title: A comparison of spatial analysis methods for the construction of topographic maps of retinal cell density.
abstract: Topographic maps that illustrate variations in the density of different neuronal sub-types across the retina are valuable tools for understanding the adaptive significance of retinal specialisations in different species of vertebrates. To date, such maps have been created from raw count data that have been subjected to only limited analysis (linear interpolation) and, in many cases, have been presented as iso-density contour maps with contour lines that have been smoothed 'by eye'. With the use of stereological approach to count neuronal distribution, a more rigorous approach to analysing the count data is warranted and potentially provides a more accurate representation of the neuron distribution pattern. Moreover, a formal spatial analysis of retinal topography permits a more robust comparison of topographic maps within and between species. In this paper, we present a new R-script for analysing the topography of retinal neurons and compare methods of interpolating and smoothing count data for the construction of topographic maps. We compare four methods for spatial analysis of cell count data: Akima interpolation, thin plate spline interpolation, thin plate spline smoothing and Gaussian kernel smoothing. The use of interpolation 'respects' the observed data and simply calculates the intermediate values required to create iso-density contour maps. Interpolation preserves more of the data but, consequently includes outliers, sampling errors and/or other experimental artefacts. In contrast, smoothing the data reduces the 'noise' caused by artefacts and permits a clearer representation of the dominant, 'real' distribution. This is particularly useful where cell density gradients are shallow and small variations in local density may dramatically influence the perceived spatial pattern of neuronal topography. The thin plate spline and the Gaussian kernel methods both produce similar retinal topography maps but the smoothing parameters used may affect the outcome.
authors.affiliation: School of Animal Biology and The UWA Oceans Institute, The University of Western Australia, Crawley, Western Australia, Australia.
authors.forename: Eduardo
authors.initials: E
authors.lastname: Garza-Gisholt
authors.affiliation: School of Animal Biology and The UWA Oceans Institute, The University of Western Australia, Crawley, Western Australia, Australia.
authors.forename: Jan M
authors.initials: JM
authors.lastname: Hemmi
authors.affiliation: School of Animal Biology and The UWA Oceans Institute, The University of Western Australia, Crawley, Western Australia, Australia.
authors.forename: Nathan S
authors.initials: NS
authors.lastname: Hart
authors.affiliation: School of Animal Biology and The UWA Oceans Institute, The University of Western Australia, Crawley, Western Australia, Australia.
authors.forename: Shaun P
authors.initials: SP
authors.lastname: Collin
mesh_terms: D000465:Algorithms; D000818:Animals; D002452:Cell Count / Q000379:methods*; D005399:Fishes; D005584:Fovea Centralis / Q000166:cytology; D008962:Models, Theoretical; D012160:Retina / Q000166:cytology*; D012165:Retinal Ganglion Cells / Q000166:cytology; D062206:Spatial Analysis
references.citation: Brain Behav Evol. 2010;75(2):111-21
references.pmid: 20516656
references.citation: Vis Neurosci. 1999 Mar-Apr;16(2):291-302
references.pmid: 10367964
references.citation: J Physiol. 1975 Jan;244(1):61P-63P
references.pmid: 1123779
references.citation: Brain Behav Evol. 1995;45(5):257-65
references.pmid: 7620874
references.citation: Brain Behav Evol. 1988;31(5):283-95
references.pmid: 3395837
references.citation: Braz J Med Biol Res. 1991;24(2):199-214
references.pmid: 1726652
references.citation: Brain Behav Evol. 2001;58(1):15-27
references.pmid: 11799275
references.citation: J Theor Biol. 2000 Aug 7;205(3):443-55
references.pmid: 10882563
references.citation: Brain Behav Evol. 1988;31(5):269-82
references.pmid: 3395836
references.citation: Brain Behav Evol. 1991;37(4):189-203
references.pmid: 1878774
references.citation: Vision Res. 1973 Jun;13(6):1101-14
references.pmid: 4713921
references.citation: Brain Behav Evol. 2006;68(1):15-25
references.pmid: 16567928
references.citation: Vis Neurosci. 1995 Nov-Dec;12(6):1151-75
references.pmid: 8962834
references.citation: J Exp Biol. 2002 Dec;205(Pt 24):3925-35
references.pmid: 12432014
references.citation: Vis Neurosci. 2006 May-Aug;23(3-4):429-35
references.pmid: 16961976
references.citation: J Comp Neurol. 2006 Jan 20;494(3):381-97
references.pmid: 16320259
references.citation: J Comp Neurol. 2009 May 1;514(1):66-73
references.pmid: 19260061
references.citation: Brain Behav Evol. 2012;80(4):254-68
references.pmid: 23038153
references.citation: Brain Behav Evol. 1992;39(2):69-76
references.pmid: 1555111
references.citation: Vis Neurosci. 1989;2(3):221-35
references.pmid: 2562148
references.citation: J Comp Neurol. 1983 May 10;216(2):211-31
references.pmid: 6863603
references.citation: J Comp Neurol. 2013 Jun 15;521(9):2042-57
references.pmid: 23595815
references.citation: Vis Neurosci. 2009 Mar-Apr;26(2):167-75
references.pmid: 19250601
references.citation: Clin Exp Optom. 2008 Jan;91(1):85-95
references.pmid: 18045254
references.citation: Brain Behav Evol. 1989;34(2):84-95
references.pmid: 2819413
references.citation: Acta Physiol Scand Suppl. 1997;638:5-24
references.pmid: 9421576
references.citation: Brain Behav Evol. 2012;79(1):26-44
references.pmid: 22142853
references.citation: J Comp Neurol. 2008 Mar 20;507(3):1336-50
references.pmid: 18189305
references.citation: Biol Rev Camb Philos Soc. 2004 Aug;79(3):671-712
references.pmid: 15366767
references.citation: Histol Histopathol. 1999 Apr;14(2):369-82
references.pmid: 10212798
references.citation: J Vis. 2012 Nov 20;12(12):13
references.pmid: 23169995