Determination of the physical parameters of coral distributions using line transect data

Coral Reefs - Tập 2 - Trang 175-180 - 1984
L. M. Marsh1, R. H. Bradbury2, R. E. Reichelt2
1Mathematics Department, James Cook University of North Queensland, Townsville, Australia
2Australian Institute of Marine Science, Townsville MSO, Australia

Tóm tắt

We present a new method for extracting a comprehensive suite of biologically significant parameters from line transect data of coral communities. In addition to the percentage coral cover (the traditionally extracted parameter), the method extracts the population density of the coral colonies, their mean diameter and associated standard deviation and, for adequate data, their size frequency distribution. The method assumes only that the coral colonies form a system of non-overlapping circles in the plane, that the diameters of the circles are random quantities with an unknown distribution function, and that the transects are placed randomly. We test the method on both theoretical and real data to show that it performs as well as, if not better than, current methods in extracting the traditional parameter as well as being able to extract the additional useful parameters indicated. Because the method makes few restrictive assumptions and seems robust when used with field data, we suggest that it has wide application wherever line transects are used for ecological survey. The method is implemented in a Fortran program available from the senior author.

Tài liệu tham khảo

Anderssen RS, Jakeman AJ (1975a) Product integration for functionals of particle size distributions. Utilitas Mathematica 8:111–126 Anderssen RS, Jakeman AJ (1975b) Abel type integral equations in stereology. II. Computational methods of solution and the random spheres approximation. J Microsc (Oxford) 105:135–153 Bradbury RH, Loya Y (1978) An heuristic analysis of spatial patterns of hermatypic corals at Eilat, Red Sea. Am Nat 112:493–507 Bradbury RH, Young PC (1981) The effects of a major forcing function, wave energy, on a coral reef ecosystem. Mar Ecol Prog Ser 5:229–241 Cox GW (1972) Laboratory manual of general ecology, Brown, Iowa Greig-Smith P (1964) Quantitative plant ecology. Butterworths, London Jakeman AJ, Anderssen RS (1975) Abel type integral equations in stereology. I. General discussion. J Microsc (Oxford) 105:121–133 Kendall MG, Moran PAP (1963) Geometrical probability. Griffin, London Kinzie RA, Snider RH (1978) A simulation study of coral reef survey methods. In: Stoddart DR, Johannes RE (eds) Coral reefs: research methods. Unesco, Paris, pp 231–250 Loya Y (1978) Plotless and transect methods. In: Stoddart DR, Johannes RE (eds) Coral reefs: research methods Unesco, Paris, pp 197–217 McIntyre GA (1953) Estimation of plant density using line transects. J Ecol 41:319–330 Mergner H, Schuhmacher H (1981) Quantitative Analyse der Korallen-besiedlung eines Vorriffareals bei Aquaba (Rotes Meer). Helgol Wiss Meeresunters 34:337–354 Pielou EC (1977) Mathematical ecology. Wiley, New York Southwood TRE (1966) Ecological methods. Methuen, London Strong CW (1966) An improved method of obtaining density from linetransect data. Ecology 47:311–313 Watson GS (1971) Estimating functionals of particle size distribution. Biometrika 58:483–490 Weinberg S (1981) A comparison of coral reef survey methods. Bijdr Dierkd 51:199–218 Young A (1954) Approximate product integration. Proc R Soc London Ser A 244:552–561