# Null expectations and null hypothesis testing for the species abundance distribution

@inproceedings{Arellano2021NullEA, title={Null expectations and null hypothesis testing for the species abundance distribution}, author={Gabriel Arellano}, year={2021} }

The number of elements (N) and types (S) sampled from an ecological system are among the most powerful constraints on observations of abundance, distribution, and diversity. Together, N and S determine sets of possible forms (i.e., feasible sets) for the species abundance distribution (SAD). There are three approaches to the description of the null SAD (= the average feasible SAD). The first approach is based on the random uniform sampling of surjections. I calculate the probability of a given…

## References

SHOWING 1-10 OF 40 REFERENCES

### How species richness and total abundance constrain the distribution of abundance.

- Environmental ScienceEcology letters
- 2013

It is found that feasible sets are dominated by similarly shaped hollow curves, most of which are highly correlated with empirical SADs, revealing a strong influence of N and S on the form of the SAD and an a priori explanation for the ubiquitous hollow curve.

### Species abundance distribution results from a spatial analogy of central limit theorem

- Environmental ScienceProceedings of the National Academy of Sciences
- 2009

It is argued that an SAD for a study plot must be viewed as spliced from the SADs of many smaller nonoverlapping subplots covering that plot, and it is shown that this splicing, if applied repeatedly to produceSubplots of progressively larger size, leads to the observed shape of the S AD for the whole plot regardless of that of theSADsof those subplot.

### Confronting different models of community structure to species-abundance data: a Bayesian model comparison.

- Environmental ScienceEcology letters
- 2005

A Bayesian analysis of species-abundance data that yields a full joint probability distribution of each model's parameters plus a relatively parameter-independent criterion, the posterior Bayes factor, to compare these models.

### ON THE RELATIVE ABUNDANCE OF BIRD SPECIES.

- Environmental ScienceProceedings of the National Academy of Sciences of the United States of America
- 1957

The observed populations are not under the control of very local or rapid temporal processes; i.e., they are in a near-equilibrium state, and the hypotheses will be ones which yield an equilibrium or near-Equilibrium population.

### Fitting and comparing competing models of the species abundance distribution: assessment and prospect

- Environmental Science
- 2014

An overview of SADs is provided, including descriptions of the commonly used distributions, and few attempts have been made to synthesise the vast array of methods which have been employed in SAD model evaluation.

### Entropy Maximization and the Spatial Distribution of Species

- Environmental ScienceThe American Naturalist
- 2010

It is argued that the appropriate choice of the EM model assumptions is nontrivial and can be determined only by comparison with empirical data.

### A statistical theory for sampling species abundances.

- Environmental ScienceEcology letters
- 2007

A statistical sampling theory is developed to describe how observed patterns of species abundances are influenced by the spatial distributions of populations, and derives exact expressions for the sampled abundance distributions, as a function of sample size and the degree of conspecific spatial aggregation.

### Species abundance distributions: moving beyond single prediction theories to integration within an ecological framework.

- Environmental ScienceEcology letters
- 2007

Theoretical, empirical and statistical developments in the study of Species abundance distributions are reviewed and it is optimistic that SADs can provide significant insights into basic and applied ecological science.

### A test of the unified neutral theory of biodiversity

- Environmental ScienceNature
- 2003

Whether the zero-sum multinomial distribution fits several empirical data sets better than the lognormal distribution does not, and there is no evidence that the ZSM predicts abundancesbetter than the much more parsimonious null hypothesis.

### Beals smoothing revisited

- BiologyOecologia
- 2008

The statistical and ecological bases underlying the Beals smoothing function are studied, and the factors that may affect the reliability of transformed values are explored using simulated data sets.