Ecological and biogeographic null hypotheses for comparing rarefaction curves

Abstract

The statistical framework of rarefaction curves and asymptotic estimators allows for an effective standardization of biodiversity measures. However, most statistical analyses still consist of point comparisons of diversity estimators for a particular sampling level. We introduce new randomization methods that incorporate sampling variability encompassing the entire length of the rarefaction curve and allow for statistical comparison of i !2 individual-based, sample-based, or coverage-based rarefaction curves. These methods distinguish between two distinct null hypotheses: the ecological null hypothesis (H 0eco ) and the biogeographical null hypothesis (H 0biog ).H 0eco states that the i samples were drawn from a single assemblage, and any differences among them in species richness, composition, or relative abundance reflect only sampling effects. H 0biog states that the i samples were drawn from assemblages that differ in their species composition but share similar species richness and species abundance distributions. To test H 0eco , we created a composite rarefaction curve by summing the abundances of all species from the i samples. We then calculated a test statistic Z eco , the (cumulative) summed areas of difference between each of the i individual curves and the composite curve. For H 0biog , the test statistic Z biog was calculated by summing the area of difference between all possible pairs of the i individual curves. Bootstrap sampling from the composite curve (H 0eco ) or random sampling from different simulated assemblages using alternative abundance distributions (H 0biog ) was used to create the null distribution of Z, and to provide a frequentist test of Z j H 0 . Rejection of H 0eco does not pinpoint whether the samples differ in species richness, species composition, and/or relative abundance.In benchmark comparisons, both tests performed satisfactorily against artificial data sets randomly drawn from a single assemblage (low Type I error). In benchmark comparisons with different species abundance distributions and richness, the tests had adequate power to detect differences among curves (low Type II error), although power diminished at small sample sizes and for small differences among underlying species rank abundances.

Colitis‐induced colorectal cancer and intestinal epithelial estrogen receptor beta impact gut microbiota diversity

“…Rarefaction curves were used to confirm that sufficient sequencing coverage had been achieved, and to identify differences of species diversity between groups. Significant differences between rarefaction curves of different groups were calculated as described by Cayuela et al 33 using the function EcoTest.sample from R package rareNMtests v1.1. Alpha diversity is a measure of microbiota abundance and how evenly these are distributed (evenness), and was estimated through Shannon's diversity index.…”

If you build it, they will go: A case study of stream fish diversity loss in an urbanizing riverscape

“…This suggested that space‐for‐time substitutions can be invalid for assessing ecological responses to urbanization and supports the value of historical land‐use data for assessing patterns in biodiversity change (Harding, Benfield, Bolstad, Helfman, & Jones, ). Implementing multiple scales of resolution into assemblage change with multiple Hill numbers is an effective method for measuring spatial and temporal changes in assemblage structure (Cayuela et al, ), and can be combined with functional trait data to assess potential mechanisms that might be contributing to observed assemblage change (Crumby, Webb, Bulow, & Cathey, ; Hoeinghaus, Winemiller, & Birnbaum, ). Our approach here suggests that combining a riverscape perspective with new rarefaction‐based analyses is a promising avenue for identifying the spatiotemporal extents of change in stream fish assemblages.…”

Trophic‐specific responses to migration in empirical metacommunities

“…While there are standard methods to extrapolate the number of species (Colwell and Coddington , Chao et al ) and compare the overall shape of rarefaction curves (Cayuela et al ), we were interested in the statistical differences between our rarefaction curves across the range of resampled levels. To assess differences between the control and migration treatments, we conducted a bootstrapping procedure to compare the difference in the mean number of species at every resampling level, x i , along the rarefaction curves.…”