Elsevier

Journal of Theoretical Biology

Volume 99, Issue 4, 21 December 1982, Pages 777-795
Journal of Theoretical Biology

Quantitative matrix comparisons in ecological and evolutionary investigations

https://doi.org/10.1016/0022-5193(82)90197-7Get rights and content

Abstract

The pair-wise statistical comparison of data matrices is a methodological problem which must be dealt with in a variety of disciplines. In this report we demonstrate an innovative approach using the Mantel test (a nonparametric, multivariate evaluation of test matrices) to quantitatively contrast observed color polymorphisms in male Poecilia reticulata collected from 41 samples sites in Trinidad against four evolutionary models: (1) response to an environmental gradient, (2) localized environmental patches, (3) isolation by distance, and (4) historical factors. To represent these models we derived pair-wise distances between study sites for the following data: (1) altitude, (2) density of predators, and (3) kilometric distances. To represent model four above, we generated an imposed asymptotic distance matrix for geographically contiguous sites, and a Gabriel connectivity matrix for stream-connected sites (e.g. those within the same watershed). We found that differences in color polymorphisms covary significantly with differences in predator densities and in altitudes, suggesting that male color polymorphisms track clinally distributed communities of visually hunting predators. These data substantiate previously published results from field and laboratory experiments. The utility of the Mantel procedure is that it permits a quantitative evaluation of ecological and evolutionary problems which have previously been difficult to approach statistically.

References (38)

  • L.J. Hubert et al.

    J. math Psychol

    (1977)
  • F.B. Baker et al.

    J. Am. Stat. Ass

    (1975)
  • J.A. Bishop

    J. Animal Ecol

    (1972)
  • R. Borowsky

    Evolution

    (1981)
  • C.A. Clarke et al.

    Evolution

    (1962)
  • J.A. Endler

    Geographic Variation, Speciation, and Clines

    (1977)
  • J.A. Endler

    Evol. Biol

    (1978)
  • J.A. Endler

    Evolution

    (1980)
  • J.A. Farr et al.

    Anim. Behav

    (1974)
  • J.S. Farris

    Syst. Zool

    (1969)
  • J.S. Farris

    Syst. Zool

    (1973)
  • E.B. Ford

    Genetic Polymorphism

    (1965)
  • R.K. Gabriel et al.

    Syst. Zool

    (1969)
  • R.J. Harris

    A Primer of Multivariate Statistics

    (1975)
  • C.P. Haskins et al.
  • C.P. Haskins et al.

    Heredity

    (1970)
  • G.E. Hutchinson
  • J.S. Jones et al.

    Biol. J. Linnean Soc

    (1980)
  • K.D. Kallman
  • Cited by (145)

    • High frequency cropping of pulses modifies soil nitrogen level and the rhizosphere bacterial microbiome in 4-year rotation systems of the semiarid prairie

      2018, Applied Soil Ecology
      Citation Excerpt :

      The relative influence of these predictors on the soil and root bacterial communities was quantified using the varpart function, an RDA-based variance partitioning method. The possibility of a relationship between the rhizosphere (phase-3) and wheat root (phase-4) bacterial communities was tested based on Jaccard distance using Mantel‘s asymptotic approximation (Douglas and Endler, 1982) in PC-ORD v. 6.19 (Peck, 2010). EstimateR (Chao1 richness estimator) and rarefy (observed richness) were used to calculate richness, and diversity was used to calculate the Shannon diversity index using the vegan add-on package in R and all OTUs.

    • Contextualizing macroecological laws: A big data analysis on electrofishing and allometric scalings in Ohio, USA

      2017, Ecological Complexity
      Citation Excerpt :

      We used the Mantel test to validate the allometric outcome and to verify if the scaling was inflated by outliers (large-sized individuals occasionally occurring in the last 2 vs. 3 bins of our complete spectra). This partial Mantel analysis has been carried out to assess whether the association between sampling method and size–biomass slope is stronger than could result from chance (algorithm based on Douglas and Endler, 1982). This preliminary approach is intended to yield an increased understanding of the multiple relationships between fish sizes, environment, and sampling.

    • Effects of time since fire on birds in a plant diversity hotspot

      2013, Acta Oecologica
      Citation Excerpt :

      We assessed the role of vegetation structure and plant functional composition on bird species composition using Mantel tests (Mantel, 1967). The Mantel procedure circumvents the lack of independence among data values associated with traditional matrix correlations between all pairs of plots (Douglas and Endler, 1982). We calculated the Canberra distance between all pairs of plots for bird species composition (twenty-nine species), vegetation structure (seven variables) and plant functional composition (three variables).

    • Reconstructing climate variability on the northeastern Tibetan Plateau since the last Lateglacial - a multi-proxy, dual-site approach comparing terrestrial and aquatic signals

      2011, Quaternary Science Reviews
      Citation Excerpt :

      Smol et al. (2005) and Birks (2007) applied Detrended Canonical Correspondence Analysis (DCCA) to palaeo-records in the Arctic and in Norway, respectively, to gain quantitative estimates of compositional species turnover. A direct comparison of multivariate data sets was often assessed using the Mantel test (e.g., Douglas and Endler, 1982; Dutilleul et al., 2000) and Procrustes rotation (e.g., Peres-Neto and Jackson, 2001; Davidson et al., 2007). To date, however, no such analyses have been carried out on sites on the Tibetan Plateau.

    View all citing articles on Scopus

    This project was initiated with MED was an NIH Post-Doctoral Fellow in Genetics at Princeton University (Public Health Service 1-T32-GM07625-01 to Princeton University). Computer analyses were completed while he was a Research Associate with the Oklahoma Biological Survey and Department of Zoology, University of Oklahoma, Norman. Preparation of this manuscript was supported by the Bureau of Biological Research, Rutgers—The State University (New Brunswick, NJ) JAE received support for field work in the West Indies from the Eugene Higgins Trust Fund to the Biological Department, Princeton University, and from NSF Grants BMS-75-11903 and DEB-79-11200. Manuscript reviews were graciously provided by Drs N. A. Buroker, J. D. Felley, W. J. Matthews, G. D. Schnell, R. R. Sokal, and Mr R. A. Schneck. However, all errors remain the responsibility of the senior author.

    View full text