Restricted adaptive cluster sampling

Adaptive cluster sampling can be a useful design for sampling rare and patchy populations. With this design the initial sample size is fixed but the size of the final sample (and total sampling effort) cannot be predicted prior to sampling. For some populations the final sample size can be quite variable depending on the level of patchiness. Restricted adaptive cluster sampling is a proposed modification where a limit is placed on the sample size prior to sampling and quadrats are selected sequentially for the initial sample size. As a result there is less variation in the final sample size and the total sampling effort can be predicted with some certainty, which is impor- tant for many ecological studies. Estimates of density are biased with the restricted design but under some circumstances the bias can be estimated well by bootstrapping. © Rapid Science 1998     

Habitat selection in a coastal dolphin species (<Emphasis Type="Italic">Cephalorhynchus hectori</Emphasis>)

Hector's dolphin ( Cephalorhynchus hectori) is a small New Zealand delphinid with a coastal distribution. Within a strip of 1 km from shore, the present study quantified the habitat used by the dolphins ( n=461 groups) over a 19-month period (216 field days with 966 survey hours) by recording the abiotic factors sea surface temperature (SST), water depth and water clarity. Resource selection functions were used to distinguish the properties of 461 "used" sites (dolphins present) from 425 "unused" sites (no dolphins present) in six different study areas. Most dolphins were encountered in waters <39 m depth, with <4 m Secchi disk visibility and >14°C temperature. The preference of Hector's dolphins for warm and turbid waters was tested using eight models. Water depth, water clarity, SST and the study area explained dolphin presence to a very significant degree ( p<0.001), and the model allowed the creation of probability plots for a variety of combinations of the variables. Habitat selection by dolphins differed between study areas, particularly between east and west coasts, in summer (December–February) and winter (June–August). Dolphin abundance appeared to change seasonally in some study areas, possibly due to a more offshore distribution of their prey in the winter, with its lower SSTs. This was so especially in summer (the main reproductive season), when dolphins (frequently with calves) occupied shallow and turbid waters, whereas in winter less use was made of this habitat.     

Using the bootstrap with two-phase adaptive stratified samples from multiple populations at multiple locations

Recently the two-phase adaptive stratified sampling design proposed by Francis (1984) has been extended by Manly et al. (2002) for situations where several biological populations are sampled simultaneously, and where this is done at several different geographical locations in order to estimate population totals or means. The method uses the results from a first phase sample to decide how best to allocate a second phase sample to locations and strata, in order to maximise a criterion (based on estimated coefficients of variation) that measures the accuracy of estimation for population totals, for all variables at all locations. One potential problem with this method is bias in the estimators of the population totals and means. In this paper bootstrapping is considered as a means of overcoming these biases. It is shown using model populations of Pacific walrus and shellfish, based on real data, that bootstrapping is a useful tool for removing about half of the bias. This is also confirmed from some simulations using artificial data.     

On the use of correlated beta random variables with animal population modelling

We give reasons why demographic parameters such as survival and reproduction rates are often modelled well in stochastic population simulation using beta distributions. In practice, it is frequently expected that these parameters will be correlated, for example with survival rates for all age classes tending to be high or low in the same year. We therefore discuss a method for producing correlated beta random variables by transforming correlated normal random variables, and show how it can be applied in practice by means of a simple example. We also note how the same approach can be used to produce correlated uniform, triangular, and exponential random variables.     

Using selection functions to describe changes in environmental variables

The selection function (which shows how the frequency of sampling units with the value X = x at one point in time must change in order to produce the distribution that occurs at a later point in time) is proposed for describing the changes over time in an environmentally important variable X. It is shown that the theory of selection functions as used in the study of natural selection and resource selection by animals requires some modifications in this new application and that a selection function is a useful tool in long-term monitoring studies because all changes in a distribution can be examined (rather than just changes in single parameters such as the mean), and because graphical presentations of the selection function are easy for non-statisticians to understand. Estimation of the selection function is discussed using a method appropriate for normal distributions and bootstrapping is suggested as a method for assessing the precision of estimates and for testing for significant differences between samples taken at different times. Methods are illustrated using data on water chemical variables from a study of the effects of acid precipitation in Norway.     

CUSUM environmental monitoring in time and space

We consider the situation where there are n sampling sites in an area, with an environmental variable measured at some or all of the sites at m sample times. We assume that there is interest in knowing whether the environmental variable displays systematic changes over time at the sites. A cumulative sum type of analysis with associated randomization tests has been proposed before for this situation, when there is negligible correlation between the observations in different times at one site, and no correlation between the results at different sites. A modification that allows for serial correlation at the individual sites but with no correlation between sites has also been proposed before. In the present paper we discuss how the method can be modified further to allow for spatial correlation between the sites, by applying it only to a reduced set of sites that are far enough apart to give effectively independent results. Simulation results indicate that this strategy is effective providing that the level of spatial correlation is not too high.     

Extending null scenarios with Faddy distributions in a probabilistic randomization protocol for presence-absence data

Environmental and Ecological Statistics - Navarro and Manly (Popul Ecol 51:505–512, 2009) (NM) have proposed a randomization protocol for null model analysis of species occurrences at...