A consumer's guide to nestedness analysis

Nestedness analysis has become increasingly popular in the study of biogeographic patterns of species occurrence. Nested patterns are those in which the species composition of small assemblages is a nested subset of larger assemblages. For species interaction networks such as plant–pollinator webs, nestedness analysis has also proven a valuable tool for revealing ecological and evolutionary constraints. Despite this popularity, there has been substantial controversy in the literature over the best methods to define and quantify nestedness, and how to test for patterns of nestedness against an appropriate statistical null hypothesis. Here we review this rapidly developing literature and provide suggestions and guidelines for proper analyses. We focus on the logic and the performance of different metrics and the proper choice of null models for statistical inference. We observe that traditional 'gap-counting' metrics are biased towards species loss among columns (occupied sites) and that many metrics are not invariant to basic matrix properties. The study of nestedness should be combined with an appropriate gradient analysis to infer possible causes of the observed presence–absence sequence. In our view, statistical inference should be based on a null model in which row and columns sums are fixed. Under this model, only a relatively small number of published empirical matrices are significantly nested. We call for a critical reassessment of previous studies that have used biased metrics and unconstrained null models for statistical inference.     

A comparative evaluation of sequence classification programs

Background

Here we present two new computer tools, PREMIM and EMIM, for the estimation of parental and child genetic effects, based on genotype data from a variety of different child-parent configurations. PREMIM allows the extraction of child-parent genotype data from standard-format pedigree data files, while EMIM uses the extracted genotype data to perform subsequent statistical analysis. The use of genotype data from the parents as well as from the child in question allows the estimation of complex genetic effects such as maternal genotype effects, maternal-foetal interactions and parent-of-origin (imprinting) effects. These effects are estimated by EMIM, incorporating chosen assumptions such as Hardy-Weinberg equilibrium or exchangeability of parental matings as required.

Results

In application to simulated data, we show that the inference provided by EMIM is essentially equivalent to that provided by alternative (competing) software packages such as MENDEL and LEM. However, PREMIM and EMIM (used in combination) considerably outperform MENDEL and LEM in terms of speed and ease of execution.

Conclusions

Together, EMIM and PREMIM provide easy-to-use command-line tools for the analysis of pedigree data, giving unbiased estimates of parental and child genotype relative risks.     

Significance test for comparing complex microbial community fingerprints using pairwise similarity measures

Modern electrophoresis techniques are often applied to investigate complex microbial communities. Analysis systems like GelCompare transform the optical pattern of the electrophoresis lanes into high-dimensional observation vectors and calculate measures of difference or similarity between pairs of lanes. Usually, these measures are applied in cluster analyses. Here, we apply permutation tests for the comparison of groups of lanes based on these pairwise measures together with some extensions for a combined analysis of several electrophoresis gels. The procedures are available as a computer program. An example is given for the comparison of bacterial soil communities, testing the effect of different crop plants. Each community was represented by amplified ribosomal gene fragments separated in a denaturing gradient gel.     

Evaluation of jackknife and bootstrap for defining confidence intervals for pairwise agreement measures

Several research fields frequently deal with the analysis of diverse classification results of the same entities. This should imply an objective detection of overlaps and divergences between the formed clusters. The congruence between classifications can be quantified by clustering agreement measures, including pairwise agreement measures. Several measures have been proposed and the importance of obtaining confidence intervals for the point estimate in the comparison of these measures has been highlighted. A broad range of methods can be used for the estimation of confidence intervals. However, evidence is lacking about what are the appropriate methods for the calculation of confidence intervals for most clustering agreement measures. Here we evaluate the resampling techniques of bootstrap and jackknife for the calculation of the confidence intervals for clustering agreement measures. Contrary to what has been shown for some statistics, simulations showed that the jackknife performs better than the bootstrap at accurately estimating confidence intervals for pairwise agreement measures, especially when the agreement between partitions is low. The coverage of the jackknife confidence interval is robust to changes in cluster number and cluster size distribution.     

A null model for randomization tests of nestedness in species assemblages

Analysis of the degree of order in species assemblages in terms of nested subsets has received increased interest during the last decade. However, recently a series of papers have questioned the validity of methods employed for testing whether observed patterns deviate from random expectations. The current view seems to be that the randomization procedure should control for both number of species per site and species frequencies. The randomization procedures used also choose to keep the total number of observations constant in each resample. In this paper I question some of these assumptions when analyzing species-by-site matrices for detecting whether the biota is significantly nested or not. My basic assumption is that the observed species frequency is only an estimate of the probability of occurrence for the particular species. For a test of degree of nestedness all sites should be regarded as being equal. To what extent size, isolation or habitat quality may influence species distribution is a secondary question if nestedness can be statistically proven. This implies that generation of random matrices should only consider the frequency of the species (as an estimate of their probability of occurring in any patch). Such matrices are computationally simple and besides providing a test of nestedness also open the possibility of testing whether the range in species richness is smaller or larger than expected under random expectations. The choice of null model for the test should always be viewed in relation to the question asked. If nestedness is concerned the methods proposed here should be used. However, if other questions are at hand the restrictions of previous approaches may be valid. This is for instance the case if pairwise species co-occurrences are analyzed. In this case, the richness of each site should obviously be incorporated in the randomization to control for the higher probability of co-occurrence at species-rich sites.     

Statistical evaluation of pairwise protein sequence comparison with the Bayesian bootstrap

MOTIVATION: Protein sequence comparison methods are routinely used to infer the intricate network of evolutionary relationships found within the rapidly growing library of protein sequences, and thereby to predict the structure and function of uncharacterized proteins. In the present study, we detail an improved statistical benchmark of pairwise protein sequence comparison algorithms. We use bootstrap resampling techniques to determine standard statistical errors and to estimate the confidence of our conclusions. We show that the underlying structure within benchmark databases causes Efron's standard, non-parametric bootstrap to be biased. Consequently, the standard bootstrap underpredicts average performance when used in the context of evaluating sequence comparison methods. We have developed, as an alternative, an unbiased statistical evaluation based on the Bayesian bootstrap, a resampling method operationally similar to the standard bootstrap. RESULTS: We apply our analysis to the comparative study of amino acid substitution matrix families and find that using modern matrices results in a small, but statistically significant improvement in remote homology detection compared with the classic PAM and BLOSUM matrices. AVAILABILITY: The sequence sets and code for performing these analyses are available from http://compbio.berkeley.edu/. Contact: brenner@compbio.berkeley.edu.     

A comparative evaluation of models of cinnabar moth dynamics

Summary 1. A complex model of cinnabar moth dynamics proposed by Dempster and Lakhani (1979) with 23 parameters is reduced to a single equation with five parameters, and the behaviour of the reduced model shown to explain most features of the full model. 2. The efficiency of the full model is compared with the reduced model and with two even simpler models (the two parameter discrete logistic and a four parameter model based on a step-function for mortality) in their abilities to describe time series data of cinnabar moth population densities from Weeting Heath. Models with more parameters were not significantly better than few-parameter models in describing population trajectories. 3. Models that included a driving variable (in this case observed rainfall data) were no better at describing the data than simpler models without driving variables. It appears, therefore, that the routine inclusion of driving variables may be counterproductive, unless there is compelling empirical or theoretical evidence of their importance and the mode of action of the driving variables can be modelled mechanistically. For example, the regression model used to describe the relationship between rainfall and plant biomass in Dempster and Lakhani (1979), breaks down if rainfall is assumed to be constant, because there is no explicit model for the regulation of plant biomass. 4. The parameter values of the cinnabar-ragwort interaction suggest that cinnabar moth dynamics may be chaotic. Whether or not field data exhibit chaos or environmental stochasticity (or a mixture of both) is impossible to determine from inspection of time series data on population density. There is an urgent need for experimental and theoretical protocols to disentangle these two sources of population fluctuation.     

A neutral‐niche theory of nestedness in mutualistic networks

Recently, there has been a vigorous interest in community ecology about the structure of mutualistic networks and its importance for species persistence and coevolution. However, the mechanisms shaping mutualistic networks have been rarely explored. Here we extend for the first time the neutral theory of biodiversity to a multi trophic system. We focus on nestedness, a distinctive pattern of mutualistic community assembly showing two characteristics, namely, asymmetrical specialization (specialists interacting with generalists) and a generalist core (generalists interacting with generalists). We investigate the importance of relative species abundance (RSA) for the nested assembly of plant–animal mutualistic networks. Our results show that neutral mutualistic communities give rise to networks considerably more nested than real communities. RSA explains 60–70% of nested patterns in two real communities studied here, while 30–40% of nestedness is still unexplained. The nested pattern in real communities is better explained when we introduce interaction‐specific species traits such as forbidden links and intensity of dependence (relative importance of fruits for the diet of a frugivore) in our analysis. The fact that neutral mutualistic communities exhibit a perfectly nested structure and do not show a random or compartmentalized structure, underlines the importance of RSA in the assembly of mutualistic networks.     

A comparative evaluation of cinecoronarography and digital subtraction coronarography

The results of cinecoronarography (cine-CG) and computerized subtraction angiography (CSA) in 60 CHD patients were analyzed. The percentage of narrowing of the coronary arterial diameter, the percentage of a stenosed area, the minimum diameter of a stenosed part and the extent of lesion were determined. Insignificant correlation was noted in important categories of lesions of medium extent and expression resulting from lesser spatial resolution of CSA.     

Toward ecologically explicit null models of nestedness

A community is nested when species assemblages in less rich sites form nonrandom subsets of those at richer sites. Conventional null models used to test for statistically nonrandom nestedness are under- or over-restrictive because they do not sufficiently isolate ecological processes of interest, which hinders ecological inference. We propose a class of null models that are ecologically explicit and interpretable. Expected values of species richness and incidence, rather than observed values, are used to create random presence-absence matrices for hypothesis testing. In our examples, based on six datasets, expected values were derived either by using an individually based random placement model or by fitting empirical models to richness data as a function of environmental covariates. We describe an algorithm for constructing unbiased null matrices, which permitted valid testing of our null models. Our approach avoids the problem of building too much structure into the null model, and enabled us to explicitly test whether observed communities were more nested than would be expected for a system structured solely by species-abundance and species-area or similar relationships. We argue that this test or similar tests are better determinants of whether a system is truly nested; a nested system should contain unique pattern not already predicted by more fundamental ecological principles such as species-area relationships. Most species assemblages we studied were not nested under these null models. Our results suggest that nestedness, beyond that which is explained by passive sampling processes, may not be as widespread as currently believed. These findings may help to improve the utility of nestedness as an ecological concept and conservation tool.     

Disentangling community patterns of nestedness and species co-occurrence

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).     

A maximum-likelihood estimation of pairwise relatedness for autopolyploids

Relatedness between individuals is central to ecological genetics. Multiple methods are available to quantify relatedness from molecular data, including method-of-moment and maximum-likelihood estimators. We describe a maximum-likelihood estimator for autopolyploids, and quantify its statistical performance under a range of biologically relevant conditions. The statistical performances of five additional polyploid estimators of relatedness were also quantified under identical conditions. When comparing truncated estimators, the maximum-likelihood estimator exhibited lower root mean square error under some conditions and was more biased for non-relatives, especially when the number of alleles per loci was low. However, even under these conditions, this bias was reduced to be statistically insignificant with more robust genetic sampling. We also considered ambiguity in polyploid heterozygote genotyping and developed a weighting methodology for candidate genotypes. The statistical performances of three polyploid estimators under both ideal and actual conditions (including inbreeding and double reduction) were compared. The software package POLYRELATEDNESS is available to perform this estimation and supports a maximum ploidy of eight.     

A comparative evaluation of Cephalosporin C production using various immobilization modes

The production of Cephalosporin C was investigated in a lab-scale 1.4 l air-lift reactor (ALR), using various immobilization modes. Bioparticles were developed by forming biofilm of growing hyphae around an inorganic siran particle which contained spores of the organism. Silk sachet was the other immobilization matrix. The maximum specific growth rate of the Cephalosporium acremonium, free cells, pellets, siran carrier and silk sachets were 0.037, 0.003, 0.047, and 0.035 h(-1), and specific antibiotic productivities (as compared to 100% for free cells) were 180, 150, and 125% for siran carrier, silk sachets and pellets, respectively. Immobilization modes exhibited enhanced volumetric oxygen transfer coefficient and well-controlled, three-phase hydrodynamics.