On species-area relationships. 1, Fit of power function and exponential model

Ulrich, Werner

doi:ISSN 1505-2249

Pobierz

Tytuł: On species-area relationships. 1, Fit of power function and exponential model

Abstrakt:

A FORTRAN program is developed that generates model assemblages on the basis of three basic features of animal communities: the species weight relationship, the density-weight relationship, and the minimal density. Samplings from random placed individuals of such assemblages revealed the influence of the sampling method (sequential adding, nested and non-nested), the scale, and the underlying relative abundance distribution on resulting species-area relationships (SPARs). It is concluded that the type of the species-area relationship is not an intrinsic factor of an assemblage but depends especially on the sampling method and the unit of area. The fraction of species found only once in the sample (singletons) was the major factor influencing the model that fitted the SPAR best (at low fractions the exponential, at higher fractions the power function model). All sampling and structural factors that influence the fraction of singletons also influence the fit of the SPAR model. A mathematical derivation showed that at a certain fraction of singletons in the sample a shift from the power function to the exponential model is expected independent of assemblage type. This shift will occur between 20 and 30% singletons.

Bibliografia:

Addicot J. M., Ado J. M., Antolin M. F., Padilla D. K. Richardson J. S., Soluk D. A. 1987 - Ecological neighborhoods: scaling environmental patterns - Oikos, 49: 340-346.
Archibald E. E. A. 1949 – The specific character of plant communities. II. A quantitative approach - J. Ecol. 37: 260-274.
Arrhenius O. 1921 – Species and area - J. Ecol. 9: 95 99.
Coleman B. D. 1981 – On random placement and species area relations - Math. Bioscience, 54: 191-215.
Coleman B. D., Mares M. A., Willig M. R., Hsieh Y. H. 1982 - Randomness, area, and species richness - Ecology, 63: 1121-1133.
Colwell R. K., Coddington J. A. 1994 - Estimating terrestrial biodiversity through extrapolation – Phil. Trans. R. Soc. Lond. B: 345: 101-118.
Connor E. F., McCoy E. D. 1979 - The statistics and biology of the species-area relationship - Am. Nat. 113: 791-833.
Currie D. J. 1993 - What shape is the relationship between body mass and population density - Oikos, 66: 353.
Currie D. J., Fritz J. T. 1993 - Global patterns of animal abundance and species energy use - Oikos, 67: 56-68.
De Caprariis P., Lindemann R. H., Collins C. 1976 - A method for determining optimum sample size in species diversity studies - Math. Geol. 8: 575-581.
Engen S. 1977 - Exponential and logarithmic species area curves - Am. Nat. 111: 591-594.
Fahrig L. 1992 - Relative importance of spatial and temporal scales in a patchy environment - Theor. Pop. Biol. 41: 300-314.
Fisher A. G., Corbet S. A., Williams S. A. 1943 - The relation between the number of species and the number of individuals in a random sample of an animal population - J. Anim. Ecol. 12: 42-58.
Frontier S. 1985 - Diversity and structure in aquatic ecosystems (in: Oceanography and Marine Biology - An Annual Review Ed. M. Barnes) - Aberdeen, pp. 253-312.
Gleason H. A. 1922 - On the relation between species and area - Ecology, 3: 158-162.
Hanski I., Gyllenberg M. 1997 - Uniting two general patterns in the distribution of species - Science, 275: 397-400.
Harte J., Kinzig A. P. 1997 - On the implications of species-area relationships for endemism, spatial turnover, and food web patterns - Oikos, 80: 417-427.
Harte J., Kinzig A. P., Green J. 1999 - Self-similarity in the distribution and abundance of species - Science, 284: 334-336.
He F., Legendre P. 1996 - On species area relations - Am. Nat. 148: 719-737.
Humboldt A. V., Bonpland A. 1807 - Essai sur la Geographie des Plantes - Paris, Librairie Lebrault Schoell.
Hurlbert S. H. 1984 - Pseudoreplication and the design of ecological field experiments - Ecol. Monogr. 54: 187-211.
Jonsson B. G., Moen J. 1998 - Patterns in species association in plant communities: the importance of scale - J. Veg. Sci. 9: 327-332.
Kilburn P. D. 1963 - Exponential values for the species area relation – Science, 141: 1276.
Kilburn P. D. 1966 - Analysis of the species area relation - Ecology, 47: 831-843.
Kylin H. 1926 - Uber Begriffsbildung und Statistik in der Pflanzensoziologie - Bot. Not. 1926: 81-180.
LaBarbera M. 1985 - The Evolution and ecology of body size (In: Patterns and processes in the History of Life Eds. D. M. Raup, D. Jabłoński) - Springer (Berlin), pp. 69-98.
Leitner W. A., Rosenzweig M. L. 1997 - Nested species-area curves and stochastic sampling: a new theory - Oikos, 79: 503-512.
MacArthur R. H., Wilson E. O. 1967 - The theory of island biogeography - Princeton Univ. Press, 203 pp.
Martin T. E. 1981 - Species-area slopes and coefficients: a caution on their interpretation - Am. Nat. 118: 823-837.
May R. M. 1975 - Patterns of species abundance and diversity (In: Ecology and evolution of communities Eds.: M. L. Cody, J. M. Diamond) - Belknap (Cambridge), pp. 81-120.
McGuinness K. A. 1984 - Equations and explanations in the study of species-area curves - Biol. Rev. 59: 423-440.
Ney-Nifle M., Mangel M. 1999 - Species-area curves based on geographic range and occupancy - J. Theor. Biol. 196: 327-342.
Novotny V., Kindlmann P. 1996 - Distribution of body sizes in arthropod taxa and communities - Oikos, 75: 75-82.
Palmer M. W., White P. S. 1994 - Scale dependence and the species-area relationship - Am. Nat. 144: 717-740.
Pielou E. C. 1977 - Mathematical Ecology - John Wiley & Sons, New York, 385 pp.
Preston F. W. 1962 - The canonical distribution of commonness and rarity. Part I and II – Ecology, 43: 185-215, 410-432.
Ricker W. E. 1973 - Linear regression in fishery research - J. Fish. Res. Board Can. 30: 409-434.
Rosenzweig M. L. 1999 - Heeding the warning in biodiversity's basic law - Science, 284: 276-277.
Schoener T. W. 1976 - The species-area relation within archipelagos: models and evidence from island land birds (In: Proc. I6th Int. Ornith. Congr. 1976 Eds. H. J. Frith, J. H. Calaby) - Canberra, pp. 629-642.
Seim E., Saether B. E. I983 - On rethinking allometry: which regression model to use - L. Theor. Biol. 104: 161-168.
Sugihara G. 1980 - Minimal community structure: an explanation of species abundance patterns - Am. Nat. 116: 770-787.
Tokeshi M. 1993 - Species abundance patterns and community structure - Adv. Ecol. Res. 24: 111-186.
Tokeshi M. 1996 - Power fraction: a new explanation of relative abundance patterns in species-rich assemblages - Oikos, 75: 543-550.
Ulrich W. 1999a - The numbers of species of Hymenoptera in Europe and assessment of the total number of Hymenoptera in the world - Pol. J. Entomol. 68: 151-164.
Ulrich W. 1999b - Estimating species numbers by extrapolation I: Comparing the performance of various estimators using large model communities - Pol. J. Ecol. 47: 271-291.
Ulrich W. 1999c - Abundance, biomass and density boundaries in the Hymenoptera: analysis of the abundance-body size relationship and differences between forest and open landscape habitats - Pol. J. Ecol. 47: 73-86.
Ulrich W. 2000a - On species-area relationships II: Parameter values ofthe power and the exponential model and their dependence on sampling method, habitat and assemblage structure - Pol. J. Ecol. 48: 21-35.
Ulrich W. 2000b - On species-area relationships III: The intercept of the power function and the exponential model - Pol. J. Ecol. 48: 37-48.
Williams C. B. 1943 - Area and the number of species - Nature, 152: 264-267.
Williams M. R. 1995 - An extreme -value function model of the species incidence and species-area relations - Ecology, 76: 2607-2616.
Williamson M. 1988 - Relationship of species number to area, distance and other variables (In: Analytical biogeography, Eds. A. A. Myers, P. S. Giller) - Chapman & Hall (New York), pp. 91-115.
Wilson W. B., Gitay H., Steel J. B., King W. McG. 1998 - Relative abundance distributions in plant communities: effects of species richness and spatial scale - J. Veg. Sci. 9: 213-220.
Wissel Ch., Maier B. 1992 - A stochastic model for the species-area relationship - J. Biogeogr. 19: 355-362.
Wright S. J. 1988 - Patterns of abundance and the form of the species-area relation - Am. Nat. 131: 401-411.