A simple method to fit geometric series and broken stick models in community ecology and island biogeography

Abstract Species abundance distributions are widely used in explaining natural communities, their natural evolution and the impacts of environmental disturbance. A commonly used approach is that of rank-abundance distributions. Favored, biologically founded models are the geometric series (GS) and the broken stick (BS) model. Comparing observed abundance distributions with those predicted by models is an extremely time-consuming task. Also, using goodness-of-fit tests for frequency distributions (like Chi-square or Kolmogorov–Smirnov tests) to compare observed with expected frequencies is problematic because the best way to calculate expected frequencies may be controversial. More important, the Chi-square test may prove if an observed distribution statistically differs from a model, but does not allow the investigator to choose among competing models from which the observed distribution does not differ. Both models can be easily tested by regression analysis. In GS, if a log scale is used for abundance, the species exactly fall along a straight line. The BS distribution shows up as nearly linear when a log scale is used for the rank axis. Regression analysis is proposed here as a simpler and more efficient method to fit the GS and BS models. Also, regression analysis (1) does not suffer from assumptions related to Chi-square tests; (2) obviates the need to establish expected frequencies, and (3) offers the possibility to choose the best fit among competing models. A possible extension of abundance-rank analysis to species richness on islands is also proposed as a method to discriminate between relict and equilibrial models. Examples of application to field data are also presented.

[1]  Han Olff,et al.  A novel genealogical approach to neutral biodiversity theory , 2004 .

[2]  B. Anderson,et al.  Are bryophyte communities different from higher‐plant communities? Abundance relations , 2004 .

[3]  P. Inchausti,et al.  Lognormality in ecological time series , 2002 .

[4]  A. Magurran,et al.  Measuring Biological Diversity , 2004 .

[5]  Kinzig,et al.  Self-similarity in the distribution and abundance of species , 1999, Science.

[6]  G. Sugihara.  Minimal Community Structure: An Explanation of Species Abundance Patterns , 1980, The American Naturalist.

[7]  Steinar Engen,et al.  Analyzing Spatial Structure of Communities Using the Two‐Dimensional Poisson Lognormal Species Abundance Model , 2002, The American Naturalist.

[8]  D. Strayer,et al.  Patterns of the abundance of species: a comparison of two hierarchical models , 1988 .

[9]  J. Keeley,et al.  Species–area relationships in Mediterranean‐climate plant communities , 2003 .

[10]  F. W. Preston.  Noncanonical Distributions of Commonness and Rarity , 1980 .

[11]  R. May.  Patterns of species abundance and diversity , 1975 .

[12]  T. O. Kvålseth.  Cautionary Note about R 2 , 1985 .

[13]  R. Fisher,et al.  The Relation Between the Number of Species and the Number of Individuals in a Random Sample of an Animal Population , 1943 .

[14]  Mutsunori Tokeshi,et al.  Species Abundance Patterns and Community Structure , 1993 .

[15]  Ricard V Solé,et al.  Self-organized instability in complex ecosystems. , 2002, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[16]  Michel Loreau,et al.  Carabid Beetles: Ecology and Evolution , 1994, Series Entomologica.

[17]  G. Quinn,et al.  Experimental Design and Data Analysis for Biologists , 2002 .

[18]  Fiona K. A. Schmiegelow,et al.  ARE BOREAL BIRDS RESILIENT TO FOREST FRAGMENTATION? AN EXPERIMENTAL STUDY OF SHORT‐TERM COMMUNITY RESPONSES , 1997 .

[19]  R. Ferguson.  River Loads Underestimated by Rating Curves , 1986 .

[20]  David Mouillot,et al.  Introduction of Relative Abundance Distribution (RAD) Indices, Estimated from the Rank-Frequency Diagrams (RFD), to Assess Changes in Community Diversity , 2000 .

[21]  A. Magurran.  Ecological Diversity and Its Measurement , 1988, Springer Netherlands.

[22]  J. Diamond,et al.  Ecology and Evolution of Communities , 1976, Nature.

[23]  P. Giller,et al.  Community structure and the niche , 1984 .

[24]  S. Fattorini.  A comparison of relict versus dynamic models for tenebrionid beetles (Coleoptera: Tenebrionidae) of Aegean Islands (Greece) , 2002 .

[25]  Martin Büssenschütt,et al.  Diversity patterns in climax communities , 1999 .

[26]  Ian P. Woiwod,et al.  Diversity Statistics and the Log-Series Model , 1976 .

[27]  Pierre Legendre,et al.  SPECIES DIVERSITY PATTERNS DERIVED FROM SPECIES–AREA MODELS , 2002 .

[28]  A. K. Dewdney.  The stochastic community and the logistic-J distribution , 2003 .

[29]  James H. Brown,et al.  Spatial Scaling of Species Composition: Body Masses of North American Land Mammals , 1991, The American Naturalist.

[30]  J. Wilson,et al.  Methods for fitting dominance/diversity curves , 1991 .

[31]  Steinar Engen.  Stochastic abundance models, with emphasis on biological communities and species diversity , 1978 .

[32]  S. Hubbell,et al.  The unified neutral theory of biodiversity and biogeography at age ten. , 2011, Trends in ecology & evolution.

[33]  D. Tilman,et al.  Abundance, diversity and body size: patterns from a grassland arthropod community , 1999 .

[34]  J. Diamantopoulos,et al.  Collembolan assemblages in Lesvos, Greece. Effects of differences in vegetation and precipitation , 2000 .

[35]  A. Georges.  Carabid beetle spatial patterns in cultivated wetlands. The effects of engineering works and agricultural management in Marais Poitevin (western France) , 1994 .

[36]  B. Parresol.  Assessing Tree and Stand Biomass: A Review with Examples and Critical Comparisons , 1999, Forest Science.

[37]  Simone Fattorini,et al.  Biogeography of the tenebrionid beetles (Coleoptera, Tenebrionidae) on the Aegean Islands (Greece) , 2002 .

[38]  M. Tokeshi.  Power fraction: A new explanation of relative abundance patterns in species-rich assemblages , 1996 .

[39]  Christine J. Small,et al.  Spatial and temporal variability of herbaceous vegetation in an eastern deciduous forest , 2004, Plant Ecology.

[40]  R. G. Hughes.  Theories and Models of Species Abundance , 1986, The American Naturalist.

[41]  Hal Caswell,et al.  Community Structure: A Neutral Model Analysis , 1976 .