sads-package: Maximum Likelihood Models for Species Abundance Distributions

Description Details Author(s) References See Also Examples


Maximum likelihood tools to fit and compare models of species abundance distributions and of species rank-abundance distributions.


The distribution of abundances of species is one of the basic patterns of ecological communities. The empirical distributions of abundances (SADs) or their ranks (RADs) are traditionally modelled through probability distributions. Hence, the maximum likelihood method can be used to fit and compare competing models for SADs and RADs. The sads package provides functions, classes and methods to:


Paulo I. Prado, Murilo Dantas Miranda and Andre Chalom

Maintainer: Paulo I. Prado <>


Magurran, A.E. 2004. Measuring Biological Diversity. Blackwell.

Magurran, A.E. and McGill, B.J. 2011. Biological Diversity – Frontiers in measurement and assessment. Oxford University Press.

May, R.M. 1975. Patterns of Species Abundance and Diversity. In M. L. Cody and J. M. Diamond (Eds.), (pp. 81–120). Harvard University Press.

Green,J. and Plotkin, J.B. 2007 A statistical theory for sampling species abundances. Ecology Letters 10:1037–1045.

Saether, B.E., Engen, S. and Grotan, V. 2013. Species diversity and community similarity in fluctuating environments: parametric approaches using species abundance distributions. Journal of Animal Ecology, 82(4): 721–738.

See Also

vignettes of sads; vegan-package and poilog-package


## Rank-abundance plot
plot( rad(moths) )
## Preston's plots
plot (octav(moths) )
## Fit logseries model <-  fitsad(moths, sad = 'ls')
## Diagnostic plots
par(mfrow = c(1,1))
## Model summary
## Confidence interval

Example output

Loading required package: bbmle
Loading required package: stats4
Maximum likelihood estimation

mle2(minuslogl = function (N, alpha) 
-sum(dls(x, N, alpha, log = TRUE)), start = list(alpha = 40.247281791951), 
    method = "Brent", fixed = list(N = 15609L), data = list(x = c(1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
    3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 
    4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 5L, 
    5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 6L, 6L, 6L, 6L, 6L, 6L, 
    6L, 6L, 6L, 6L, 6L, 7L, 7L, 7L, 7L, 7L, 8L, 8L, 8L, 8L, 8L, 
    8L, 9L, 9L, 9L, 9L, 10L, 10L, 10L, 10L, 11L, 11L, 12L, 12L, 
    13L, 13L, 13L, 13L, 13L, 14L, 14L, 15L, 15L, 15L, 15L, 16L, 
    16L, 16L, 17L, 17L, 17L, 18L, 18L, 18L, 19L, 19L, 19L, 20L, 
    20L, 20L, 20L, 21L, 22L, 22L, 22L, 23L, 23L, 23L, 24L, 25L, 
    25L, 25L, 26L, 27L, 28L, 28L, 28L, 29L, 29L, 32L, 34L, 34L, 
    36L, 36L, 36L, 37L, 37L, 43L, 43L, 44L, 44L, 45L, 49L, 49L, 
    49L, 51L, 51L, 51L, 51L, 52L, 53L, 54L, 54L, 57L, 58L, 58L, 
    60L, 60L, 60L, 61L, 64L, 67L, 73L, 76L, 76L, 78L, 84L, 89L, 
    96L, 99L, 109L, 112L, 120L, 122L, 129L, 135L, 141L, 148L, 
    149L, 151L, 154L, 177L, 181L, 187L, 190L, 199L, 211L, 221L, 
    226L, 235L, 239L, 244L, 246L, 282L, 305L, 306L, 333L, 464L, 
    560L, 572L, 589L, 604L, 743L, 823L, 2349L)), lower = 0, upper = 240L)

      Estimate Std. Error z value     Pr(z)    
alpha   40.247      6.961  5.7818 7.391e-09 ***
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Fixed parameters:

-2 log L: 2175.425 
   2.5 %   97.5 % 
28.01537 55.36267 

sads documentation built on May 2, 2019, 1:56 p.m.