Imagine going for a swim on a shallow reef. You might see mantis shrimp striking at fish or snails, and reef fish gulping down smaller fish and plankton. Despite how different these movements are, rapid mantis shrimp strikes and fish suction are guided by the same mechanics: four-bar linkages. These shared mechanical systems evolved independently, much like the wings of birds and butterflies. Certain researchers study how organisms evolve based on biomechanics, the field of science that applies principles from mechanics to study biological systems.

Four-bar linkages, which are widespread in nature, consist of a loop made of four bars (or links) connected by four joints. The system allows a wide range of motions, and it is found anywhere from oil pumpjacks to the inside of the human knee. Researchers are interested in how similar mechanical systems like four-bar linkages influence the diversification of distantly related organisms, such as fish and crustaceans.

Changes in an element of a four-bar linkage can have widely different consequences because of a phenomenon known as mechanical sensitivity. Modifications of highly mechanically sensitive parts will have a dramatic effect on the system, while alterations in other areas have little or no effect.

Whether the most mechanically sensitive parts evolve faster or slower than the less sensitive elements is still up for debate. Changes in the sensitive elements could be severely constrained because these modifications may compromise the survival of the organisms. However, they could also help species adapt quickly to new environments. So far, researchers have found that in the four-bars linkage of the mantis shrimp, the most mechanically sensitive parts evolve the fastest. Yet, it was unclear whether this would also apply to other species.

Here, Muñoz et al. compared four-bar linkages in three families of fish and in mantis shrimp, and discovered that the most mechanically sensitive elements are the smallest links. These can undergo changes in length that have a strong impact on how the linkage works. In addition, evolutionary analyses showed that the most mechanically sensitive parts do indeed evolve the fastest in both mantis shrimp and fish. More work is now required to see if this pattern holds across various organisms, and if it can be considered as a general principle that drives evolution.

The uneven tempo of phenotypic evolution is a universal feature of biological systems, from proteins to whole-organism traits (Simpson, 1944; Gingerich, 2009; Zhang and Yang, 2015). Intrinsic and extrinsic mechanisms affecting rates of evolution have been probed extensively (Wake et al., 1983; Gillooly et al., 2005; Eberhard, 2010; Zhang and Yang, 2015). However, biomechanics – the intersection of mechanics and biology – is a key axis influencing phenotypic evolution (Arnold, 1992) that has been less often examined, and infrequently through the use of quantitative and comparative datasets (Holzman et al., 2012; Wainwright et al., 2012; Collar et al., 2014; Muñoz et al., 2017). Because rates of morphological divergence and speciation are often coupled (Rabosky and Adams, 2012), connecting biomechanics to morphological evolution enriches our understanding of the processes shaping diversification.

An enduring paradox in evolutionary biomechanics and functional morphology is whether strong correlations among traits (sometimes termed constraints) enhance or limit evolutionary diversification (Gould, 1989; Antonovics and van Tienderen, 1991; Schwenk, 1994). For example, strong morphological correlations could be predicted to reduce the rate or amount of morphological evolution, because even slight changes could compromise the system’s proper functioning (Raup and Gould, 1974). Conversely, a strong correlation could enhance evolutionary change by providing a morphological pathway for adaptation (Holzman et al., 2012; Muñoz et al., 2017). A weak association could enhance the freedom to vary (Collar et al., 2014; Schaefer and Lauder, 1996), or, conversely, weaken, and thereby reduce, the pathways to morphological change (Alfaro et al., 2005; Collar and Wainwright, 2006). Therefore, depending on the context, strong and weak correlations have been construed to enhance or restrict evolutionary diversification. A comparative approach can empirically resolve this conundrum, for example, by comparing rates and phylogenetic patterns of morphological evolution in similar, independently-evolved systems.

Here, we leverage the multiple independent evolutionary origins of four-bar linkage systems (Figure 1) to test how morphological and mechanical correlations impact two key aspects of morphological evolution: tempo (rate at which morphological disparity accumulates) and mode (evolutionary pattern of trait shifts across phylogeny). Four-bar linkages are closed-chain systems comprised of four rigid links that rotate to transmit motion and force (Anker, 1974; Muller, 1996; Westneat, 1990; Martins, 1994) (Figure 1A). Mechanical output of four-bar linkages is often measured in terms of kinematic transmission (KT), a simple metric that can quantify a tradeoff between displacement and force across different linkage configurations (see Materials and methods section for further information about KT). Four-bar linkages are widespread in nature, and enable a rich diversity of behaviors in vertebrates and invertebrates (Westneat, 1990; Wainwright et al., 2005; Patek et al., 2007; Olsen and Westneat, 2016). For example, four-bar linkages actuate mouth opening for suction feeding in fishes (Westneat, 1990; Martins, 1994; Muller, 1987), flexion and extension of the vertebrate knee (Hobson and Torfason, 1974), rapid strikes of the stomatopod raptorial appendage (Patek et al., 2004; Patek et al., 2007; McHenry et al., 2012; McHenry et al., 2016), and skull kinesis in birds (Hoese and Westneat, 1996).

Figure 1

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Four-bar linkages, like any system built of three or more parts, exhibit many-to-one mapping, meaning that similar mechanical outputs (e.g. KT) can be produced through different combinations of morphology (e.g. link lengths; Wainwright et al., 2005; Wainwright, 2007). Four-bar linkages also exhibit mechanical sensitivity, which occurs when KT is disproportionately sensitive to variation in some links and relatively insensitive to variation in others (Anderson and Patek, 2015; Muñoz et al., 2017). Therefore, four-bar linkages exhibit (1) both weak and strong correlations among parts and outputs and (2) multiple evolutionary origins across the Metazoa. As such, four-bar linkages are a fertile testing ground for comparative analyses of evolutionary biomechanics and morphology.

To our knowledge, the connection between mechanical sensitivity and morphological evolution has only been studied in the four-bar linkage system of the mantis shrimp (Stomatopoda) raptorial appendage (Muñoz et al., 2017; Anderson and Patek, 2015) (Figure 1). The mantis shrimp four-bar system is used for feeding, fighting, and substrate manipulation via extremely rapid strikes of their raptorial appendages (Patek et al., 2004;Patek et al., 2007; Patek et al., 2013; Patek and Caldwell, 2005; McHenry et al., 2016; deVries et al., 2012; Green and Patek, 2015; Green and Patek, 2018; Crane et al., 2018). Spearing stomatopods that harpoon mobile, soft-bodied prey have higher KT (greater displacement) than smashing mantis shrimp that bludgeon hard-shelled prey using linkages with lower KT (greater force) (Anderson et al., 2014; McHenry et al., 2016). In mantis shrimp, mechanical sensitivity is associated with accelerated evolution: the link most tightly correlated with KT exhibits the fastest rate of evolution (Muñoz et al., 2017).

Tantalizing patterns often occur in individual clades or mechanical systems, yet few are robust to tests in multiple lineages. Therefore, previous findings in mantis shrimp leave uncertain whether the enhanced evolutionary rate associated with mechanical sensitivity is a system-specific finding or instead occurs across an array of taxa and reflects a more general pattern. Furthermore, the initial studies in mantis shrimp were analyses of evolutionary tempo, but the phylogenetic pattern of these rate changes (mode) was not analyzed. Analysis of mode can resolve whether phylogenetic shifts to a higher or lower KT are exclusively accompanied by shifts in link(s) to which KT is most sensitive, or occur through different morphological pathways that are not necessarily tied to mechanical sensitivity.

Here we examine rates of morphological evolution (tempo) in four particularly well-studied systems (Figure 1): (1) oral four-bar linkages of 101 species of wrasses (Family: Labridae) and (2) oral four-bar linkages of 30 species of cichlids (Family: Cichlidae), (3) opercular four-bar systems in 19 species of sunfish (Family: Centrarchidae) and (4) the previously-published dataset in mantis shrimp that was analyzed using the same methods as in this study. In fish, the oral four-bar system actuates the upper jaw and the opercular four-bar actuates the lower jaw (Figure 1); together they open a large space in the mouth that creates negative pressure to suction prey (Westneat, 1990; Martins, 1994). Similarly to mantis shrimp (Anderson et al., 2014; Anderson and Patek, 2015), the mechanical tradeoffs between displacement and force represented by KT appear to generally track fish trophic ecology (Wainwright et al., 2004; Hulsey and Garcia De Leon, 2005). For example, fish that pursue elusive prey tend to have oral four-bar linkages with higher KT (resulting in greater displacement for snagging rapid prey), whereas those that scrape algae tend to have lower KT (resulting in greater force, such as for dislodging sessile, encrusted food items from hard surfaces) (Hulsey and Garcia De Leon, 2005). Finally, we examine the phylogenetic pattern (mode) of shifts in KT and links across the especially well-sampled oral four-bar system in wrasses, to test how KT and link lengths change across the phylogeny and whether these changes occur concordantly as predicted by mechanical sensitivity.

We estimated the Brownian motion evolutionary rate parameter, σ² (bounded by its 95% confidence interval), which represented the net rate of phenotypic change over time (Felsenstein, 1985; Martins, 1994; O'Meara et al., 2006) for the three mobile links – input, output, and coupler – of each four-bar system (See Materials and ethods). A single consistent result emerged from our analysis of evolutionary rates: stronger correlations between link lengths and kinematic transmission (KT) were associated with faster rates of morphological evolution. In each system, we found that mechanical sensitivity was always associated with a faster rate of link evolution (Figure 2; Supplementary file 1). Evolutionary rate can be artificially inflated by greater trait variance (O'Meara et al., 2006; Adams, 2013); we incorporated intraspecific measurement error into our rate estimates and confirmed that a higher evolutionary rate was not driven by greater variance (Supplementary file 2).

Figure 2

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Even though rates of morphological evolution consistently tracked mechanical sensitivity, the particular links associated with mechanical sensitivity differed across the four-bar systems (Supplementary files 3–6 [rotatable 3D phylomorphospace plots]; Table 1). For example, in the cichlid oral four-bar system, mechanical output was positively correlated with input link length (PGLS r²=0.62, p<10⁻⁶), inversely correlated with the coupler link length (r²=0.27, p=0.002), and exhibited no relationship with the output link length (Supplementary file 3; Table 1). By contrast, in three systems - the wrasse oral four-bar, the sunfish opercular four-bar, and the stomatopod raptorial four-bar - the output link length was a strong predictor of mechanical output (PGLS r²>0.66, p<10⁻¹¹), whereas the coupler link only weakly predicted mechanical output (PGLS r²<0.14) (Supplementary files 4–6). The oral four-bars of cichlids and wrasses share a common evolutionary origin (Alfaro et al., 2004); nonetheless, rate differences were predicted by mechanical sensitivity rather than shared ancestry. Hence, analogous four-bar systems do not result in common patterns of mechanical sensitivity, whereas mechanical sensitivity is consistently a strong predictor of evolutionary rate differences.

We next examined the phylogenetic pattern of trait shifts in KT and each mobile link in the wrasse oral four-bar system. We applied a Bayesian framework in the program bayou (Uyeda and Harmon, 2014) to reconstruct phylogenetic shifts in the Ornstein-Uhlenbeck (OU) optimal trait parameter (θ) for morphological components and mechanical output. The OU model of evolution is characterized by the presence of an adaptive peak, with the peak representing the optimal value for a given trait. Thus, θ reflects the evolutionary optimal trait value as inferred from an OU-process on the phylogeny. To be clear for interdisciplinary readers, θ is not a metric for calculating a biomechanically optimal trait for a certain mechanical function.

By estimating θ across the wrasse phylogeny, we pinpointed the nodes associated with strongly supported shifts to higher or lower values in KT and link size. We performed this analysis only on the largest and most species-rich dataset (wrasses: >100 species sampled), because evolutionary inferences are unstable with fewer than 50 taxa (Uyeda and Harmon, 2014). We detected three well-supported evolutionary shifts in KT (posterior probability [pp] range 0.65–0.99; Supplementary file 7) (Figure 3). For each of these shifts in mechanical output, we also detected strongly supported shifts in the output and input links, but never the coupler link (Figure 3; Figure 3—figure supplement 1). Therefore, the three shifts in KT occur through three different morphological pathways, but only via the changes in the links to which KT is most mechanically sensitive. The evolutionary shifts to higher mechanical output (increased KT) occur twice – once in razorfishes (pp = 0.67) and once in the branch leading to the Creole wrasse, Clepticus parrae (pp = 0.99). In razorfishes, the transition to higher KT is accompanied by a shift to a smaller output link (pp = 0.88), and in Creole wrasse, by both an increase in input link length (pp = 0.97) and a reduction in output link length (pp = 0.77). A transition to lower KT in the Anampses clade is accompanied by a reduction in input link length (pp = 0.95), with no concomitant shifts in output link length.

Figure 3 with 1 supplement see all

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Amidst the morphological, behavioral and ecological diversity of four-bar linkages, in every system we tested, greater mechanical sensitivity is associated with faster morphological evolution. The connection between mechanical sensitivity and evolutionary rate is therefore robust to independent origins and distinct behavioral functions, suggesting a generalizable phenomenon in four-bar linkage systems. These findings address a longstanding conundrum of constraints in evolution (discussed in Gould, 1989; Antonovics and van Tienderen, 1991; Schwenk, 1994) – specifically, whether strong correlations among traits should enhance or reduce evolutionary change – by demonstrating that strong correlations between components and mechanical output accelerate evolutionary change (Figure 4). Our results further reveal how many-to-one mapping and mechanical sensitivity enable multiple configurations while simultaneously biasing those configurations to a subset of traits.

Figure 4

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Both absolute and relative link sizes influence evolutionary rates, and the structural geometry of four-bar linkages is central to understanding these findings (Muller, 1996). In terms of absolute size, the same length change applied to small and large links is proportionally larger for the small link, such that KT is most influenced by the change to the small link. Therefore, changes to the smallest links induce disproportionately large changes in the system’s geometry and, therefore, the transmission of force and motion (Anderson and Patek, 2015; Hu et al., 2017). In terms of relative size, greater disparity among link sizes in a four-bar system results in greater evolutionary rate disparity. These effects of size are especially apparent in the stomatopod raptorial four-bar linkage and sunfish opercular four-bar linkage. In both of these systems, the output link is approximately an order of magnitude smaller than the input and coupler links, and it also exhibits an order of magnitude faster evolution (Supplementary file 1). In contrast, relative link lengths vary less dramatically in the oral four-bar system of cichlids and wrasses, and the corresponding evolutionary rate shifts are statistically weaker, although still exhibiting two- to four-fold rate differences (Figure 2; Supplementary file 1).

Biological sizes, whether of genomes, cells, or the organisms themselves, help sculpt macroevolutionary dynamics by influencing patterns of trait evolution or shaping deeper-scale patterns of lineage diversification (Hanken and Wake, 1993; Uyeda et al., 2017). Here, link size plays a central role in determining the physical basis for mechanical sensitivity and evolutionary rate disparity, indicating that size-scaling relationships in biomechanics can mediate evolutionary dynamics. Although we connect mechanical sensitivity to a relatively faster rate of evolution, an interesting next step is to disentangle whether such traits evolve more quickly because of strong directional selection on small links or whether the other, relatively larger traits of the system evolve more slowly due to stabilizing selection (Arnold, 1983; Arnold, 1992). Statistically comparing these two possibilities requires especially broad sampling: in the growing age of big data in digital morphology and phylogenetics, this task is rapidly becoming feasible (Davies et al., 2017).

Our analysis of the phylogenetic pattern (mode) of trait evolution exemplifies the integration of mechanical sensitivity and many-to-one mapping. An implicit assumption of many-to-one mapping is freedom of evolution: theoretically, any alternative configurations yielding a similar mechanical output should be equally likely to evolve (Wainwright et al., 2005; Wainwright, 2007). Our findings in wrasses, however, demonstrate that mechanical sensitivity biases evolutionary transitions to traits with the greatest influence on mechanical output (input and output links). For each of the three major KT shifts in wrasses, we detected three distinct morphological pathways involving either the input link, output link, or both (but never the coupler link). Correspondingly, both the output link and input link are strong predictors of KT in the wrasse oral four-bar, and the coupler is a weak predictor of KT. Among these links, there is some redundancy, as evidenced by the various morphological pathways accompanying transitions in KT. Therefore, mechanical sensitivity restricts the freedom of evolution central to many-to-one mapping by biasing evolutionary transitions to traits with the strongest effect on mechanical output.

When considered in the broader context of ecology and behavioral function, our findings raise as many questions as they answer. For example, if the shortest link is the output link, an animal achieves greater output rotation of the system than they input. Mantis shrimp use their shortest link (output link) to dramatically amplify an approximately nine-degree rotation of the input link; this enables the notoriously fast angular velocity of their predatory appendages (Patek et al., 2004,Patek et al., 2007; Cox et al., 2014; McHenry et al., 2016). In the centrarchids, the input rotation is controlled by a muscle too small to generate a large gape: instead they use linkage geometry to amplify gape (Durie and Turingan, 2004; Camp and Brainerd, 2015; Camp et al., 2015). In both cases, the location of the smallest link as the output link is directly related to the behavioral and ecological function of the linkage mechanism. Do small links participate in fewer or more mechanical functions than the larger links? Does selection favor the evolution of small linkages as pathways for strong mechanical sensitivity? Are macroevolutionary shifts in linkage geometry concordant with changes in diversification rate? In the case of the oral four-bar of teleosts, the maxilla (output link) is correlated with jaw protrusion, a key ecological aspect of fish diversification (Hulsey and Garcia De Leon, 2005). As such, the most mechanically influential links may play a crucial role in shaping diversification during speciation and adaptive radiation.

Perhaps the most imperative message of these findings is the necessity for multiple levels of analysis (Jablonski, 2017a;Jablonski, 2017b). Simply demonstrating many-to-one mapping in biomechanical systems is likely to miss a rich suite of evolutionary and mechanical dynamics that shape diversification (Figure 4). By considering the tempo and mode of evolution, generalizable interactions between mechanics and diversification are likely to emerge (Scales and Butler, 2016; Blanke et al., 2017). Evolutionary studies of many-to-one mapping have flourished in recent years, with particular focus on how natural selection and developmental constraints impact the evolution of complex mechanical systems in the wild (e.g. Martinez and Sparks, 2017; Moody et al., 2017; Thompson et al., 2017). Explicit consideration of mechanical sensitivity can enhance these studies by providing a general blueprint of the mechanical and evolutionary expectations for phenotypic diversification.

Deciphering the abiotic and biotic factors impacting the tempo and mode of phenotypic diversification is a topic of perennial interest and debate (Simpson, 1944; Mayr, 1963; Gould, 1977; Gould, 2002; Schluter, 2000; West-Eberhard, 2003; Arnold, 2014 and references therein). Our findings reveal that mechanical sensitivity impacts macroevolutionary dynamics and point toward general rules connecting biomechanics and morphological diversification (Figure 4). Mechanical sensitivity is consistently associated with increased rates of evolutionary change, and the biomechanical impacts of link length provide a proximate explanation for the association between four-bar mechanics and the tempo of evolutionary change. Whereas many-to-one mapping in four-bar linkages theoretically supplies multiple morphological pathways for mechanical variation (Alfaro et al., 2004; Alfaro et al., 2005; Wainwright, 2007), mechanical sensitivity influences the tempo and mode of how these pathways evolve. This conclusion is relevant beyond mechanical systems. Many-to-one mapping is widespread in biomechanics (Wainwright et al., 2005) and can be applied even more broadly to assess various hierarchical phenomena in biology, such as molecular and cellular processes, including epistatic genotype-phenotype interactions (Phillips, 2008), physiological adaptations (Scott, 2011; Cheviron et al., 2014), and organism-level phenomena, including neurophysiological processes governing behavior (Katahira et al., 2013; York and Fernald, 2017). Extending this framework within and beyond biomechanics may yield a predictive understanding of the tempo and mode of evolutionary diversification.

All datasets and phylogenies are included in full in the supplementary materials. Citations to the original papers containing these datasets and phylogenies are included with the supplementary files.

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Author details

1. Martha M Muñoz

   1. Department of Biological Sciences, Virginia Tech, Blacksburg, United States
   2. Department of Biology, Duke University, Durham, United States

   Contribution

   Conceptualization, Data curation, Formal analysis, Supervision, Investigation, Visualization, Methodology, Writing—original draft, Writing—review and editing

   For correspondence

   mmunoz5@vt.edu

   Competing interests

   No competing interests declared

2. Y Hu

   Department of Biological Sciences, University of Rhode Island, Kingston, United States

   Contribution

   Data curation, Writing—review and editing

   Competing interests

   No competing interests declared

3. Philip S L Anderson

   Department of Animal Biology, University of Illinois, Urbana-Champaign, United States

   Contribution

   Data curation, Writing—review and editing

   Competing interests

   No competing interests declared

4. SN Patek

   Department of Biology, Duke University, Durham, United States

   Contribution

   Conceptualization, Resources, Supervision, Funding acquisition, Investigation, Methodology, Writing—original draft, Project administration, Writing—review and editing

   For correspondence

   snp2@duke.edu

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-9738-882X

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