On trends and patterns in macroevolution: Williston's law and the branchiostegal series of extant and extinct osteichthyans

Abstract

Background: The branchiostegal series consists of an alignment of bony elements in the posterior portion of the skull of osteichthyan vertebrates. We trace the evolution of the number of elements in a comprehensive survey that includes 440 extant and 66 extinct species. Using a newly updated actinopterygian tree in combination with phylogenetic comparative analyses, we test whether osteichthyan branchiostegals follow an evolutionary trend under 'Williston's law', which postulates that osteichthyan lineages experienced a reduction of bony elements over time.

Results: We detected no overall macroevolutionary trend in branchiostegal numbers, providing no support for 'Williston's law'. This result is robust to the subsampling of palaeontological data, but the estimation of the model parameters is much more ambiguous.

Conclusions: We find substantial evidence for a macroevolutionary dynamic favouring an 'early burst' of trait evolution over alternative models. Our study highlights the challenges of accurately reconstructing macroevolutionary dynamics even with large amounts of data about extant and extinct taxa.

Keywords: Early burst; Evolutionary trend; Palaeontology; Phylogeny; Williston’s law.

Fig. 1

Skull of the Devonian actinopterygian Cheirolepis trailli^† in lateral (a), anterior (b), and ventral (c) view (after [59]). Opercular/ branchiostegal series in red outlines with branchiostegal rays in light red fill. The pattern of these bones in this stem-actinopterygian may be considered the basic actinopterygian pattern. The elements in this succession include the operculum, suboperculum, branchiostegal rays, and gulars. Some authors include also Dh dermohyale, aOp accessory operculum, Pop preoperculum (and other absent bones here) in the series, while others exclude the gulars from it (for references see text). Any of these elements may be missing, hence the synonymous names ‘opercular series’, ‘branchiostegal series’, ‘operculo-branchiostegal series’, and ‘operculo-gular series’. Op, operculum; Sop, suboperculum; Br, branchiostegal rays; lG, lateral gular; mG medial gular

Fig. 2

Diversity of the opercular/branchiostegal series (in red outlines; branchiostegal rays in light red fill) in osteichthyans (skulls in left lateral view); a Dialipina^† (Devonian; [60]). The region of the cheek and the gill cover is studded with multiple bony plates that makes it impossible to delineate an opercular/branchiostegal series [56]. b Guiyu^† (Silurian; [32]) showing the “standard pattern” of the opercular/branchiostegal series, including (from dorsal to ventral) operculum, suboperculum, a number of branchiostegal rays, and gular. c The recent paddlefish Polydon ([5]) without operculum, the larger bone being the suboperculum and the smaller one a single branchiostegal ray. d Saurichthys^† (Triassic; [11]) with a single element, the suboperculum. e The gar Lepisosteus ([5]) with operculum and suboperculum and three branchiostegals. f The zebrafish Danio rerio ([61]); as in all cypriniforms its opercular series consists of three elements. g The salmon Salmo ([6]), with variable number of branchiostegal rays (9–13), even within the same species. h The Australian lungfish Neoceratodus ([5]), with a small suboperculum and no branchiostegal rays. Elements from the opercular series may be missing (e.g. the operculum and the gulars in paddlefish, the branchiostegals in lungfish, all elements in saccopharyngiforms ([62] not shown in Fig. 2)

Fig. 3

Phylogenetic distribution of mean branchiostegal ray numbers (left), and histograms of the species mean and range of branchiostegal numbers (right). The nodal ancestral values were reconstructed under the EB model, and interpolated along branches using the contMap function of the R package phytools v. 0.6 [63, 64]. Branch lengths are proportional to time. The silhouettes show the approximate position of selected clades. The age of the root is 443 Ma. Note that the intraspecific variation in the number of branchiostegals is probably underreported

Fig. 4

Effect of fossil sample size on model support and parameter estimates. Random subsampling of the fossil data shows that model support (Akaike weight) for EB becomes overwhelming with just 7 sampled fossils (extinct taxa), but the relative support of other models only stabilizes at some point between 40 and 47 sampled fossils (left side). In contrast, the model parameter estimates (right side) do not seem to approach an asymptote as more fossils are added, except the adaptive optimum (θ₁) of the OU model and, to a lesser extent, the rate of exponential decay (β) of the EB model. Note that we introduced a small horizontal displacement in the points in order to visually separate the various model series; the analyses were performed with the fossil sample sizes labelled on the horizontal scale, with no intermediate values. Also, the Brownian diffusion rate (σ²) is shown log-transformed in order to better accommodate the large range of values. The lines connect the medians between sample size categories; θ₀ is the reconstructed number of branchiostegals at the root of the tree. The white noise is not shown here because it is strongly rejected by our results (see Table 1)