Nestedness and Species Co-occurrence: A Systematic Analysis, Exams of Theatre

Download Nestedness and Species Co-occurrence: A Systematic Analysis and more Exams Theatre in PDF only on Docsity! Disentangling community patterns of nestedness and species co-occurrence Werner Ulrich and Nicholas J. Gotelli W. Ulrich (ulrichw@uni.torun.pl), Dept of Animal Ecology, Nicolaus Copernicus Univ. in Torun, Gagarina 9, PL-87-100 Torun, Poland.
N. J. Gotelli, Dept of Biology, Univ. of Vermont, Burlington, VT 05405, USA. Two opposing patterns of meta-community organization are nestedness and negative species co-occurrence. Both patterns can be quantified with metrics that are applied to presence-absence matrices and tested with null model analysis. Previous meta-analyses have given conflicting results, with the same set of matrices apparently showing high nestedness (Wright et al. 1998) and negative species co-occurrence (Gotelli and McCabe 2002). We clarified the relationship between nestedness and co-occurrence by creating random matrices, altering them systematically to increase or decrease the degree of nestedness or co-occurrence, and then testing the resulting patterns with null models. Species co-occurrence is related to the degree of nestedness, but the sign of the relationship depends on how the test matrices were created. Low-fill matrices created by simple, uniform sampling generate negative correlations between nestedness and co-occurrence: negative species co-occurrence is associated with disordered matrices. However, high-fill matrices created by passive sampling generate the opposite pattern: negative species co-occurrence is associated with highly nested matrices. The patterns depend on which index of species co-occurrence is used, and they are not symmetric: systematic changes in the co- occurrence structure of a matrix are only weakly associated with changes in the pattern of nestedness. In all analyses, the fixed-fixed null model that preserves matrix row and column totals has lower type I and type II error probabilities than an equiprobable null model that relaxes row and column totals. The latter model is part of the popular nestedness temperature calculator, which detects nestedness too frequently in random matrices (type I statistical error). When compared to a valid null model, a matrix with negative species co-occurrence may be either highly nested or disordered, depending on the biological processes that determine row totals (number of species occurrences) and column totals (number of species per site). Nestedness and segregated species co-occurrence are two commonly reported meta-community patterns (Leibold and Mikkelson 2002, Almeida-Neto et al. 2007). Both patterns are expressed in a presence- absence matrix, in which each row represents a species, each column represents a site or a sample, and the matrix entries indicate the presence (1) or absence (0) of a particular species in a particular site (McCoy and Heck 1987). In a nested matrix (Fig. 1A, 1B), species occurrences tend to overlap with one another and share many sites in common. In the extreme case of perfect nestedness, species will overlap maximally in their occurrence, so that the composition of small assemblages is a perfectly nested subset of the composition of larger assemblages. Nestedness was originally attributed to ordered extinc- tion on small islands (Patterson and Atmar 1986), but a pattern of nestedness can also be generated by differ- ential dispersal (Cook and Quinn 1998, Loo et al. 2002, McAbendroth et al. 2005), passive sampling (Andreń 1994, Fischer and Lindenmayer 2002, Higgins et al. 2006), differential habitat quality (Hylander et al. 2005), or nesting of habitats (Hausdorf and Hennig 2003, Wethered and Lawes 2005). In a segregated species occurrence matrix (Fig. 1C), species tend to occur with one another less frequently. In the case of a perfectly segregated matrix, many species pairs will form perfect ‘‘checkerboards’’ and never co-occur together (Diamond 1975). Many sites will contain unique combinations of species, but some Oikos 116: 2053
2061, 2007 doi: 10.1111/j.2007.0030-1299.16173.x, # The authors. Journal compilation # Oikos 2007 Subject Editor: Owen Petchey, Accepted 10 July 2007 2053 combinations will be consistently missing (Pielou and Pielou 1968). Checkerboard distributions and missing species combinations were originally attributed to species interactions (especially competition) or environ- mental filters, but these same patterns can also be generated by unique habitat associations (Peres-Neto et al. 2001), limited dispersal (Ulrich 2004), and also historical or evolutionary processes that prevent species from co-occurring in the absence of species interactions (Gotelli et al. 1997, Bloch et al. 2007). Patterns of nestedness and species co-occurrence are usually de- scribed as deviations from a statistical null model (Gotelli and Graves 1996), in which the pattern in an observed matrix is randomized to mimic the stochastic assembly of a community that is not constrained by species interactions (Gotelli 2001). Superficially, nestedness and segregated co-occur- rence would seem to be describing opposite patterns of community organization (see Leibold and Mikkelson 2002 and Almeida-Neto et al. 2007 for further discussion). However, two empirical meta-analyses of nestedness and co-occurrence in published presence- absence matrices have generated supposedly conflicting results. On the one hand, Wright et al. (1998) found that, by some tests, as many as 70% of their matrices were significantly nested. In contrast, Gotelli and McCabe (2002) used a large subset of these same matrices and found strong evidence for segregated species occurrences: many matrices exhibited more checkerboard species pairs and fewer species combina- tions than expected by chance. However, these compar- isons are complicated by the fact that the two analyses used different null models to test for co-occurrence and nestedness. In this paper, we systematically explore the relation- ship between nestedness and species co-occurrence by creating artificial data sets with specified amounts of species segregation, nestedness, or randomness. These matrices were then analyzed with the same set of null models to reveal the expected associations between nestedness and species co-occurrence. Material and methods Matrix types We created two types of random presence-absence matrices (200 matrices each) to study the properties of two randomization algorithms, three measures of co- occurrence, and one measure of nestedness. We created the first type of presence-absence matrices (MN) by randomly sampling individuals from a metacommunity in which population sizes of the species were distributed according to a lognormal species rank order distribu- tion: SS0e [a(RR0) 2] (1) in which S is the number of species, R is the abundance octave, S0 is the number of species in the modal octave R0, and a is the shape-generating parameter. For each matrix, the shape-generating parameter a was sampled randomly from a uniform distribution between 0.1 and 0.5 (a canonical lognormal has a0.2; May 1975). The size of each matrix was also determined by drawing two integers from a uniform distribution to establish the number of rows (m species) and the number of columns (n sites; 35m5200 and 35n550). A B C D Fig. 1. Four presence
absence matrices with ten species and five sites. In (A) the matrix is highly nested: only two species pairs (10 and 7, 10 and 9) form checkerboard distributions, and species 1 through 9 form a perfectly nested pattern. (B) is the typical product of a passive sampling from a metacommunity having a lognormal species
abundance distribution. (C) is a typical product of a sampling from an equiprobable distribution. The matrix in (D) has nearly the maximum number of checkerboards without any exclusive species combinations. It is highly disordered. Under the fixed
fixed model, the Brualdi and Sanderson nestedness index (BR) does not identify A, B, and C as being nested and does not identify D as being disordered (ZB2.0). The co-occurrence indices C-score (CS), number of checkerboard pairs (CH), and number of species combinations (CO) identify matrix C as being segregated (all Z10.0), but matrices (A), (B) and (C) as being random (2.0B ZB2.0). Note that matrix (A) is so highly nested and matrix (D) is so highly segregated that the fixed-fixed model cannot be applied to these extreme cases because there are too few matrix re-arrangements that satisfy the row and column constraints. 2054 Table 1. Numbers of scores of BR, CS, CH, and CO below or above the 95% confidence limits of matrices with small and medium increases (IN I and IN II)) or decreases (DN I and DN II) in the degree of nestedness. Manipulated scores are marked in grey. For each test, there were 200 matrices created. Metacommunity Null model Matrix type 95% confidence limits BR CS CH CO Below Above Below Above Below Above Below Above Lognormal Fixed-fixed Original 2 7 7 18 0 16 2 8 MN IN I 35 0 2 28 1 10 0 13 IN II 107 0 1 36 2 5 0 13 DN I 0 51 19 8 1 3 3 2 DN II 0 121 32 2 0 1 2 4 Equiprobable Original 194 0 195 1 38 58 0 154 IN I 196 1 196 1 40 57 0 148 IN II 196 0 197 1 41 50 0 148 DN I 195 0 197 1 41 55 0 153 DN II 192 2 197 1 42 48 0 141 Equal Fixed-fixed Original 2 2 4 0 1 3 3 1 ME IN I 18 0 11 0 0 3 6 0 IN II 68 0 18 0 0 12 3 1 DN I 0 21 0 7 4 5 2 12 DN II 0 54 0 23 6 3 1 12 Equiprobable Original 1 35 1 135 11 2 92 0 IN I 3 10 0 125 10 3 99 1 IN II 8 6 0 125 13 2 99 1 DN I 1 86 1 133 11 3 90 3 DN II 0 113 0 135 13 2 86 1 2 0 5 7 Table 2. Numbers of scores of BR, CS, CH, and CO below or above the 95% confidence limits of matrices with small and medium increases (IN I and IN II)) or decreases (DN I and DN II) in species co-occurrence. Manipulated scores are marked in grey. For each test, there were 200 matrices created. Metacommunity Null model Matrix type 95% confidence limits BR CS CH CO Below Above Below Above Below Above Below Above Lognormal Fixed-fixed Original 4 5 5 26 0 13 1 11 MN IC I 3 14 46 1 0 5 6 4 IC II 0 18 117 0 0 2 8 4 DC I 14 4 1 73 0 13 1 19 DC II 10 3 0 131 0 12 1 15 Equiprobable Original 196 0 197 0 50 52 0 143 IC I 196 0 198 0 57 43 0 144 IC II 195 1 197 0 59 42 0 146 DC I 198 0 196 1 55 48 0 144 DC II 197 0 196 1 54 51 0 144 Equal Fixed-fixed Original 2 2 5 7 5 0 0 5 ME IC I 5 1 30 1 1 0 9 1 IC II 10 1 73 0 0 2 16 1 DC I 2 4 0 24 1 3 0 16 DC II 1 7 0 70 1 7 0 27 Equiprobable Original 2 43 1 124 11 4 90 3 IC I 1 30 3 116 14 1 99 2 IC II 3 22 4 113 5 4 104 3 DC I 0 44 0 134 9 7 82 3 DC II 0 58 1 139 15 6 74 9 2 0 5 8 nestedness, 12% had CS scores smaller than expected by chance. In contrast, CH and CO were largely unaffected by the changes in nestedness. Between 0.5 and 10% of the matrices fell beyond the 95% confidence limits of the null model. The equiprobable null model, in turn, was insensitive to changes in nestedness while pointing to high degrees of non- random co-occurrences (CS, CH and CO) irrespective to the degree of nestedness. The increase or decrease in species co-occurrence (measured by CS) had little effect on the performance of BR (Table 2). Between 2 and 10% of the matrices were identified as being significantly nested or dis- ordered. For the MN matrices, BR and CS were negatively correlated, and for the ME matrices BR and CS were positively correlated (Table 2). Discussion Fig. 2A and 2B clarify the general relationships that are to be expected between nestedness and species co- occurrence. In the simplest and most general case (Fig. 2B), we created random matrices by sampling from row and column distributions that were uniform. For this set of matrices, high levels of nestedness are associated with low levels of species segregation, which matches our intuition about how these two metrics should behave. However, if random matrices are created by sampling from log-normal species abundance distribu- tions, the relationship reverses (Fig. 2A), and matrices with high levels of nestedness are associated with high levels of species segregation. This counterintuitive behaviour might point to some shortcomings in our understanding of co-occurrence within a presence- absence matrix. Leibold and Mikkelson (2002) analyze a broader range of patterns, and distinguish between patterns of coherence, species turnover, and boundary clumping in presence-absence matrices. They and Almeida-Neto et al. (2007) argue for a negative correlation between the degrees of nestedness and species segregation. However, our results show that this relationship depends on the way the matrix was constructed (particularly on matrix fill). The analyses presented here support previous studies (Gotelli 2000, Ulrich and Gotelli 2007) suggesting that the fixed-fixed model is superior to the equiprobable model for both nestedness and co-occurrence analyses. Our results also corroborate recent critiques of the equiprobable model by Fischer and Lindenmayer (2002), Rodrı́guez-Gironés and Santamarı́a (2006) and Ulrich and Gotelli (2007), who all found that this model is prone to sampling artefacts. Although the fixed-fixed model has good statistical properties when tested with most kinds of random matrices, there is a slight bias towards detecting segregated co-occurrence with the C-score and the fixed-fixed model at high values of matrix fill (Fig. 3A) and size (Fig. 3B). The CS metric should be used with care for large matrices (nm 2500) and/or matrices that are highly filled (50%). In these cases the more conservative CH and CO metrics appeared to be more appropriate. However, Gotelli and McCabe (2002) did not find an effect of matrix fill in their meta- analysis of co-occurrence patterns, although matrix size was weakly correlated with effect size. Our results help to interpret the previous meta- analyses of Wright et al. (1998) and Gotelli and McCabe (2002). The most important difference be- tween these studies is that the Wright et al. (1998) study found that nestedness was widespread when tested with the nestedness temperature calculator. However, both the metric and the randomization algorithm in the nestedness calculator have since been shown to be -4 -2 0 2 4 6 -6 -4 -2 0 2 4 6 -6 -4 -2 0 2 4 6 Z-BR Z -C S Z -C S A -6 -4 -2 0 2 4 6 Z-BR B Fig. 2. Dependence of the C-score co-occurrence index (CS) on the Brualdi and Sanderson nestedness index (BR). In both cases, the patterns are measured as standardized Z-scores. 200 initial matrices were created in each case, and then the degree of nestedness was artificially increased (200 matrices) or decreased (200 matrices) by sequential swapping of subma- trices. (A) 200 initial matrices created by passive sampling (MN) from a log-normal species abundance distribution. (B) 200 initial matrices created by simple sampling (ME) from uniform distributions of species and site occurrences. (A) R20.30; pB0.0001. (reduced major axis regression CS 0.77 BR0.36. (B) R20.32; pB0.0001; CS0.08 0.66 BR. 2059