Regression analysis of spatial data

Many of the most interesting questions ecologists ask lead to analyses of spatial data. Yet, perhaps confused by the large number of statistical models and fitting methods available, many ecologists seem to believe this is best left to specialists. Here, we describe the issues that need consideration when analysing spatial data and illustrate these using simulation studies. Our comparative analysis involves using methods including generalized least squares, spatial filters, wavelet revised models, conditional autoregressive models and generalized additive mixed models to estimate regression coefficients from synthetic but realistic data sets, including some which violate standard regression assumptions. We assess the performance of each method using two measures and using statistical error rates for model selection. Methods that performed well included generalized least squares family of models and a Bayesian implementation of the conditional auto-regressive model. Ordinary least squares also performed adequately in the absence of model selection, but had poorly controlled Type I error rates and so did not show the improvements in performance under model selection when using the above methods. Removing large-scale spatial trends in the response led to poor performance. These are empirical results; hence extrapolation of these findings to other situations should be performed cautiously. Nevertheless, our simulation-based approach provides much stronger evidence for comparative analysis than assessments based on single or small numbers of data sets, and should be considered a necessary foundation for statements of this type in future.

Spatial turnover in the global avifauna

Despite its wide implications for many ecological issues, the global pattern of spatial turnover in the occurrence of species has been little studied, unlike the global pattern of species richness. Here, using a database on the breeding distributions of birds, we present the first global maps of variation in spatial turnover for an entire taxonomic class, a pattern that has to date remained largely a matter of conjecture, based on theoretical expectations and extrapolation of inconsistent patterns from different biogeographic realms. We use these maps to test four predictions from niche theory as to the form that this variation should take, namely that turnover should increase with species richness, towards lower latitudes, and with the steepness of environmental gradients and that variation in turnover is determined principally by rare (restricted) species. Contrary to prediction, we show that turnover is high both in areas of extremely low and high species richness, does not increase strongly towards the tropics, and is related both to average environmental conditions and spatial variation in those conditions. These results are closely associated with a further important and novel finding, namely that global patterns of spatial turnover are driven principally by widespread species rather than the restricted ones. This complements recent demonstrations that spatial patterns of species richness are also driven principally by widespread species, and thus provides an important contribution towards a unified model of how terrestrial biodiversity varies both within and between the Earth's major land masses.

Molecular documentation of polyembryony and the micro-spatial dispersion of clonal sibships in the nine-banded armadillo, Dasypus novemcinctus.

A battery of allelic markers at highly polymorphic microsatellite loci was developed and employed to confirm genetically the clonal nature of sibships in nine-banded armadillos. This phenomenon of consistent polyembryony, otherwise nearly unknown among the vertebrates, then was capitalized upon to describe the micro-spatial distributions of numerous clonal sibships in a natural population of armadillos. Adult clonemates were significantly more dispersed than were juvenile sibs, suggesting limited opportunities for altruistic behavioral interactions among mature individuals. These results, and considerations of armadillo natural history, suggest that evolutionary explanations for polyembryony in this species may not reside in the kinds of ecological and kin selection theories relevant to some of the polyembryonic invertebrates. Rather, polyembryony in armadillos may be associated evolutionarily with other reproductive peculiarities of the species, including delayed uterine implantation of a single egg.

What motion distributions yield global transparency and spatial segmentation?

We have examined the ability of observers to parse bimodal local-motion distributions into two global motion surfaces, either overlapping (yielding transparent motion) or spatially segregated (yielding a motion boundary). The stimuli were random dot kinematograms in which the direction of motion of each dot was drawn from one of two rectangular probability distributions. A wide range of direction distribution widths and separations was tested. The ability to discriminate the direction of motion of one of the two motion surfaces from the direction of a comparison stimulus was used as an objective test of the perception of two discrete surfaces. Performance for both transparent and spatially segregated motion was remarkably good, being only slightly inferior to that achieved with a single global motion surface. Performance was consistently better for segregated motion than for transparency. Whereas transparent motion was only perceived with direction distributions which were separated by a significant gap, segregated motion could be seen with abutting or even partially overlapping direction distributions. For transparency, the critical gap increased with the range of directions in the distribution. This result does not support models in which transparency depends on detection of a minimum size of gap defining a bimodal direction distribution. We suggest, instead, that the operations which detect bimodality are scaled (in the direction domain) with the overall range of distributions. This yields a flexible, adaptive system that determines whether a gap in the direction distribution serves as a segmentation cue or is smoothed as part of a unitary computation of global motion.

Neurobiological model of visuo-spatial cognition in young Williams Syndrome children: measures of dorsal-stream and frontal function

We examine hypotheses for the neural basis of the profile of visual cognition in young children with Williams syndrome (WS). These are: (a) that it is a consequence of anomalies in sensory visual processing; (b) that it is a deficit of the dorsal relative to the ventral cortical stream; (c) that it reflects deficit of frontal function, in particular of fronto-parietal interaction; (d) that it is related to impaired function in the right hemisphere relative to the left. The tests reported here are particularly relevant to (b) and (c). They form part of a more extensive programme of investigating visual, visuospatial, and cognitive function in large group of children with WS children, aged 8 months to 15 years. To compare performance across tests, avoiding floor and ceiling effects, we have measured performance in children with WS in terms of the ‘age equivalence’ for typically developing children. In this paper the relation between dorsal and ventral function was tested by motion and form coherence thresholds respectively. We confirm the presence of a subgroup of children with WS who perform particularly poorly on the motion (dorsal) task. However, such performance is also characteristic of normally developingchildren up to 5 years: thus the WS performance may reflect an overall persisting immaturity of visuospatial processing which is particularly evident in the dorsal stream. Looking at the performance on the global coherence tasks of the entire WS group, we find that there is also a subgroup who have both high form and motion coherence thresholds, relative to the performance of children of the same chronological age and verbal age on the BPVS, suggesting a more general global processing deficit. Frontal function was tested by a counterpointing task, ability to retrieve a ball from a ‘detour box’, and the Stroop-like ‘day-night’ task, all of which require inhibition of a familiar response. When considered in relation to overall development as indexed by vocabulary, the day-night task shows little specific impairment, the detour box shows a significant delay relative to controls, and the counterpointing task shows a marked and persistent deficit in many children. We conclude that frontal control processes show most impairment in WS when they are associated with spatially directed responses, reflecting a deficit of fronto-parietal processing. However, children with WS may successfully reduce the effect of this impairment by verbally mediated strategies. On all these tasks we find a range of difficulties across individual children and a small subset of WS who show very good performance, equivalent to chronological age norms of typically developing children. Neurobiological models of visuo-spatial cognition in children with WS p.4 Overall, we conclude that children with WS have specific processing difficulties with tasks involving frontoparietal circuits within the spatial domain. However, some children with WS can achieve similar performance to typically developing children on some tasks involving the dorsal stream, although the strategies and processing may be different in the two groups.

Selective migration from deprived areas in Northern Ireland and the spatial distribution of inequalities: implications for monitoring health and inequalities in health

Much of the evidence suggesting that inequalities in health have been increasing over the last two decades has come from studies that compared the changes in relative health status of areas over time. Such studies ignore the movement of people between areas. This paper examines the population movement between small areas in Northern Ireland in the year prior to the 1991 census as well as the geographical distribution of migrants to Northern Ireland over the same period. It shows that deprived areas tended to become depopulated and that those who left these areas were the more affluent residents. While immigrants differed a little from the indigenous population, the overall effect of their distribution would be to maintain the geographical socio-economic status quo. The selective movement of people between areas would result in the distribution of health and ill-health becoming more polarized, i.e. produce a picture of widening inequalities between areas even though the distribution between individuals is unchanged. These processes suggest potential significant problems with the area-based approaches to monitoring health and inequalities in health.

Effect of chronic angiotensin converting enzyme inhibition on spatial memory and anxiety-like behavours in rats

Angiotensin converting enzyme inhibitors (ACEis) are widely used anti-hypertensive agents that are also reported to have positive effects on mood and cognition. The present study examined the influence of the ACEi, perindopril, on cognitive performance and anxiety measures in rats. Two groups of rats were treated orally for one week with the ACEi, perindopril, at doses of 0.1 and 1.0mg/kg/day. Learning was assessed by the reference memory task in the water maze, comparing treated to control rats. Over five training days both perindopril-treated groups learnt the location of the submerged platform in the water maze task significantly faster than control rats. A 60s probe trial on day 6 showed that the 1.0mg/kg/day group spent significantly longer time in the training quadrant than control rats. This improved performance in the swim maze task was not due to the effect of perindopril on motor activity or the anxiety levels of the rats as perindopril-treated and control animals behaved similarly in activity boxes and on the elevated+maze. These results confirm the anecdotal human studies that ACEis have a positive influence on cognition and provide possibilities for ACEis to be developed into therapies for memory loss.

Spatial Demultiplexing in the sub-millimeter wave band using multlayer free-standing frequency selective surfaces

In this paper, we show that a multilayer freestanding slot array can be designed to give an insertion loss which is significantly lower than the value obtainable from a conventional dielectric backed printed frequency selective surface (FSS). This increase in filter efficiency is highlighted by comparing the performance of two structures designed to provide frequency selective beamsplitting in the quasioptical feed train of a submillimeter wave space borne radiometer. A two layer substrateless FSS providing more than 20 dB of isolation between the bands 316.5â??325.5 GHz and 349.5â??358.5 GHz, gives an insertion loss of 0.6 dB when the filter is orientated at 45 incidence in the TM plane, whereas the loss exhibited by a conventional printed FSS is in excess of 2 dB. A similar frequency response can be obtained in the TE plane, but here a triple screen structure is required and the conductor loss is shown to be comparable to the absorption loss of a dielectric backed FSS. Experimental devices have been fabricated using a precision micromachining technique. Transmission measurements performed in the range 250â??360 GHz are in good agreement with the simulated spectral performance of the individual periodic screens and the two multilayer freestanding FSS structures.