Disparities in the analysis of morphological disparity

Analyses of morphological disparity have been used to characterize and investigate the evolution of variation in the anatomy, function and ecology of organisms since the 1980s. While a diversity of methods have been employed, it is unclear whether they provide equivalent insights. Here, we review the most commonly used approaches for characterizing and analysing morphological disparity, all of which have associated limitations that, if ignored, can lead to misinterpretation. We propose best practice guidelines for disparity analyses, while noting that there can be no ‘one-size-fits-all’ approach. The available tools should always be used in the context of a specific biological question that will determine data and method selection at every stage of the analysis.


Introduction
Clades of organisms are characterised by variation in both numbers of species and range of phenotypes through time. At the extremes, clades may be exceptionally rich in species and phenotypic diversity (hereafter disparity) (e.g. cichlids or molluscs), species-rich but disparitypoor (e.g. rodents or nematodes), species-poor but rich in disparity (e.g. afrotherian mammals), or depauperate in both species diversity and disparity (e.g. lungfish). These phenomena suggest that taxonomic diversity and phenotypic disparity are not inextricably linked, raising important questions, such as: How does disparity evolve? Are some morphologies more common than others? Is anatomical evolution unbounded or are some anatomies impossible to achieve? What role does ecology play in structuring disparity? Analyses of species diversity have a venerable history, but those of disparity are comparatively more recent. Originally defined as "multidimensional morphological dissimilarity at a macroevolutionary scale" [1,2], the concept of disparity emerged from attempts by palaeobiologists to characterise the evolutionary origin of animal bodyplans and from attempts by comparative developmental biologists to provide causal explanations for their emergence. However, disparity analyses have since expanded into comparative biology as a means of capturing how intrinsic and extrinsic causal agents affect morphological evolution. Typically, methods to capture disparity are based on multidimensional spaces where each dimension represents an aspect of morphological variation (a trait) and biological observations (e.g. taxa) can be placed in this space based on their trait values. Such multidimensional spaces (or morphospaces -defined broadly hereafter as a mathematical space relating morphological configurations generally based on some measure of similarity [3]) can then be used to tackle a diverse array of questions that can be grouped into four main (nonmutually exclusive) classes: 1.
Descriptive disparity. Pioneering studies of disparity characterised the shapes of organisms and how they differed among groups [4,5]. These studies described multidimensional patterns in morphological trait diversity by addressing pertinent questions: why are some morphological trait combinations more common than others, and what are the biological (or mathematical) properties of the resulting morphospace? [4,6,7]. More recently, this approach has been used to understand the relationship between developmental processes and morphology in the field of evolutionary development (evo-devo). For example, patterns of disparity have been used successfully to compare modules of evolution in various groups [8,9], allowing researchers to link variation in shape to a group's evolutionary or developmental constraints [10].
2. Disparity through time. This approach investigates how the morphologies of organisms have changed over time, by focussing on the disparity of taxa in particular time intervals or slices. This approach has been used widely in palaeobiology to answer a range of macroevolutionary questions, such as: how does disparity accumulate over the history of a clade [11][12][13], or how does disparity change up to and across mass extinction events [14]?
3. Disparity and taxonomic diversity. Morphological disparity provides another perspective on biodiversity; high morphological disparity represents a high diversity of morphologies (i.e. shapes or body plans) and is, presumably, associated with high levels of ecological and functional diversity (but see [15]). This makes disparity an informative complement to diversity measures based on species richness alone. Indeed, most studies that have investigated disparity and taxonomic diversity support an effective decoupling of the two (e.g. [16,17]). The approach has been used to investigate whether some groups are more successful than others in their exploration of new evolutionary strategies [18].
4. Disparity as a proxy for ecology. The disparity of a group can be used as a proxy for either the functional role it plays within an ecosystem or its ecological niche. This approach assumes that groups with high disparity are also likely to be functionally and ecologically diverse, and that groups found in similar regions of shape space will have similar functional and ecological roles [14,19]. The links between form and function, however, are not always clear. Traits can be linked to multiple functions and multiple functions can be linked to a single trait [20]. This approach has been used to investigate hypotheses of competitive replacement [21] and changes in ecosystem function during and after mass extinctions [14].
It is one of the primary ways to investigate ecosystem functioning in palaeobiology when the study species (and their functional characteristics) are extinct [20].
Fundamental insights into evolutionary biology have been elicited from these four types of disparity analysis. One of the most important insights is the discovery that morphological disparity is often greatest early in the evolutionary history of clades [22][23][24], indicating that capacity for evolutionary innovation wanes as clade age, which some have argued reflects the evolutionary assembly of gene regulatory networks that constrain later fundamental change [23,24]. However, this example also highlights one of the greatest challenges confronting researchers who are attempting, increasingly, to obtain general insights from multiple independent studies: can the insights gained from studies using a diversity of methods, approaches and data types be considered equivalent?
In attempting to answer this question, we review current methods and highlight their limitations, as part of a more general attempt to propose best practice guidelines for studies of disparity. We first discuss the appropriate data required for characterising disparity, then review various challenging aspects of these approaches. Throughout, it is important to remember that these tools should always be used in the context of a specific scientific question, as this will drive data and methodological choices at every stage of the process.

Data and disparity
Disparity analyses are based on traits, but traits can be characterised in a number of ways: 1) discrete morphological characters, e.g. coding the absence or presence of features or a discrete characteristic of a trait (e.g. [25,26]); 2) continuous measurements of features (e.g. lengths in [14]); or 3) more mathematical descriptors from geometric morphometric landmark data (e.g. The points above assume that researchers are collecting their own data for disparity analyses, but this is often not the case. Discrete characters are commonly recycled from phylogenetic studies (e.g. [11,32]). This approach may artifactually increase disparity between phylogenetically distinct groups, since phylogenetic characters are often collected to discriminate among groups.
This needs to be considered when interpreting results, especially as synapomorphies can lead to apparent shifts or increases in disparity when new clades appear (particularly if the characterstate distribution is skewed towards a particular clade). Furthermore, many datasets are limited to subsets of anatomy that are at least implicit samples of overall anatomy, but explicit tests of this assumption have shown that different aspects of morphology can exhibit different patterns of disparity [31]. The influence of trait choice on resulting disparity patterns can be especially challenging where the available data has non-random missing anatomical parts, such as the absence of soft tissue in the fossil record [26].
Ultimately, disparity analyses are characterised by the data they use. Unfortunately, trait data suffer from the same shortcomings as most biological datasets. The data within them can be nonoverlapping, hierarchical, inapplicable, ambiguous, polymorphic, and/or correlated [33]. There are also issues of missing data, both where a particular character cannot be measured for a given taxon, or where a given taxon cannot be sampled at all. Trait data may also be influenced by biological phenomena such as allometry and sexual dimorphism. More practically, data collection is constrained by the time and money available, making collating a "perfect" dataset impossible.
Even when care is taken, subsamples of the universe of possible data may not have the power to uncover the full patterns of disparity. These issues should be considered when collecting data. It is particularly important to collect trait data with the scientific question in mind, or, where there are limits on the data available, to tailor the question being asked to match the data.

Disparity analysis methods
Once suitable trait data have been collected, the design of the disparity analysis itself needs to be considered. Study design encompasses several key aspects including 3.1 the difficulty of dealing with multidimensional data; 3.2 the indices used to summarise the relative disparity of groups; 3.3 the methods used for hypothesis testing within the disparity analysis framework; and 3.4 the influence of phylogeny on disparity analyses. We consider these aspects in order below. should not be overlooked when using PCO.
One of the reasons why ordination techniques are common in disparity analysis is that they make it easier for researchers to comprehend patterns in two or three spatial dimensions at a time, which can be more intuitive than through disparity indices (see section 3.2 below). Additionally, after ordinating the data, it is possible to focus on just a subset of axes of the morphospace (i.e. selecting only those axes that describe the majority of the variation in the dataset -e.g. 95%). In Like most other aspects of disparity analyses, however, reducing dimensionality can be fraught.
In the case of ordination, subsampling axes from the ordination can lead to misinterpretation of the results. Although a common technique is to consider the d axes that encompass 95% or 99%

(d) Disparity and phylogeny
As with all comparative datasets, the data used in disparity analyses are not independent because close relatives will tend to have more similar morphologies than more distant relatives [60]. Thus, for disparity analyses that consider groups with phylogenetic relationships (which is common), the non-independence between observations should be taken into account. It has been noted, however, that some popular phylogenetic correction methods (like phylogenetic PCA) can be inappropriate, especially when using only the first d axes of the ordination, and can lead to incorrect interpretations of the data (such as wrongly supporting "early burst" type One other common way to take phylogeny into account in disparity analyses is using ancestral state estimations in disparity through time analyses to extract disparity estimates for nonsampled taxa and/or nodes of a phylogeny [13,64]. Ancestral state estimation can be performed at two points in the disparity analysis pipeline: either (1) pre-transformation, i.e. the estimation is done before transformation of the data (e.g. ordination, or distance matrix construction) and is simply based on the original data; or (2) post-transformation, i.e. the estimation is done after transformation of the data by estimating the ancestral states using the transformed matrix (e.g. the ordination scores; [44]).
Pre-transformation ancestral state estimation will change the way the ordination space is defined -i.e. the relationship between the points is not yet estimated -and requires longer computational times. However, once the morphospace is defined, its properties will not change.
Post-transformation ancestral state estimation will not change the empirical ordination space and is faster to compute, but it will add elements in the space, whose estimated positions can be

Disparity analyses for the future
Morphological disparity analyses are widely employed in evolutionary palaeobiology, and are based on a diversity of methods and data. There is no "one-size-fits-all" pipeline for morphological disparity analyses. As with any multidimensional analysis, there are many variables that have to be considered when deciding which data to use and how to analyse them, stemming from the explicit hypotheses being tested. Although this makes comparison between disparity analyses difficult and renders premature attempts to achieve the generalisation required to answer the broad biological questions (e.g. how does phenotypic variation evolves?), this diversity of methodological approaches provides researchers with a great number of tools tailored to answer specific biological questions.
Many of the problems in morphological disparity analysis arise from "blind" application of represented as an isotope-space; ecosystem functioning in [70] as an ecosystem-space [75], etc.
These generalisations could also be exported for any set of traits: cognate approaches have been adopted in the analysis of single cell comparative transcriptome data [76] where interpretation of the resulting transcriptome-spaces would be improved by giving careful attention to the concerns we highlight concerning morphospaces.
Although disparity analyses are now simple to implement in freely available software [43,[66][67][68][69] it is crucial to remember that they are multidimensional analyses and that multidimensional analyses are complex. We assert that future morphological analyses will benefit from emphasising the methodological decisions made, rather than simply using disparity analysis because it exists.

Data accessibility
No data was is used in this paper.

Author contributions
TG, NC and PD proposed this review; TG and NC led the writing supported by PD and GT. All authors edited drafts and approved the final version.

Competing interests
We have no competing interests.    Visualisations can use either trait plots (directly from the trait matrix); or ordination axis plots (directly from the ordinated matrix). Note that in 2D representations, it is good practice to plot both axes on the same scale to avoid visually distorting the importance of one axis).