (GLM, CT) and investigate the effect of scale on the prediction of snow petrel habitats. While the Casey models created with data collected at the nest scale did not perform well at Mawson due to regional variations in nest micro-characteristics, the predictive performance of models created with data compiled at a coarser scale (habitat units) was satisfactory. Substrate type was the most robust predictor of nest presence between Casey and Mawson. This study demonstrate that it is possible to predict at the large scale the presence of snow petrel nests based on simple predictors such as topography and substrate, which can be obtained from aerial photography. Such methodologies have valuable applications in the management and conservation of this top predator and associated resources and may be applied to other Antarctic, Sub-Antarctic and lower latitudes species and in a variety of habitats.     

Bayesian Small Area Models for Assessing Wildlife Conservation Risk in Patchy Populations

Abstract:  Species conservation risk assessments require accurate, probabilistic, and biologically meaningful maps of population distribution. In patchy populations, the reasons for discontinuities are not often well understood. We tested a novel approach to habitat modeling in which methods of small area estimation were used within a hierarchical Bayesian framework. Amphibian occurrence was modeled with logistic regression that included third-order drainages as hierarchical effects to account for patchy populations. Models including the random drainage effects adequately represented species occurrences in patchy populations of 4 amphibian species in the Oregon Coast Range (U.S.A.). Amphibian surveys from other locations within the same drainage were used to calibrate local drainage-scale effects. Cross-validation showed that prediction errors for calibrated models were 77% to 86% lower than comparable regionally constructed models, depending on species. When calibration data were unavailable, small area and regional models performed similarly, although poorly. Small area estimation models complement wildlife ecology and habitat studies, and can help managers develop a regional picture of the conservation status for relatively rare species.     

Sampling design trade-offs in occupancy studies with imperfect detection: examples and software.

Researchers have used occupancy, or probability of occupancy, as a response or state variable in a variety of studies (e.g., habitat modeling), and occupancy is increasingly favored by numerous state, federal, and international agencies engaged in monitoring programs. Recent advances in estimation methods have emphasized that reliable inferences can be made from these types of studies if detection and occupancy probabilities are simultaneously estimated. The need for temporal replication at sampled sites to estimate detection probability creates a trade-off between spatial replication (number of sample sites distributed within the area of interest/inference) and temporal replication (number of repeated surveys at each site). Here, we discuss a suite of questions commonly encountered during the design phase of occupancy studies, and we describe software (program GENPRES) developed to allow investigators to easily explore design trade-offs focused on particularities of their study system and sampling limitations. We illustrate the utility of program GENPRES using an amphibian example from Greater Yellowstone National Park, U.S.A.     

A robust weighted EM algorithm for use-availability data

Wildlife sampling for habitat selection often combines a random background sample with a random sample of used sites, because the background sample could contain too few used sites to be informative for rare species. This approach is referred to as use-availability sampling. Two variants are considered where there is: (1) a random background sample including used and unused sites augmented with a sample of used sites, and (2) a sample of used sites augmented with a contaminated background sample, i.e. use is not recorded. A weighted estimator first proposed by Manski and Lerman (Econometrica 45(8):1977?C1988, 1977) forms the basis for our suggested approach. The weighted estimator has been shown to perform better than the usual unweighted approach with uncontaminated data and mis-specified logit models (Xie and Manski in Sociol Methods Res 17(3):283?C302, 1989). A weighted EM algorithm is developed for use with contaminated background data. We show that the weighted estimator continues to perform well with contaminated data and maintains its robustness to model mis-specification. The weighted estimator has not been previously used for use-availability sampling due to reliance on the assumption that only the intercept is biased, which is valid for a correct logit model. We show that adjusting the intercept may not eliminate the bias with an incorrect logit model. In this case, the weighted estimator is a relatively simple and effective alternative.     

Estimates of minimum patch size depend on the method of estimation and the condition of the habitat

Minimum patch size for a viable population can be estimated in several ways. The density-area method estimates minimum patch size as the smallest area in which no new individuals are encountered as one extends the arbitrary boundaries of a study area outward. The density-area method eliminates the assumption of no variation in density with size of habitat area that accompanies other methods, but it is untested in situations in which habitat loss has confined populations to small areas. We used a variant of the density area method to study the minimum patch size for the gopher tortoise (Gopherus polyphemus) in Florida, USA, where this keystone species is being confined to ever smaller habitat fragments. The variant was based on the premise that individuals within populations are likely to occur at unusually high densities when confined to small areas, and it estimated minimum patch size as the smallest area beyond which density plateaus. The data for our study came from detailed surveys of 38 populations of the tortoise. For all 38 populations, the areas occupied were determined empirically, and for 19 of them, duplicate surveys were undertaken about a decade apart. We found that a consistent inverse density area relationship was present over smaller areas. The minimum patch size estimated from the density-area relationship was at least 100 ha, which is substantially larger than previous estimates. The relative abundance of juveniles was inversely related to population density for sites with relatively poor habitat quality, indicating that the estimated minimum patch size could represent an extinction threshold. We concluded that a negative density area relationship may be an inevitable consequence of excessive habitat loss. We also concluded that any detrimental effects of an inverse density area relationship may be exacerbated by the deterioration in habitat quality that often accompanies habitat loss. Finally, we concluded that the value of any estimate of minimum patch size as a conservation tool is compromised by excessive habitat loss.     

Asymptotics in adaptive cluster sampling

In this article we consider asymptotic properties of the Horvitz-Thompson and Hansen-Hurwitz types of estimators under the adaptive cluster sampling variants obtained by selecting the initial sample by simple random sampling without replacement and by unequal probability sampling with replacement. We develop an asymptotic framework, which basically assumes that the number of units in the initial sample, as well as the number of units and networks in the population tend to infinity, but that the network sizes are bounded. Using this framework we prove that under each of the two variants of adaptive sampling above mentioned, both the Horvitz-Thompson and Hansen-Hurwitz types of estimators are design-consistent and asymptotically normally distributed. In addition we show that the ordinary estimators of their variances are also design-consistent estimators.     

Patch Isolation, Corridor Effects, and Colonization by a Resident Sparrow in a Managed Pine Woodland

The isolation of habitat patches is often cited as having a major impact on the dynamics of small populations occupying patches in a complex landscape. Few studies, however, have provided field data demonstrating that isolation has an identifiable effect on specific populations independent of other factors such as local habitat quality or that landscape factors such as corridors can alleviate such effects. We conducted field surveys of Bachman's Sparrow ( Aimophila aestivalis ) populations in regions, which we call linear landscapes, where suitable habitat patches were isolated to varying degrees from potential sources of dispersing birds. In these linear landscapes, isolated patches of habitat were less likely to be colonized than were nonisolated patches. We also found that corridor configurations of habitat patches improved the ability of sparrows to find and settle in newly created patches. These results suggest that, for species that do not disperse easily through inhospitable landscapes, habitat occupancy at a regional scale can be enhanced by careful landscape design and planning.     

Assessing the status and trend of bat populations across broad geographic regions with dynamic distribution models

Bats face unprecedented threats from habitat loss, climate change, disease, and wind power development, and populations of many species are in decline. A better ability to quantify bat population status and trend is urgently needed in order to develop effective conservation strategies. We used a Bayesian autoregressive approach to develop dynamic distribution models for Myotis lucifugus, the little brown bat, across a large portion of northwestern USA, using a four-year detection history matrix obtained from a regional monitoring program. This widespread and abundant species has experienced precipitous local population declines in northeastern USA resulting from the novel disease white-nose syndrome, and is facing likely range-wide declines. Our models were temporally dynamic and accounted for imperfect detection. Drawing on species-energy theory, we included measures of net primary productivity (NPP) and forest cover in models, predicting that M. lucifugus occurrence probabilities would covary positively along those gradients. Despite its common status, M. lucifugus was only detected during -50% of the surveys in occupied sample units. The overall naive estimate for the proportion of the study region occupied by the species was 0.69, but after accounting for imperfect detection, this increased to -0.90. Our models provide evidence of an association between NPP and forest cover and M. lucifugus distribution, with implications for the projected effects of accelerated climate change in the region, which include net aridification as snowpack and stream flows decline. Annual turnover, the probability that an occupied sample unit was a newly occupied one, was estimated to be low (-0.04-0.14), resulting in flat trend estimated with relatively high precision (SD = 0.04). We mapped the variation in predicted occurrence probabilities and corresponding prediction uncertainty along the productivity gradient. Our results provide a much needed baseline against which future anticipated declines in M. lucifugus occurrence can be measured. The dynamic distribution modeling approach has broad applicability to regional bat monitoring efforts now underway in several countries and we suggest ways to improve and expand our grid-based monitoring program to gain robust insights into bat population status and trend across large portions of North America.     

Refining logistic regression models for wildlife habitat suitability modeling—A case study with muntjak and goral in the Central Himalayas, India

High quality habitat suitability maps are indispensable for the management and planning of wildlife reserves. This is particularly important for megadiverse developing countries where shortages in skilled manpower and funding may preclude the use of mathematically complex modeling techniques and resource-intensive field surveys. In this study, we propose a simulation based k-fold partitioning and re-substitution approach to refine and update logistic regression models that are widely used for habitat suitability assessment and modeling. We test the modeling strategy using data from a rapid field survey conducted for habitat suitability assessment for muntjak (Muntiacus muntjak) and goral (Naemorrhaedus goral) in the central Himalayas, India. Results obtained from simulations match expectations in terms of model behavior and in terms of published habitat associations of the investigated species. Qualitative comparisons with predictions from the GARP, MaxEnt and Bioclimatic Envelopes modeling systems also show broad agreement with predictions obtained from the proposed technique. The proposed technique is suggested as a rapid-assessment precursor to detailed habitat studies such as patch occupancy modeling in situations where funds or trained manpower are not available.     

Resampling methods for estimating dispersion indices in random and adaptive designs

In many surveys in environmental and natural phenomena the aim is to evaluate the heterogeneity, and the skewness of the distribution of the number point-objects in the study area opportunely partitioned in sub-regions. For this purpose, in this paper the estimation of dispersion indices is considered by using simple random sampling and adaptive sampling with initial simple random sampling selected with replacement or without replacement. The jackknife and the bootstrap procedures are proposed in both cases for reducing bias. Finally, both a simulation study and a case study on biological population referred to a Oidium tuckeri contamination in a growing vineyard is performed to assess the accuracy of the proposed estimators.     

Using forest inventory data to assess fisher resting habitat suitability in California.

The fisher (Martes pennanti) is a forest-dwelling carnivore whose current distribution and association with late-seral forest conditions make it vulnerable to stand-altering human activities or natural disturbances. Fishers select a variety of structures for daily resting bouts. These habitat elements, together with foraging and reproductive (denning) habitat, constitute the habitat requirements of fishers. We develop a model capable of predicting the suitability of fisher resting habitat using standard forest vegetation inventory data. The inventory data were derived from Forest Inventory and Analysis (FIA), a nationwide probability-based sample used to estimate forest characteristics. We developed the model by comparing vegetation and topographic data at 75 randomly selected fisher resting structures in the southern Sierra Nevada with 232 forest inventory plots. We collected vegetation data at fisher resting locations using the FIA vegetation sampling protocol and centering the 1-ha FIA plot on the resting structure. To distinguish used and available inventory plots, we used nonparametric logistic regression to evaluate a set of a priori biological models. The top model represented a dominant portion of the Akaike weights (0.87), explained 31.5% of the deviance, and included the following variables: average canopy closure, basal area of trees <51 cm diameter breast height (dbh), average hardwood dbh, maximum tree dbh, percentage slope, and the dbh of the largest conifer snag. Our use of routinely collected forest inventory data allows the assessment and monitoring of change in fisher resting habitat suitability over large regions with no additional sampling effort. Although models were constrained to include only variables available from the list of those measured using the FIA protocol, we did not find this to be a shortcoming. The model makes it possible to compare average resting habitat suitability values before and after forest management treatments, among administrative units, across regions and over time. Considering hundreds of plot estimates as a sample of habitat conditions over large spatial scales can bring a broad perspective, at high resolution, and efficiency to the assessment and monitoring of wildlife habitat.     

Assessing Risks to Biodiversity from Future Landscape Change

We examined the impacts of possible future land development patterns on the biodiversity of a landscape. Our landscape data included a remote sensing derived map of the current habitat of the study area and six maps of future habitat distributions resulting from different land development scenarios. Our species data included lists of all bird, mammal, reptile, and amphibian species in the study area, their habitat associations, and area requirements for each. We estimated the area requirements using home ranges, sampled population densities, or genetic area requirements that incorporate dispersal distances. Our measures of biodiversity were species richness and habitat abundance. We calculated habitat abundance in two ways. First, we computed the total habitat area for each species in each landscape. Second, we calculated the number of habitat units for each species in each landscape by dividing the size of each habitat patch in the landscape by the area requirement and summing over all patches. Species richness was based on presence of habitat. Species became extinct in the landscape if they had no habitat area or no habitat units, respectively. We then computed ratios of habitat abundance in each future landscape to habitat abundance in the present for each species. We also computed the ratio of future to present species richness. We then calculated summary statistics across all species. Species richness changed little from present to future. There were distinctly greater risks to habitat abundance in landscapes that extrapolated from present trends or zoning patterns, however, as opposed to landscapes in which land development activities followed more constrained patterns. These results were stable when tested using Monte Carlo simulations and sensitivity tests on the area requirements. We conclude that this methodology can begin to discriminate the effects of potential changes in land development on vertebrate biodiversity.     

Multivariate bootstrap confidence regions for abundance vector using

Abundance vector estimation is a well investigated problem in statistical ecology. The use of simple random sampling with replacement or replicated sampling ensures good asymptotic properties of the abundance vector estimators. However, real surveys are based on small sample sizes, and assuming any specific distribution of the abundance vector estimator may be hazardous.In this paper we focus our attention on situations where the population is not too large and the sample size is small. We propose bootstrap multivariate confidence regions based on data depth. Data depth is a geometrical concept of ordering data from the center outwardly in higher dimensions. The Simplicial depth, the Tukey's depth and the Mahalanobis depth are presented. In order to build confidence regions in the presence of a skewed distribution of the abundance vector estimator, the use of Tukey's depth is suggested. The proposed method has been applied to the benthic community of Lake Lesina. A comparison with Mahalanobis depth and standard existing methods is reported.     

A permutation-based combination of sign tests for assessing habitat selection

The analysis of habitat selection in radio-tagged animals is approached by comparing the portions of use against the portions of availability observed for each habitat type. Since data are linearly dependent with singular variance-covariance matrices, standard multivariate statistical tests cannot be applied. To bypass the problem, compositional data analysis is customarily performed via log-ratio transform of sample observations. The procedure is criticized in this paper, emphasizing the several drawbacks which may arise from the use of compositional analysis. An alternative nonparametric solution is proposed in the framework of multiple testing. The habitat use is assessed separately for each habitat type by means of the sign test performed on the original observations. The resulting p values are combined in an overall test statistic whose significance is determined permuting sample observations. The theoretical findings of the paper are checked by simulation studies. Applications to case studies previously considered in literature are discussed.     

Using Niche-Based Models to Improve the Sampling of Rare Species

Abstract:  Because data on rare species usually are sparse, it is important to have efficient ways to sample additional data. Traditional sampling approaches are of limited value for rare species because a very large proportion of randomly chosen sampling sites are unlikely to shelter the species. For these species, spatial predictions from niche-based distribution models can be used to stratify the sampling and increase sampling efficiency. New data sampled are then used to improve the initial model. Applying this approach repeatedly is an adaptive process that may allow increasing the number of new occurrences found. We illustrate the approach with a case study of a rare and endangered plant species in Switzerland and a simulation experiment. Our field survey confirmed that the method helps in the discovery of new populations of the target species in remote areas where the predicted habitat suitability is high. In our simulations the model-based approach provided a significant improvement (by a factor of 1.8 to 4 times, depending on the measure) over simple random sampling. In terms of cost this approach may save up to 70% of the time spent in the field.     

A method for the detection of non-random associations among flocking birds and its application to sanderlings Calidris alba wintering in N.E. England

Summary Indices of association are frequently used in studies of social behaviour. Observed association indices may be compared with those obtained from computer randomizations of the data in order to test whether any two individuals in a population tend to occur together more than would be expected by chance. Data for individually-identifiable colour-ringed sanderlings Calidris alba are presented to illustrate the importance of the assumptions on which such null models are built. When each individual was given an equal chance of appearing in each flock associations differed from those expected by chance. But when the different numbers of times that each individual occurred at the study site were taken into account associations were not different from those expected by chance. Hypotheses relating association levels to a number of factors were tested. None of the factors examined had significant and appreciable effects on association levels. In particular, there was no evidence for sanderlings moving around in stable groups. Taking into account the different distributions of different individuals, the population of birds present on any day represented a random sample from the population of birds seen during the winter. Correspondence to: G. Roberts