Christine Donnelly

Modelling the abundance of rare species: statistical models for counts with extra zeros

Abstract We consider several statistical models for the analysis of the abundance of a rare species and these are illustrated in detail with data for the abundance of Leadbeaters Possum in montane ash forests of south-eastern Australia. These data are characterised by a discrete distribution with the zero class inflated. In many statistical problems the parameters of this distribution depend on covariates, such as the number of hollow bearing trees. We advocate a conditional model which is simple to interpret and readily fitted. We show how to obtain standard errors for the parameter estimates. We also show how to estimate the mean abundance of animals at a site. The methods outlined in this paper offer a powerful framework for the study of problems having a discrete response (like abundance) with the zero class inflated.

EFFECTS OF FOREST FRAGMENTATION ON BIRD ASSEMBLAGES IN A NOVEL LANDSCAPE CONTEXT

We report findings of a large-scale study in a 100 000-ha subsection of the Tumut region in southern New South Wales, southeastern Australia. The study was designed to measure the effects of landscape context and habitat fragmentation on forest birds. The study region consisted of a forest mosaic characterized by different landscape contexts: large, continuous areas of native Eucalyptus forest, extensive stands of exotic softwood (radiata pine, Pinus radiata) plantation, and remnant patches of native Eucalyptus forest scattered throughout the extensive areas of radiata pine plantation. A set of 85 eucalypt remnants was randomly selected across several stratifying variables: four patch size classes (1-3 ha, 4-10 ha, 11-20 ha, and .20 ha), two isolation age classes (,20 years and .20 years since fragmentation), and five dominant eucalypt forest type classes. In addition to the 85 eucalypt remnants, a further 80 3-ha sites were selected for study: 40 in large, continuous areas of eucalypt forest and 40 in radiata pine stands. Point-interval counts of forest birds at the 165 sites were conducted in 1996 and 1997. Of 90 species recorded, 23.1 species (95% confidence interval, 22.0, 24.2 species), on average, were present in continuous eucalypt forest, 20.6 (19.5, 21.7) species in patch- shaped eucalypt remnants, 20.6 (19.5, 21.7) species in strip-shaped eucalypt remnants, and 16.7 (15.6, 17.8) species in radiata pine. Strong gradients in bird assemblages were found. These gradients were governed by a combination of landscape context, remnant size, and remnant shape effects, and, in the case of radiata pine sites, the extent of native forest surrounding the pine. These gradients could, in part, be explained by bird life history attributes such as foraging guild and nesting height. For example, birds more often detected in patch-shaped remnants were smaller, produced smaller clutches, were more likely to be migratory, and typically had cup nests or burrows. The results of our study showed that eucalypt fragments of all sizes and shapes have significant conservation value. This is because they contain many native species of birds, some of which are more abundant in fragments than they are in continuous eucalypt forests, and also because they increase native bird populations in nearby non-native pine plantations.

The abundance and development of cavities in Eucalyptus trees: a case study in the montane forests of Victoria, southeastern Australia

Abstract A study of the abundance of cavities in Eucalyptus regnans, Eucalyptus delegatensis, Eucalyptus nitens, Eucalyptus obliqua and Eucalyptus cypellocarpa is described. The investigation used a database of 2315 living and dead trees with cavities, measured on 523 sites each of 3 ha throughout the montane ash forests of the Central Highlands of Victoria, southeastern Australia. Poisson regression analysis was used to examine the relationships between the number and type of cavities and a range of attributes of trees. These analyses demonstrated that, for all species of trees, the abundance of holes, fissures and hollow branches increased with tree diameter. Log-linear analysis of contingency tables demonstrated that various combinations of cavity types typically occur. Patterns of co-occurrence of cavities changed significantly according to the diameter, height and form of trees. The application of restricted maximum likelihood estimation (REML) for examining multi-level data, enabled the relatioships between the number of cavities, tree characteristics and site parameters to be analysed The characteristics of trees that were important were height, diameter and form. Site parameter that had a significant influence on the total number of cavities in trees included slope, latitude and stand age. This highlights the range of factors, at several measured spatial scales, that may influence the development of cavities in Eucalyptus trees. Although the various relationships derived in this study were highly significant, the statistical models had limited predictive ability. Thus for any given tree the development of cavities will be influenced by site and tree attributes as well as highly stochastic episodic events that may occur during its lifetime. The key findings from the study are discussed in terms of their relevance to forest wildlife management.

DECAY AND COLLAPSE OF TREES WITH HOLLOWS IN EASTERN AUSTRALIAN FORESTS: IMPACTS ON ARBOREAL MARSUPIALS

We studied the decay and collapse of trees with hollows in the montane ash forests of the Central Highlands of Victoria, southeastern Australia. We monitored the condition of >1400 trees for varying periods of time between 1983 and 1993 on 181 sites that varied considerably in stand age, tree species composition, slope, aspect, disturbance history, and a wide range of other parameters. The data analyzed in this study were from: (1) 302 trees on 32 sites, each of 3 ha, measured first in 1983 and then again in 1988 and 1993; (2) 1006 trees on 132 3-ha sites surveyed both in 1988 and 1993; and (3) 399 trees, measured in 1990 and again 1993, that occurred within 49 wildlife corridors where the surrounding forest recently had been clearcut. Our results revealed that >40% of the 302 trees first measured during 1983 had collapsed and fallen to the forest floor by 1993. The annual rate of collapse of trees was more rapid between 1988 and 1993 (4.8%) than between 1983 and 1988 (3.6%). Transition matrices construct...

THE RESPONSE OF ARBOREAL MARSUPIALS TO LANDSCAPE CONTEXT: A LARGE-SCALE FRAGMENTATION STUDY

We describe a landscape-scale study of fragmentation effects on arboreal marsupials at Tumut, southeastern Australia. Embedded within a 55000-ha plantation of exotic Monterey pine (Pinus radiata) are 192 patches of remnant Eucalyptus forest, with large contiguous areas of eucalypt forest beyond the plantation boundary. We compared presence and estimated abundance of arboreal marsupials in three broad groups of sites: remnants of native Eucalyptus forest in the P. radiata plantation; P. radiata stands in the plantation; and large areas of contiguous Eucalyptus forest surrounding the plantation. The study animals were Trichosurus vulpecula, T. caninus, Petaurus breviceps, P. norfolcensis, P. australis, Acrobates pygmaeus, Pseudocheirus peregrinus, and Petauroides volans. We used randomized, replicated statistical procedures to sample 86 eucalypt remnants varying in size, shape, and other features. We matched 40 sites in large contiguous Eucalyptus forest to those remnants, based on environment, climate, ter...

On the use of landscape surrogates as ecological indicators in fragmented forests

Abstract Given the potentially negative effects of forest fragmentation on biodiversity, governments and management agencies have sought generic landscape measures of forest fragmentation to monitor changes in forest cover—measures that also may be informative for decisions relating to changes in biodiversity. In this paper, we discuss issues relating to the evaluation of landscape surrogate measures and their usefulness as ecological indicators. We illustrate some of these points by a detailed examination of statistical relationships among several target responses (defined as the occurrence of particular species), and a selection of landscape surrogate measures in two forest regions of southeastern Australia. There was no evidence in our data that surrogate landscape measures have generic applicability for the conservation of large sets of species. Although landscape surrogates may be useful where the aim is to quantify current landscape patterns from a human perspective or to monitor the extent and rate of change in that pattern over time, they may not have biological and statistical significance for particular elements of the biota. There is a need for a clear definition of units and measures, a need to be aware of redundancy among potential surrogates, and a need for the establishment of a framework for rigorously evaluating ecological indicators.

Fitting and Interpreting Occupancy Models

We show that occupancy models are more difficult to fit than is generally appreciated because the estimating equations often have multiple solutions, including boundary estimates which produce fitted probabilities of zero or one. The estimates are unstable when the data are sparse, making them difficult to interpret, and, even in ideal situations, highly variable. As a consequence, making accurate inference is difficult. When abundance varies over sites (which is the general rule in ecology because we expect spatial variance in abundance) and detection depends on abundance, the standard analysis suffers bias (attenuation in detection, biased estimates of occupancy and potentially finding misleading relationships between occupancy and other covariates), asymmetric sampling distributions, and slow convergence of the sampling distributions to normality. The key result of this paper is that the biases are of similar magnitude to those obtained when we ignore non-detection entirely. The fact that abundance is subject to detection error and hence is not directly observable, means that we cannot tell when bias is present (or, equivalently, how large it is) and we cannot adjust for it. This implies that we cannot tell which fit is better: the fit from the occupancy model or the fit ignoring the possibility of detection error. Therefore trying to adjust occupancy models for non-detection can be as misleading as ignoring non-detection completely. Ignoring non-detection can actually be better than trying to adjust for it.

Cavity sizes and types in Australian eucalypts from wet and dry forest types–a simple of rule of thumb for estimating size and number of cavities

Abstract We describe the relationships between the number, size and type of cavities in six species of eucalypt trees from southern New South Wales (south-eastern Australia) and tree diameter, tree height, tree species and other measures. The eucalypt species studied were:-Narrow-leaved Peppermint ( Eucalyptus radiata ), Mountain Swamp Gum ( Eucalyptus camphora ), Mountain Gum ( Eucalyptus dalrympleana ), Red Stringybark ( Eucalyptus macrorhyncha ), Ribbon Gum ( Eucalyptus viminalis ), and, Broad-leaved Peppermint ( Eucalyptus dives ). E. radiata and E. macrorhyncha supported almost twice the proportion of branch-end hollows than cavities assigned to other categories. Cavities in the main trunk were the predominant hollow class in E. viminalis and E. dalrympleana . Large diameter trees were characterised by more branch-end hollows, whereas main trunk cavities were typically the most prevalent cavity type in smaller diameter stems. We identified a simple, general rule that highlights the relationships between cavities and readily measured tree attributes. Our data show that, in general, both the number of cavities and cavity size were directly proportional to tree diameter, but inversely proportional to the square root of tree height. This proportionality changed between different tree species. E. dives and E. viminalis supported, on average, larger cavities than other species, whereas the cavities in E. macrorhyncha were smaller than the other taxa sampled. This simple general relationship may make it possible to make rapid crude estimates of cavity abundance across large areas of forest by measuring simple tree attributes such as tree diameter and tree height.

The conservation of arboreal marsupials in the montane ash forests of the Central Highlands of Victoria, south-east Australia. IV. The presence and abundance of arboreal marsupials in retained linear habitats (wildlife corridors) within logged forest

Arboreal marsupials were censused in 49 retained linear habitats (wildlife corridors) that were excluded from timber harvesting in mountain ash Eucalyptus regnans F. Muell. and alpine ash E. delegatensis R. T. Bak. forests in the Central Highlands of Victoria, south-eastern Australia. The study sites varied in mean width from 30 to 264 m and were bounded by clearfelled and regenerated forests that were aged four years or younger. Of the 402 large trees with hollows that were measured and censused on the 49 study sites, a total of 69 animals was observed from 54 occupied trees, giving one occupied tree per 7·4 trees that were watched. The species of arboreal marsupials recorded during the study included greater glider Petauroides volans Kerr, mountain brushtail possum Trichosurus caninus Ogilby, feather-tail glider Acrobates pygmaeus Shaw, common ringtail possum Pseudocheirus peregrinus Boddaert, yellow-bellied glider Petaurus australis Shaw, sugar glider Petaurus breviceps Waterhouse and Leadbeaters possum Gymnobelideus leadbeateri McCoy. P. volans and T. caninus were the most commonly observed species and accounted for 78% of the animals seen. These species may survive better, at least in the short term, than others in linear strips that are retained after timber harvesting. Colonial and social species of arboreal marsupials that consume widely dispersed food such as saps and gums were uncommon, as predicted by the theory of central place foraging. The presence and abundance of arboreal marsupials in retained linear strips were compared with predictions from models of the habitat requirements of these species developed from sites in contiguous forest. These comparisons revealed that the presence of P. volans, P. breviceps and P. australis in retained linear strips was not significantly different from predictions derived from measures of the suitability of habitat in such areas. T. caninus was recorded at fewer sites than predicted, although the abundance of the species when present was not different from expected values. The endangered G. leadbeateri was recorded only once during the study, despite many sites providing apparently suitable habitat. Retained linear strips supported a significantly lower total abundance of arboreal marsupials than predicted from measures of habitat suitability. A combination of habitat parameters and other measured attributes of retained linear strips such as width and length were used to explain the variation in the presence and abundance of arboreal marsupials. The presence of T. caninus was influenced significantly by the number of trees with hollows and by the length of the site. P. volans was most likely to occur on sites with many trees with hollows, a westerly aspect and where there was no watercourse. Sites with the highest probability of supporting any species of arboreal marsupial occurred in E. regnans forests with numerous trees with hollows and which spanned the topographic sequence (e.g connected a ridge to a gully). The implications of our findings for the use, design and location of strips of retained linear habitat in timber production forests are discussed.

A prospective longitudinal study of landscape matrix effects on fauna in woodland remnants: experimental design and baseline data

The design of a longitudinal landscape-scale “natural experiment” of Australian woodland vertebrates is described. The experiment will allow the direct study of changes in fauna inhabiting woodland fragments as the surrounding grazed landscape is transformed into a radiata pine (Pinus radiata) plantation. It will also provide data to enable the study of relationships between fauna and habitat and landscape variables, both over time and among sites. Data for terrestrial mammals, arboreal marsupials, and reptiles occurring in woodland remnants surrounded by newly planted radiata pine seedlings and pasture are presented. These data provide a reference set against which future changes in vertebrate fauna can be assessed and hence will be baseline data for the longitudinal study. Statistical analyses for several species showed that arboreal marsupials are more likely to be found in larger remnants that contain more trees with cavities and the four-fingered skink (Carlia tetradactyla) is more likely to be found either where there are more exposed rocks or more dead trees. We predict that these responses will change as the surrounding landscape matrix is transformed, particularly for arboreal marsupials such as the common ringtail possum (Pseudocheirus peregrinus), a species for which stands of radiata pine will provide suitable or partially suitable habitat.