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Infestation and spatial dependence of weed seedling and mature weed populations in corn
- Dawn Y. Wyse-Pester, Lori J. Wiles, Philip Westra
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- Journal:
- Weed Science / Volume 50 / Issue 1 / February 2002
- Published online by Cambridge University Press:
- 20 January 2017, pp. 54-63
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Knowing the distribution of weed seedlings in farmer-managed fields could help researchers develop reliable distribution maps for site-specific weed management. With a knowledge of the spatial arrangement of a weed population, cost effective sampling programs and management strategies can be designed, so inputs can be selected and applied to specific field areas where management is warranted. In 1997 and 1998, weeds were sampled at 612 to 682 sites in two center pivot irrigated corn fields (71 and 53 ha) in eastern Colorado. Weeds were enumerated when corn reached the two-leaf, four-leaf, and physiological maturity stages in a 76.2- by 76.2-m grid, a random-directed grid where sites were established at intervals of 76.2 m, and a star configuration based on a 7.62- by 7.62-m grid within three 23,225 m2 areas. Directional correlograms were calculated for 0, 30, 60, 90, 120, and 150° from the crop row. Fifteen weed species were observed across fields. Spatial dependence occurred in 7 of the 93 samples (a collection of sampling units for a particular weed species that was detected within a field at a particular sampling time and year) for populations of field sandbur, pigweed species, nightshade species, and common lambsquarters. Correlogram analysis indicated that 18 to 72% of the variation in sample density was a result of spatial dependence over a geographic distance not exceeding 5 to 363 m among the examined data. Because of the lack of spatial correlation for weed seedling distributions in these eastern Colorado corn fields, interpolated density maps should be based on grid sizes (separation distances) less than 7.62 m for weed seedling infestations.
Spatial properties of retinal mosaics: An empirical evaluation of some existing measures
- J. E. Cook
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- Journal:
- Visual Neuroscience / Volume 13 / Issue 1 / January 1996
- Published online by Cambridge University Press:
- 02 June 2009, pp. 15-30
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Mosaics of neurons are usually quantified by methods based on nearest-neighbor distance (NND). The commonest indicator of regularity has been 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 sampling distribution known, making it impossible to test its significance. Instead, significance was assessed from goodness-of-fit to a Rayleigh 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 experimental 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. Ns independent random-point samples of size Np were generated for 13 Np values between 25 and 6400, where Ns × Np ≥ 144,000. Samples were generated with rectangular boundaries of aspect ratio 1:1, 1:5, and 1:10 to examine the influence of sample geometry. NND distributions, conformity ratios, and dispersion indices were computed for the resulting 45,997 independent random patterns. From these, empirical sampling distributions and critical values were determined. NND distributions for small-to-medium, bounded, random populations were shown to differ significantly from Rayleigh distributions. Thus, goodness-of-fit tests are invalid for most experimental mosaics. Charts 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 and safe test. The dispersion index is nonconservative, making its use problematic. Tests based on the theoretical distribution of the dispersion index are unreliable for all but the largest samples. Random deletions were also made from 33 real retinal ganglion cell mosaics. The mean NND, conformity ratio, and dispersion index were determined for each 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 calculated for each of these 10,725 mosaic samples. The mean NND was moderately 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 the cells still remained. For the same 33 original mosaics, linear regression showed the exclusion radius to be 62 ± 3% of the mean NND.
Modeling cat retinal beta-cell arrays
- XUE J. ZHAN, JOHN B. TROY
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- Journal:
- Visual Neuroscience / Volume 17 / Issue 1 / January 2000
- Published online by Cambridge University Press:
- 01 January 2000, pp. 23-39
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There were three objectives to the work undertaken for this paper: (1) to provide a comprehensive characterization of the statistical properties of arrays of β-cell somata; (2) to develop a model that simulates cellular arrays with the same properties; and (3) to use this model to examine whether the array of β-cells should be viewed as one array or as two arrays, one each for its OFF- and ON-center cells. β-cells are morphological correlates of the electrophysiological X-cells and those β-cells whose dendrites stratify within the outer and inner sublamina of the retina's inner plexiform layer correspond, respectively, to OFF- and ON-center X-cells. Arrays of peripheral β-cell somata from two retinas were studied. A Delaunay triangulation and a Voronoi tessellation were generated for each array and measures derived from these constructs used to analyze the arrays' spatial organization. As others have shown previously with a less complete statistical characterization, we found that the arrays of OFF- and ON-center β-cells have similar spatial properties and are more regular than the array of all β-cells. We developed a model to simulate cellular arrays with spatial properties like those of arrays of β-cells. A good fit between model and real arrays was found when the model assumed an explicit spatial dependence between the placement of OFF- and ON-center cells. We propose therefore that a single array of β-cells formed of both OFF- and ON-center cells is consistent with the data currently available for β-cell somatic arrays.
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