SPATIAL PROPERTIES OF RETINAL MOSAICS - AN EMPIRICAL-EVALUATION OF SOME EXISTING MEASURES

Mosaics of neurons are usually quantified by methods based on nearest- neighbor distance (NND). The commonest indicator of regularity has bee n the ratio of the mean NND to the standard deviation, here termed the 'conformity ratio.' However, an accurate baseline value of this ratio for bounded random samples has never been determined; nor was its sam pling distribution known, making it impossible to test its significanc e. Instead, significance was assessed from goodness-of-fit to a Raylei gh distribution, or from another ratio, that of the observed mean NND to an expected mean predicted by theory, termed the dispersion index. Neither approach allows for boundary effects that are common in experi mental mosaics. Equally common are 'missing' neurons, whose effects on the statistics have not been studied. To address these deficiencies, random patterns and real neuronal mosaics were analyzed statistically. N-s independent random-point samples of size N-p were generated for 1 3 N-p values between 25 and 6400, where N-s x N-p greater than or equa l to 144,000. Samples were generated with rectangular boundaries of as pect ratio 1:1, 1:5, and 1:10 to examine the influence of sample geome try. NND distributions, conformity ratios, and dispersion indices were computed for the resulting 45,997 independent random patterns. From t hese, empirical sampling distributions and critical values were determ ined. NND distributions for small-to-medium, bounded, random populatio ns were shown to differ significantly from Rayleigh distributions. Thu s, goodness-of-fit tests are invalid for most experimental mosaics. Ch arts are presented from which the significance of conformity ratios or dispersion indices can be read directly. The conformity ratio reacts conservatively to extremes of sample geometry, and provides a useful a nd safe test. The dispersion index is nonconservative, making its use problematic. Tests based on the theoretical distribution of the disper sion index are unreliable for all but the largest samples. Random dele tions were also made from 33 real retinal ganglion cell mosaics. The m ean NND, conformity ratio, and dispersion index were determined for ea ch original mosaic and 36 independent samples at each of nine sampling levels, retaining between 90% and 10% of the original population. An exclusion radius, based on a spatial autocorrelogram, was also calcula ted for each of these 10,725 mosaic samples. The mean NND was moderate ly insensitive to undersampling, rising smoothly. The exclusion radius was remarkably insensitive. The conformity ratio and dispersion index fell steeply, sometimes failing to reach significance while half of t he cells still remained. For the same 33 original mosaics, linear regr ession showed the exclusion radius to be 62 +/- 3% of the mean NND.