2 Null model analysis has been a popular tool for detecting pattern in binary presence–absence matrices, and previous tests have identiied algorithms and metrics that have good statistical properties. However, the behavior of diferent metrics is often correlated, making it diicult to distinguish diferent patterns. We compared the performance of a suite of null models and metrics that have been proposed to measure patterns of segregation, aggregation, nestedness, coherence, and species turnover. We found that any matrix with segregated species pairs can be re-ordered to highlight aggregated pairs. As a consequence, the same null model can identify a single matrix as being simultaneously aggregated, segregated or nested. hese results cast doubt on previous conclusions of matrix-wide species segregation based on the C-score and the ixed-ixed algorithm. Similarly, we found that recently proposed classiication schemes based on patterns of coherence, nestedness, and segregation and aggregation cannot be uniquely distinguished using proposed metrics and null model algorithms. It may be necessary to use a combination of diferent metrics and to decompose matrix-wide patterns into those of individual pairs of species or pairs of sites to pinpoint the sources of non-randomness. Pattern detection in null model analysis Werner Ulrich and Nicholas J. Gotelli W. Ulrich (ulrichw@umk.pl), Nicolaus Copernicus Univ. in Toruń, Chair of Ecology and Biogeography, Gagarina 9, PL-87-100 Toruń, Poland. – N. J. Gotelli, Dept of Biology, Univ. of Vermont, Burlington, VT 05405, USA. Oikos 122: 2–18, 2013 doi: 10.1111/j.1600-0706.2012.20325.x © 2012 he Authors. Oikos © 2012 Nordic Society Oikos Subject Editor: Paulo Guimaraes Jr. Accepted 16 March 2012 C h o i c e E d i t o r ’ s OIKOS A major research efort in community ecology has been to infer mechanisms of community organization from patterns in a binary presence–absence matrix. In such a matrix, species are represented by rows, sites are represented by columns, and the entries are the presence or absence of a species in a particular site (McCoy and Heck 1987). Early research (and controversy) focused on the role of inter- speciic competition in producing checkerboard patterns (Diamond 1975), species segregation (Stone and Roberts 1990), and missing species combinations (Pielou and Pielou 1968). A largely independent focus on species nestedness (Darlington 1957, Patterson and Atmar 1986) emphasized the role of selective, orderly extinction (and immigration) in producing species-poor assemblages whose composition is a perfectly nested subset of more species-rich assemblages. Leibold and Mikkelson (2002) signiicantly expanded this framework by proposing tests for additional patterns of Clementsian, Gleasonian, and evenly-spaced gradients. heir method involves re-ordering the rows and columns of a presence–absence matrix by reciprocal averaging to maximize the coherence of species range sizes. A maxi- mally coherent matrix state is one that contains the greatest number of uninterrupted sequences of species occurrences within rows of the re-ordered matrix. In such a re-ordered matrix, ‘species turnover’ is the replacement of one species by another, and ‘boundary clumping’ is the extent to which species boundaries are clumped or over-dispersed. Checker- boards, nestedness, Clementsian gradients, Gleasonian gradients, and evenly-spaced gradients are recognized by a combination of patterns of coherence, species turnover, and boundary clumping. Presley et al. (2010) further expanded Leibold and Mikkelson’s (2002) framework, distinguishing among 12 diferent models based on the combination of bound- ary clumping and turnover patterns for matrices in which there is positive coherence. hey distinguished three types of nested patterns, depending on whether boundary clump- ing was positive, random, or negative, and they recognized six additional ‘quasi-structures’ based on weakly positive or negative patterns of species turnover. he review and decision to publish this paper has been taken by the above noted SE. he decision by the handling SE is shared by a second SE and the EiC. Synthesis The identification of distinctive patterns in species x site presence-absence matrices is important for under- standing meta-community organisation. We compared the performance of a suite of null models and metrics that have been proposed to measure patterns of segregation, aggregation, nestedness, coherence, and species turnover. We found that any matrix with segregated species pairs can be re-ordered to highlight aggregated pairs, indicating that these seemingly opposite patterns are closely related. Recently proposed classification schemes failed to correctly classify realistic matrices that included multiple co-occurrence structures. We propose using a combination of metrics and decomposing matrix-wide patterns into those of individual pairs of species and sites to pinpoint sources of non-randomness.