Species richness is a fundamental measurement of community and regional diversity, and it underlies many ecological models and conservation strategies. In spite of its importance, ecologists have not always appreciated the effects of abundance and sampling effort on richness measures and comparisons. We survey a series of common pitfalls in quantifying and comparing taxon richness. These pitfalls can be largely avoided by using accumulation and rarefaction curves, which may be based on either individuals or samples. These taxon sampling curves contain the basic information for valid richness comparisons, including category‐subcategory ratios (species-to-genus and species-toindividual ratios). Rarefaction methods ‐ both sample-based and individual-based ‐ allow for meaningful standardization and comparison of datasets. Standardizing data sets by area or sampling effort may produce very different results compared to standardizing by number of individuals collected, and it is not always clear which measure of diversity is more appropriate. Asymptotic richness estimators provide lower-bound estimates for taxon-rich groups such as tropical arthropods, in which observed richness rarely reaches an asymptote, despite intensive sampling. Recent examples of diversity studies of tropical trees, stream invertebrates, and herbaceous plants emphasize the importance of carefully quantifying species richness using taxon sampling curves.

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Quantifying biodiversity: procedures and pitfalls in the measurement and comparison of species richness

Both the magnitude and the urgency of the task of assessing global biodiversity require that we make the most of what we know through the use of estimation and extrapolation. Likewise, future biodiversity inventories need to be designed around the use of effective sampling and estimation procedures, especially for 'hyperdiverse' groups of terrestrial organisms, such as arthropods, nematodes, fungi, and microorganisms. The challenge of estimating patterns of species richness from samples can be separated into (i) the problem of estimating local species richness, and (ii) the problem of estimating the distinctness, or complementarity, of species assemblages. These concepts apply on a wide range of spatial, temporal, and functional scales. Local richness can be estimated by extrapolating species accumulation curves, fitting parametric distributions of relative abundance, or using non-parametric techniques based on the distribution of individuals among species or of species among samples. We present several of these methods and examine their effectiveness for an example data set. We present a simple measure of complementarity, with some biogeographic examples, and outline the difficult problem of estimating complementarity from samples. Finally, we discuss the importance of using 'reference' sites (or sub-sites) to assess the true richness and composition of species assemblages, to measure ecologically significant ratios between unrelated taxa, to measure taxon/sub-taxon (hierarchical) ratios, and to 'calibrate' standardized sampling methods. This information can then be applied to the rapid, approximate assessment of species richness and faunal or floral composition at 'comparative' sites.

Estimating Terrestrial Biodiversity through Extrapolation

It is well established that autism spectrum disorders (ASD) have a strong genetic component; however, for at least 70% of cases, the underlying genetic cause is unknown. Under the hypothesis that de novo mutations underlie a substantial fraction of the risk for developing ASD in families with no previous history of ASD or related phenotypes--so-called sporadic or simplex families--we sequenced all coding regions of the genome (the exome) for parent-child trios exhibiting sporadic ASD, including 189 new trios and 20 that were previously reported. Additionally, we also sequenced the exomes of 50 unaffected siblings corresponding to these new (n = 31) and previously reported trios (n = 19), for a total of 677 individual exomes from 209 families. Here we show that de novo point mutations are overwhelmingly paternal in origin (4:1 bias) and positively correlated with paternal age, consistent with the modest increased risk for children of older fathers to develop ASD. Moreover, 39% (49 of 126) of the most severe or disruptive de novo mutations map to a highly interconnected β-catenin/chromatin remodelling protein network ranked significantly for autism candidate genes. In proband exomes, recurrent protein-altering mutations were observed in two genes: CHD8 and NTNG1. Mutation screening of six candidate genes in 1,703 ASD probands identified additional de novo, protein-altering mutations in GRIN2B, LAMC3 and SCN1A. Combined with copy number variant (CNV) data, these results indicate extreme locus heterogeneity but also provide a target for future discovery, diagnostics and therapeutics.

/pdf/sporadic-autism-exomes-reveal-a-highly-interconnected-2s0r2v49qb.pdf

Sporadic autism exomes reveal a highly interconnected protein network of de novo mutations

Multiple studies have confirmed the contribution of rare de novo copy number variations to the risk for autism spectrum disorders. But whereas de novo single nucleotide variants have been identified in affected individuals, their contribution to risk has yet to be clarified. Specifically, the frequency and distribution of these mutations have not been well characterized in matched unaffected controls, and such data are vital to the interpretation of de novo coding mutations observed in probands. Here we show, using whole-exome sequencing of 928 individuals, including 200 phenotypically discordant sibling pairs, that highly disruptive (nonsense and splice-site) de novo mutations in brain-expressed genes are associated with autism spectrum disorders and carry large effects. On the basis of mutation rates in unaffected individuals, we demonstrate that multiple independent de novo single nucleotide variants in the same gene among unrelated probands reliably identifies risk alleles, providing a clear path forward for gene discovery. Among a total of 279 identified de novo coding mutations, there is a single instance in probands, and none in siblings, in which two independent nonsense variants disrupt the same gene, SCN2A (sodium channel, voltage-gated, type II, α subunit), a result that is highly unlikely by chance.

De novo mutations revealed by whole-exome sequencing are strongly associated with autism

Null models in ecology

How many kinds are there? Suppose that a population is partitioned into C classes. In many situations interest focuses not on estimation of the relative sizes of the classes, but on estimation of C itself. For example, biologists and ecologists may be interested in estimating the number of species in a population of plants or animals, numismatists may be concemed with estimating the number of dies used to produce an ancient coin issue, and linguists may be interested in estimating the size of an author's vocabulary. In this article we review the problem of statistical estimation of C. Many approaches have been proposed, some purely data-analytic and others based in sampling theory. In the latter case numerous variations have been considered. The population may be finite or infinite. If finite, samples may be taken with replacement (multinomial sampling) or without replacement (hypergeometric sampling), or by Bernoulli sampling; if infinite, sampling may be multinomial or Bernoulli, or the sample may be th...

M. Fitzpatrick

Papers

Estimating the Number of Species: A Review