Journal of Paleontology, 94(6), 2020, p. 1089–1102 Copyright © 2020, The Paleontological Society. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/ licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited. 0022-3360/20/1937-2337 doi: 10.1017/jpa.2020.31 Origin and significance of Lovén’s Law in echinoderms Christopher R. C. Paul1 and Frederick H. C. Hotchkiss2 1School of Earth Sciences, University of Bristol, Bristol, UK <[email protected]> 2Marine and Paleobiological Research Institute, P.O. Box 1016, Vineyard Haven, Massachusetts, USA 02568 <hotchkiss@MPRInstitute. org> Abstract.—Lovén’s Law described the position of larger basicoronal ambulacral plates in echinoids. The smaller basi- coronal plates form first in ontogeny. We restate Lovén’s Law to describe the position of first ambulacral plates using Carpenter’s ambulacra and left (L) or right (R) as: AR, BL, CR, DL, ER, with EA the pair of ambulacra both identical and adjacent. First ambulacral plates of the Cambrian edrioasteroid, Walcottidiscus, code identically. The transition from a tri-radiate 1-1-1 pattern to the 2-1-2 ambulacral pattern of Walcottidiscus and other pentaradiate Paleozoic echinoderms results in Lovén’s Law. This provides an hypothesis for the origin of Lovén’s Law and predicts its widespread occurrence among echinoderm classes. The ‘BD different’ pattern of primary brachioles in pentaradiate glyptocystitoid Rhombifera results from subterminal branching of the ambulacra. The ontogenetic sequence was triradiate, then lateral ambulacra bifurcated, and finally second brachioles developed. Positions of second brachioles of pentaradiate glyptocystitoids code as AR, BL, CR, DL, ER. Other examples of Lovén’s Law occur in Diploporita, Ophiuroidea, Edrioasteroidea, Edrioblastoidea, Holothur- oidea, Ophiocistioidea, and Bothriocidaris. Our working hypothesis is that Lovén’s Law arose with pentaradiality. An objective test requires a reliable independent landmark across all classes, which does not exist currently. Our hypothesis is only parsimonious if Lovén’s Law arose just once in echinoderm evolution and is widespread within the phylum. So far, both conditions appear to be met, but edrioasteroid first ambulacral cover plates commonly exhibit an alternative Lovén-like pattern of AL, BL, CR, DL, ER, with AB the identical adjacent ambulacra. UUID: http://zoobank.org/4c40d338-8bfa-4515-9037-934f3bbab153 Introduction ambulacra in selected Paleozoic echinoderms with biserial ambulacral structure arranged in a 2-1-2 pattern, building on pre- Most echinoids have ambulacra consisting of two columns of vious investigations of Paleozoic echinoderms and morpho- alternating plates. The first-formed, so-called basicoronal, genetic models (e.g., Bather, 1900; Paul and Smith, 1984; ambulacral plates differ in size and which is larger alternates Hotchkiss, 1995, 1998a, b, 2000; de Lussanet, 2011; Rozhnov, left or right with each ambulacrum around the mouth. Lovén 2014). We conclude that Lovén’s Law arose as an inevitable (1874) first noticed this pattern, which has become known as result of the development of five ambulacra from three by the Lovén’s Law or Lovén’s Rule. It has been claimed to be funda- branching of the lateral ambulacra in a 2-1-2 ambulacral pattern mental to all echinoderms and hence reliable in determining (see Sprinkle, 1973, fig. 16, p. 43) and should be widespread ambulacral homologies (e.g., Mooi et al., 2005). Less broadly, within the phylum. We accept that there is no embryological evi- Lovén’s Law has also been regarded as a character unique to dence for the triradiate stage in echinoderm evolution (R. Mooi, echinoids. For example, the presence of Lovén’sLawin personal communication, 2020), yet lower Cambrian helicopla- Bothriocidaris has been used to argue that this unique Ordovi- coids were triradiate and ancestral to the pentaradiate spiral Heli- cian echinoderm was a true echinoid (e.g., Durham, 1966b, cocystis according to Smith and Zamora (2013, fig. 4). In fig. 3, p. 373). In addition, 10 theoretically possible patterns in addition, to test our conclusion requires a reliable independent which the ambulacral motifs alternate (here called ‘Lovén-like’ landmark across all classes, which at present does not exist. patterns) can occur. Thus, theoretical considerations also sug- gest that other echinoderm classes might demonstrate Lovén- Materials like patterns, but not represent Lovén’s Law exactly as found in echinoids. Here we investigate these alternatives. First, we Repositories and institutional abbreviations.—Illustrated restate Lovén’s Law in more general and less ambiguous specimens are deposited in the following institutions: terms that we hope are applicable across the phylum Echinoder- Sedgwick Museum, Cambridge, England (SM); University of mata. Then, we attempt to understand how Lovén’s Law might Tartu, Natural History Museum, Geology, Estonia (TUG); have originated by describing in detail the development of Cincinnati Museum Center, Cincinnati, Ohio, USA (UC); 1089 Downloaded from https://www.cambridge.org/core. IP address: 170.106.35.229, on 29 Sep 2021 at 07:37:07, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/jpa.2020.31 1090 Journal of Paleontology 94(6):1089–1102 United States National Museum, Washington, DC, USA between his ambulacra I and II. Under this designation, the (USNM). echinoid hydropore (madreporite) lies in interambulacrum 2 (H, Fig. 1). The only truly interambulacral structure in echinoid Lovén’sLaw coronae is the interradial suture. Four columns of plates are added at the edge of the ocular plates, according to the so-called Lovén (1874) first noticed that in irregular echinoids the first ocular plate rule (e.g., David et al., 1995): the central pair of basicoronal plates differed in size in the two ambulacral columns pore-bearing, ambulacral plates, and a single column of non- of the corona and furthermore that the larger plate occurred pore-bearing, adambulacral plates, one on either side (Mooi alternately on different sides of the ambulacrum. He instituted and David, 1997). All four columns are part of the axial skel- a system of denoting the ambulacra by Roman numerals in a eton, so in echinoids it is appropriate to restrict the term interam- clockwise direction as seen in oral view, starting with the ambu- bulacral to a position between ambulacra. lacrum immediately clockwise of the periproct (Fig. 1). He fur- In any column of alternating pairs of plates truncated at a ther identified the two ambulacral columns as a and b, so a smooth surface, such as the edge of the mouth of an echinoid, shorthand statement of the position of the larger plates in it is inevitable that one plate will be smaller than the other. Lovén’s Law (as it has become known) is: Equally, in any system of five ambulacra with a motif that alter- nates from one ambulacrum to the next, it is inevitable that one Ia, IIa, IIIb, IVa, Vb motif will occur three times and the other only twice. Further- more, a unique pair of ambulacra occurs, which are both adjacent and identical. Lovén further designated interambulacra by Arabic numer- fi ‘ ’ ’ als clockwise in oral view, starting with the interambulacrum What justi es the term Lovén sLaw is the fact that of the 32 possible arrangements of alternating ambulacral plates (10 Lovén-like and 22 non-Lovénian) only the one first described by Lovén is known to occur in echinoids. Further- more, it is also present in all regular echinoids that can be scored, not just irregulars. The uniqueness of this pattern can be tested using reliable independent landmarks. In echinoids, the hydro- pore is always in Lovén’s interambulacrum 2, in echinoid larval development the closure of the ring canal is in interambulacrum 4 in all examples studied so far (Saucède et al., 2003, 2007; Tsu- chimoto et al., 2011), and in irregular echinoids the periproct is always in interambulacrum 5. Finally, the unique pair of ambu- lacra are I and II. Thus, use of the term ‘Lovén’sLaw’ in echinoids seems justified. In a collateral study of Paleozoic lysophiurine ophiuroids, 107 rays out of 113 scorable rays, when aligned using the mad- reporite, conformed with expression of Lovén’s Law. On a per-ray basis, the fidelity was 0.947. Fidelity calculated for five rays is (0.947)5 = 0.762 (Hotchkiss, 1995, p. 424, 432– 435). At that time, Lovén’s Law was not explicit in any ‘cystoid’ despite purposeful searching (Jackson, 1929, p. 495; Mortensen, 1930, p. 343; Hotchkiss, 1995, p. 418; Smith, 1997). Modification David et al. (1995) showed that ‘Lovén’sLaw’ is more than an interesting pattern found in echinoids, but results from the mode of growth of the ambulacra and the sequence of formation of the ambulacral plates. In particular, they showed that the smaller basicoronal plate was always the first plate to develop in each ambulacrum. David et al. (1995, p. 160, fig. 3) determined this by locating the edge-defining transverse sutures in the ambulacral columns. Thus, it seems to us to make sense to iden- tify the first ambulacral plate when trying to recognize ‘Lovén’s Figure 1. Lovén’s Law as originally proposed by Lovén (1874) and seen in the ’ irregular echinoid Echinocyamus bisexus Kier, 1968. Ambulacra are indicated by Law in other classes of echinoderms. By chance, Lovén chose Roman numerals. Individual columns within ambulacra indicated by the letters the second plate in each ambulacrum by describing the positions A and B. Lovén’s Law states that starting with ambulacrum I and proceeding of the larger basicoronal plate in each ambulacrum of echinoids. clockwise in oral view, the larger basicoronal plates occur in columns IA, IIA, IIIB, IVA, VB. An = anus; H = hydropore (on the opposite surface of the echin- Furthermore, we believe that consideration of the details of oid); M = mouth (redrawn from Hotchkiss, 1978, fig.