Inferential, non-parametric statistics to assess quality of probabilistic forecast systems

Many statistical forecast systems are available to interested users. In order to be useful for decision-making, these systems must be based on evidence of underlying mechanisms. Once causal connections between the mechanism and their statistical manifestation have been firmly established, the forecasts must also provide some quantitative evidence of `quality’. However, the quality of statistical climate forecast systems (forecast quality) is an ill-defined and frequently misunderstood property. Often, providers and users of such forecast systems are unclear about what ‘quality’ entails and how to measure it, leading to confusion and misinformation. Here we present a generic framework to quantify aspects of forecast quality using an inferential approach to calculate nominal significance levels (p-values) that can be obtained either by directly applying non-parametric statistical tests such as Kruskal-Wallis (KW) or Kolmogorov-Smirnov (KS) or by using Monte-Carlo methods (in the case of forecast skill scores). Once converted to p-values, these forecast quality measures provide a means to objectively evaluate and compare temporal and spatial patterns of forecast quality across datasets and forecast systems. Our analysis demonstrates the importance of providing p-values rather than adopting some arbitrarily chosen significance levels such as p < 0.05 or p < 0.01, which is still common practice. This is illustrated by applying non-parametric tests (such as KW and KS) and skill scoring methods (LEPS and RPSS) to the 5-phase Southern Oscillation Index classification system using historical rainfall data from Australia, The Republic of South Africa and India. The selection of quality measures is solely based on their common use and does not constitute endorsement. We found that non-parametric statistical tests can be adequate proxies for skill measures such as LEPS or RPSS. The framework can be implemented anywhere, regardless of dataset, forecast system or quality measure. Eventually such inferential evidence should be complimented by descriptive statistical methods in order to fully assist in operational risk management.

Reassessing spatial and temporal dynamics of kangaroo populations

Long-running datasets from aerial surveys of kangaroos (Macropus giganteus, Macropus [uliginosus, Macropus robustus and Macropus rufus) across Queensland, New South Wales and South Australia have been analysed, seeking better predictors of rates of increase which would allow aerial surveys to be undertaken less frequently than annually. Early models of changes in kangaroo numbers in response to rainfall had shown great promise, but much variability. We used normalised difference vegetation index (NDVI) instead, reasoning that changes in pasture condition would provide a better predictor than rainfall. However, except at a fine scale, NDVI proved no better; although two linked periods of rainfall proved useful predictors of rates of increase, this was only in some areas for some species. The good correlations reported in earlier studies were a consequence of data dominated by large droughtinduced adult mortality, whereas over a longer time frame and where changes between years are less dramatic, juvenile survival has the strongest influence on dynamics. Further, harvesting, density dependence and competition with domestic stock are additional and important influences and it is now clear that kangaroo movement has a greater influence on population dynamics than had been assumed. Accordingly, previous conclusions about kangaroo populations as simple systems driven by rainfall need to be reassessed. Examination of this large dataset has permitted descriptions of shifts in distribution of three species across eastern Australia, changes in dispersion in response to rainfall, and an evaluation of using harvest statistics as an index of density and harvest rate. These results have been combined into a risk assessment and decision theory framework to identify optimal monitoring strategies.

Temporal and Spatial Patterns in Recruitment of Three Penaeid Prawns in Moreton Bay, Queensland, Australia

The size at recruitment, temporal and spatial distribution, and abiotic factors influencing abundance of three commercially important species of penaeid prawns in the sublittoral trawl grounds of Moreton Bay (Queensland, Australia) were compared. Metapenaeus bennettae and Penaeus plebejus recruit to the trawl grounds at sizes which are relatively small (14-15 mm carapace length, CL) and below that at which prawns are selected for, and retained, in the fleet's cod-ends. In contrast, Penaeus esculenlus recruit at the relatively large size of 27 mm CL from February to May, well above the size ranges selected for. Recruitment of M. bennettae extends over several months, September-October and February March, and was thus likely to be bi-annual, while the recruitment period of P. plebejus was distinct, peaking in October-November each year. Size classes of M . bennettae were the most spatially stratified of the three species. Catch rates of recruits were negatively correlated with depth for all three species, and were also negatively correlated with salinity for M. bennettae.

Spatial patterns in the biology of the chokka squid, Loligo reynaudii on the Agulhas Bank, South Africa

Although migration patterns for various life history stages of the chokka squid (Loligo reynaudii) have been previously presented, there has been limited comparison of spatial variation in biological parameters. Based on data from research surveys; size ranges of juveniles, subadults and adults on the Agulhas Bank were estimated and presented spatially. The bulk of the results appear to largely support the current acceptance of the life cycle with an annual pattern of squid hatching in the east, migrating westwards to offshore feeding grounds on the Central and Western Agulhas Bank and the west coast and subsequent return migration to the eastern inshore areas to spawn. The number of adult animals in deeper water, particularly in autumn in the central study area probably represents squid spawning in deeper waters and over a greater area than is currently targeted by the fishery. The distribution of life history stages and different feeding areas does not rule out the possibility that discrete populations of L. reynaudii with different biological characteristics inhabit the western and eastern regions of the Agulhas Bank. In this hypothesis, some mixing of the populations does occur but generally squid from the western Agulhas Bank may occur in smaller numbers, grow more slowly and mature at a larger size. Spawning occurs on the western portion of the Agulhas Bank, and juveniles grow and mature on the west coast and the central Agulhas Bank. Future research requirements include the elucidation of the age structure of chokka squid both spatially and temporally, and a comparison of the statolith chemistry and genetic characterisation between adults from different spawning areas across the Agulhas Bank.

Spatial requirements of animals: Allometry and beyond

Space allowance is a major factor influencing animal welfare. For livestock, at least, it plays a critical role in profitability, yet there is little information on the amount of space that animals require. The amount of space an animal occupies as a consequence of its shape and size can be estimated using allometry; linear dimensions (L) can be expressed as L = kW1/3 and surface area (S) as S = kW2/3, where k = a constant and W = the weight of the animal. Such equations have been used to determine the amount of space needed by standing (area [m2] = 0.019W0.66) and lying (area [m2] = 0.027W0.67) animals. Limited studies on the lying down and standing up behaviors of pigs and cattle suggest that the amount of space required can be estimated by area (m2) = 0.047W0.66. Linear space required per animal for behaviors such as feeding or drinking from a trough can be estimated from 0.064W0.33, but in groups this requirement will be affected by social interactions among group members and the amount of competition for the resource. Determining the amount of space for groups of animals is complex, as the amount of useable space can vary with group size and by how group members share space in time. Some studies have been conducted on the way in which groups of domestic fowl use space, but overall, we know very little about the ways in which livestock time-share space, synchronicity in the performance of behaviors, and the effects of spatial restrictions on behavior and welfare.

Spatial patterns of sub-tidal seagrasses and their tissue nutrients in the Torres Strait, northern Australia: Implications for management

The distribution and nutritional profiles of sub-tidal seagrasses from the Torres Strait were surveyed and mapped across an area of 31,000 km2. Benthic sediment composition, water depth, seagrass species type and nutrients were sampled at 168 points selected in a stratified representative pattern. Eleven species of seagrass were present at 56 (33.3%) of the sample points. Halophila spinulosa, Halophila ovalis, Cymodocea serrulata and Syringodium isoetifolium were the most common species and these were nutrient profiled. Sub-tidal seagrass distribution (and associated seagrass nutrient concentrations) was generally confined to northern-central and south-western regions of the survey area (spatial and nutritional information can be used by local agencies to manage and to protect the ecological, economic and cultural values of the sub-tidal seagrass ecosystems and associated fisheries of the Torres Strait.

Spatial model of site index based on Y-ray spectrometry and a digital elevation model for two Pinus species in Tuan Toolara State Forest, Queensland, Australia

Site index prediction models are an important aid for forest management and planning activities. This paper introduces a multiple regression model for spatially mapping and comparing site indices for two Pinus species (Pinus elliottii Engelm. and Queensland hybrid, a P. elliottii x Pinus caribaea Morelet hybrid) based on independent variables derived from two major sources: g-ray spectrometry (potassium (K), thorium (Th), and uranium (U)) and a digital elevation model (elevation, slope, curvature, hillshade, flow accumulation, and distance to streams). In addition, interpolated rainfall was tested. Species were coded as a dichotomous dummy variable; interaction effects between species and the g-ray spectrometric and geomorphologic variables were considered. The model explained up to 60% of the variance of site index and the standard error of estimate was 1.9 m. Uranium, elevation, distance to streams, thorium, and flow accumulation significantly correlate to the spatial variation of the site index of both species, and hillshade, curvature, elevation and slope accounted for the extra variability of one species over the other. The predicted site indices varied between 20.0 and 27.3 m for P. elliottii, and between 23.1 and 33.1 m for Queensland hybrid; the advantage of Queensland hybrid over P. elliottii ranged from 1.8 to 6.8 m, with the mean at 4.0 m. This compartment-based prediction and comparison study provides not only an overview of forest productivity of the whole plantation area studied but also a management tool at compartment scale.

Spatial and temporal variation and effects of changes in management in discard rates from the commercial reef line fishery of the Great Barrier Reef, Australia

Discarding in commercially exploited fisheries has received considerable attention in the last decade, though only more recently in Australia. The Reef Line fishery (RLF) of the Great Barrier Reef (GBR) in Australia is a large-scale multi-sector, multi-species, highly regulated hook and line fishery with the potential for high levels of discarding. We used a range of data sources to estimate discard rates and discard quantities for the two main target groups of the RLF, the coral trout, Plectropomus spp, and the red throat emperor, Lethrinus miniatus, and investigated possible effects on discarding of recent changes in management of the fishery. Fleet-wide estimates of total annual quantities discarded from 1989 to 2003 were 292-622 t and 33-95 t for coral trout and red throat emperor, respectively. Hypothetical scenarios of high-grading after the introduction of a total allowable commercial catch for coral trout resulted in increases in discard quantities up to 3895 t, while no high-grading still meant 421 t were discarded. Increasing the minimum size limit of red throat emperor from 35 to 38 cm also increased discards to an estimated 103 t. We provide spatially and temporally explicit estimates of discarding for the two most important species in the GBR RLF of Australia to demonstrate the importance of accounting for regional variation in quantification of discarding. Effects of management changes on discarding are also highlighted. This study provides a template for exploring discarding levels for other species in the RLF and elsewhere.

A comparison of plotless density estimators using Monte Carlo simulation on totally enumerated field data sets

Background: Plotless density estimators are those that are based on distance measures rather than counts per unit area (quadrats or plots) to estimate the density of some usually stationary event, e.g. burrow openings, damage to plant stems, etc. These estimators typically use distance measures between events and from random points to events to derive an estimate of density. The error and bias of these estimators for the various spatial patterns found in nature have been examined using simulated populations only. In this study we investigated eight plotless density estimators to determine which were robust across a wide range of data sets from fully mapped field sites. They covered a wide range of situations including animal damage to rice and corn, nest locations, active rodent burrows and distribution of plants. Monte Carlo simulations were applied to sample the data sets, and in all cases the error of the estimate (measured as relative root mean square error) was reduced with increasing sample size. The method of calculation and ease of use in the field were also used to judge the usefulness of the estimator. Estimators were evaluated in their original published forms, although the variable area transect (VAT) and ordered distance methods have been the subjects of optimization studies. Results: An estimator that was a compound of three basic distance estimators was found to be robust across all spatial patterns for sample sizes of 25 or greater. The same field methodology can be used either with the basic distance formula or the formula used with the Kendall-Moran estimator in which case a reduction in error may be gained for sample sizes less than 25, however, there is no improvement for larger sample sizes. The variable area transect (VAT) method performed moderately well, is easy to use in the field, and its calculations easy to undertake. Conclusion: Plotless density estimators can provide an estimate of density in situations where it would not be practical to layout a plot or quadrat and can in many cases reduce the workload in the field.

A spatial assessment of the risk to a mobile marine mammal from bycatch

Several species of marine mammals are at risk of extinction from being captured as bycatch in commercial fisheries. Various approaches have been developed and implemented to address this bycatch problem, including devices and gear changes, time and area closures and fisheries moratoria. Most of these solutions are difficult to implement effectively, especially for artisanal fisheries in developing countries and remote regions. Re-zoning of the Great Barrier Reef World Heritage Area (GBRWHA) in 2004 closed 33% of the region to extractive activities, including commercial fishing. However, the impact of re-zoning and the associated industry restructuring on a threatened marine mammal, the dugong (Dugong dugon), is difficult to quantify. Accurate information on dugong bycatch in commercial nets is unavailable because of the large geographic extent of the GBRWHA, the remoteness of the region adjacent to the Cape York Peninsula where most dugongs occur and the artisanal nature of the fishery. In the face of this uncertainty, a spatial risk-assessment approach was used to evaluate the re-zoning and associated industry restructuring for their ability to reduce the risk of dugong bycatch from commercial fisheries netting. The new zoning arrangements appreciably reduced the risk of dugong bycatch by reducing the total area where commercial netting is permitted. Netting is currently not permitted in 67% of dugong habitats of high conservation value, a 56% improvement over the former arrangements. Re-zoning and industry restructuring also contributed to a 22% decline in the spatial extent of conducted netting. Spatial risk assessment approaches that evaluate the risk of mobile marine mammals from bycatch are applicable to other situations where there is limited information on the location and intensity of bycatch, including remote regions and developing countries where resources are limited.

Odour emissions from anaerobic piggery ponds. 2: Improving estimates of emission rate through recognition of spatial variability

Odour emission rates were measured for seven different anaerobic ponds treating piggery wastes at six to nine discrete locations across the surface of each pond on each sampling occasion over a thirteen month period. Significant variability in emission rates were observed for each pond. Measurement of a number of water quality variables in pond liquor samples collected at the same time and from the same locations as the odour samples indicated that the composition of the pond liquor was also variable. The results indicated that spatial variability was a real phenomenon and could have a significant impact on odour assessment practices. Considerably more odour samples would be required to characterise pond emissions than currently recommended by most practitioners, or regulatory agencies.

From inferential statistics to climate knowledge

Climate variability and change are risk factors for climate sensitive activities such as agriculture. Managing these risks requires "climate knowledge", i.e. a sound understanding of causes and consequences of climate variability and knowledge of potential management options that are suitable in light of the climatic risks posed. Often such information about prognostic variables (e.g. yield, rainfall, run-off) is provided in probabilistic terms (e.g. via cumulative distribution functions, CDF), whereby the quantitative assessments of these alternative management options is based on such CDFs. Sound statistical approaches are needed in order to assess whether difference between such CDFs are intrinsic features of systems dynamics or chance events (i.e. quantifying evidences against an appropriate null hypothesis). Statistical procedures that rely on such a hypothesis testing framework are referred to as "inferential statistics" in contrast to descriptive statistics (e.g. mean, median, variance of population samples, skill scores). Here we report on the extension of some of the existing inferential techniques that provides more relevant and adequate information for decision making under uncertainty.

Spatial and temporal patterns of feral pig diggings in rainforests of north Queensland

Feral pigs (Sus scrofa) are believed to have a severe negative impact on the ecological values of tropical rainforests in north Queensland, Australia. Most perceptions of the environmental impacts of feral pigs focus on their disturbance of the soil or surface material (diggings). Spatial and temporal patterns of feral pig diggings were identified in this study: most diggings occurred in the early dry season and predominantly in moist soil (swamp and creek) microhabitats, with only minimal pig diggings found elsewhere through the general forest floor. The overall mean daily pig diggings were 0.09% of the rainforest floor. Most diggings occurred 3-4 months after the month of maximum rainfall. Most pig diggings were recorded in highland swamps, with over 80% of the swamp areas dug by pigs at some time during the 18-month study period. These results suggest that management of feral pig impacts should focus on protecting swamp and creek microhabitats in the rainforest, which are preferred by pigs for digging and which have a high environmental significance.

Buffel grass in Queensland's semi-arid woodlands: response to local and landscape scale variables, and relationship with grass, forb and reptile species.

Buffel grass [Pennisetum ciliare (L.) Link] has been widely introduced in the Australian rangelands as a consequence of its value for productive grazing, but tends to competitively establish in non-target areas such as remnant vegetation. In this study, we examined the influence landscape-scale and local-scale variables had upon the distribution of buffel grass in remnant poplar box (Eucalyptus populnea F. Muell.) dominant woodland fragments in the Brigalow Bioregion, Queensland. Buffel grass and variables thought to influence its distribution in the region were measured at 60 sites, which were selected based on the amount of native woodland retained in the landscape and patch size. An information-theoretic modelling approach and hierarchical partitioning revealed that the most influential variable was the percent of retained vegetation within a 1-km spatial extent. From this, we identified a critical threshold of similar to 30% retained vegetation in the landscape, above which the model predicted buffel grass was not likely to occur in a woodland fragment. Other explanatory variables in the model were site based, and included litter cover and long-term rainfall. Given the paucity of information on the effect of buffel grass upon biodiversity values, we undertook exploratory analyses to determine whether buffel grass cover influenced the distribution of grass, forb and reptile species. We detected some trends; hierarchical partitioning revealed that buffel grass cover was the most important explanatory variable describing habitat preferences of four reptile species. However, establishing causal links - particularly between native grass and forb species and buffel grass - was problematic owing to possible confounding with grazing pressure. We conclude with a set of management recommendations aimed at reducing the spread of buffel grass into remnant woodlands.

Using harvest statistics to monitor temporal variation in kangaroo density and harvest rate

Management of the commercial harvest of kangaroos relies on quotas set annually as a proportion of regular estimates of population size. Surveys to generate these estimates are expensive and, in the larger states, logistically difficult; a cheaper alternative is desirable. Rainfall is a disappointingly poor predictor of kangaroo rate of increase in many areas, but harvest statistics (sex ratio, carcass weight, skin size and animals shot per unit time) potentially offer cost-effective indirect monitoring of population abundance (and therefore trend) and status (i.e. under-or overharvest). Furthermore, because harvest data are collected continuously and throughout the harvested areas, they offer the promise of more intensive and more representative coverage of harvest areas than aerial surveys do. To be useful, harvest statistics would need to have a close and known relationship with either population size or harvest rate. We assessed this using longterm (11-22 years) data for three kangaroo species (Macropus rufus, M. giganteus and M. fuliginosus) and common wallaroos (M. robustus) across South Australia, New South Wales and Queensland. Regional variation in kangaroo body size, population composition, shooter efficiency and selectivity required separate analyses in different regions. Two approaches were taken. First, monthly harvest statistics were modelled as a function of a number of explanatory variables, including kangaroo density, harvest rate and rainfall. Second, density and harvest rate were modelled as a function of harvest statistics. Both approaches incorporated a correlated error structure. Many but not all regions had relationships with sufficient precision to be useful for indirect monitoring. However, there was no single relationship that could be applied across an entire state or across species. Combined with rainfall-driven population models and applied at a regional level, these relationships could be used to reduce the frequency of aerial surveys without compromising decisions about harvest management.