From chaos to order: the life history of Hannaea inaequidentata (Lagerstedt) Genkal and Kharitonov (Bacillariophyta), from initial cells to vegetative cells

Abstract This study presents observations on three species of Hannaea and documents and illustrates the life history of H. inaequidentata. We have divided the life history of H. inaequidentata into the following four series of successive stages: auxospore, initial cell, pre-normal vegetative cell, and normal vegetative cell. The initial cell has a cylinder-like and a frequently twisted outline, a longitudinal perizonium wholly covering the valve surface, and a disc-shaped incunabular scale, but lacks any transverse perizonium bands. The pre-normal vegetative cell cannot form ribbon-like colonies, has a wide variety of irregular outlines and is composed of two cell types: one with its epivalve composed of either the initial epivalve or the initial hypovalve, its hypovalve being newly formed, the other with both its epivalve and hypovalve newly formed. The normal vegetative cell has a regular outline and exhibits a significant length reduction so that the largest valve is at least four times longer than the smallest. From initial cell to normal vegetative cell, the developmental sequence goes from ‘chaos to order’ as happens in many phenomena in the universe. The lack of transverse perizonium bands may be the cause of the initial ‘chaos’ process during its developing period from the initial cell to the normal vegetative cell. The development of frustule/valve shape, central area, sternum, virga, vimine, rimoportula and ocellulimbus etc. during the life circle is summarised. In the genus Hannaea, some taxa lack the strongly buttressed central area as in H. inaequidentata, which also has almost parallel valve margins.


Introduction
The diatom genus Hannaea R.M. Patrick (in Patrick and Reimer 1966, p. 131) was first used to accommodate Ceratoneis arcus (Ehrenberg) Kützing (1844, p. 104) and Ceratoneis arcus var. amphioxys (Rabenhorst) R.M. Patrick (in Patrick and Reimer 1966, p. 133), the former being the type of the genus: Hannaea arcus (Ehrenberg) R.M. Patrick (in Patrick and Reimer 1966). The need for the new name Hannaea in place of Ceratoneis Ehrenberg has been fully explained in Medlin and Mann (2007) and Van de Vijver and Ector (2020). Hannaea has recently been characterised as having valves "asymmetrical to the apical axis, usually with a small, unornamented tumid area on one side of the center of the valve" (Liu et al. 2019). Since the first use of the name Hannaea (as opposed to the name Ceratoneis), a number of species (and supra-specific taxa) have been added to the genus (ca. 13 in all, excluding varieties etc., see Liu et al. 2019) that fall into roughly four groups: (1) valves having uniseriate striae and a single rimoportula; (2) valves having biseriate striae and a rimoportula at both apices; (3) valves with poorly developed asymmetry to the apical axis; and (4) valves with (almost) parallel margins. Liu et al. (2019) note that from this diversity "two distinct groups can be identified […]": one with uniseriate striae and a single rimoportula, the other with biseriate striae and two rimoportulae, one at each pole. It is not yet clear if either of these "two distinct groups" are monophyletic, if they are each other's closest relatives (hence the genus being monophyletic), or if one or another of these two sub-groups is related to species outside the genus - Liu et al. (2019) suggest that the problem is worthy of investigation.
This study offers a contribution to further that investigation. We primarily focus on specimens identified as Hannaea inaequidentata (Lagerstedt) Genkal and Kharitonov (2008), a species with valves having almost parallel margins rather than the usual arcuate shape associated with many species of Hannaea. In an effort to understand the morphology and to help resolve the general relationships of Hannaea, this paper presents details on the entire life cycle of H. inaequidentata.
At present, very little is known of 'araphid' diatom life cycles and their ontogeny (reviews in Kaczmarska et al. 2001and Kaczmarska et al. 2013, see Jewson and Bixby 2016. Herein, we document the morphological changes observed in the transition from what has been termed post-auxospore cells to the 'normal' vegetative cells, noting the changes in particular features of the valve during development. For comparative purposes we include brief descriptions of specimens identified as Hannaea cf. arcus and Hannaea cf. baicalensis (Hannaea baicalensis Genkal, Popovskaya & Kulikovskiy, 2008). The latter is possibly a new species from Lake Baikal, Siberia (see Williams 2019); the identity of the former remains uncertain. Both are used here simply as examples of the variation in Hannaea.

Material and methods
The diatom samples were collected from three different regions that are some distance from each other. The samples for Hannaea cf. arcus were collected from a tributary of the Datong River in Qinghai province of China in August 2018. The specific sampling site is in Bazha town, Huzhu County, Qinghai province, its coordinates are 37.03684°N and 102. 415849°E with an elevation of 2801 m a.s.l. Temperature, pH, and conductivity were measured in situ with a portable multimeter (HQ40D, HACH Company): pH = 8.92 ± 0.02, conductivity = 230.6 ± 0.1 μS/cm, temperature = 15.4 ± 0.1 °C.
The samples of Hannaea inaequidentata were collected from Heiwan River at the foot of Fanjing Mountain in Guizhou province of China in December 2015. The specific sampling site is beside Longquan Temple which is within the Fanjing Mountain National Nature Reserve, Jiangkou County, Guizhou province. Its coordinates are 27.860093°N and 108. 764229°E with an elevation of 532 m a.s.l. Temperature, pH, and conductivity were measured in situ with a portable multimeter (HQ40D, HACH Company): pH = 7.7 ± 0.1, conductivity = 49.7 ± 0.2 μS/cm, temperature = 9.4 ± 0.1 °C.
The samples for Hannaea cf. baicalensis were collected from Lake Baikal, Siberia, as part of a Darwin Initiative (DI) project (Flower and Williams 1999;see http://www. geog.ucl.ac.uk/ecrc/enclosed/dardata.htm). Duplicate materials for the DI Lake Baikal collections are located in CAS (California Academy of Science), E (Royal Botanical Gardens, Edinburgh), Minsk (Laboratory of Quaternary Geology, Minsk, Belarus) and the Limnological Institute, Irkutsk, Russia.
The samples from China were scraped from stone surfaces using toothbrushes, then washed into 100 ml sampling bottles and fixed with 70% ethanol. Permanent slide preparation, light microscopy observation, and scanning electron microscopy observation follow Liu et al. (2020). A similar protocol was used for the Baikal samples.

Terminology and abbreviations
Valve morphology: We mostly follow Ross et al. (1979) and Cox and Ross (1981) for valve structure terminology and Williams (1985) for girdle band terminology. With respect to the valve central area (the "unornamented tumid area" of Liu et al. 2019, the "unilateral inflation" of Bixby et al. 2005, and other descriptions), which is of some significance for species in the genus Hannaea, we follow and comment upon Bixby et al. (2005).
Life cycles: We have mostly followed Kaczmarska et al. (2013, and, to a lesser extent, its precursor, Kaczmarska et al. 2001) for life cycle terminology. We introduce a few new terms that allow more precise documentation of the various stages observed in Hannaea inaequidentata. Below we refer to the vegetative stages during which the cells exhibit regular shapes as 'normal', hence 'normal vegetative cells'. In this sense, certain 'pre-normal cells' can be identified.
Pre-normal vegetative period: The time between immediately after the initial cell's first division and the presence of the first new normal vegetative cells. The cell, frustule, and valve occurring during this period can be termed 'pre-normal vegetative cell, frustule, and valve'. Kaczmarska et al. stated that "It is often convenient to refer to the first few mitotic generations of cells produced by division of the initial cell as post-initial cells" (Kaczmarska et al. 2013, p. 266). Post-initial cells will include normal vegetative cells, so using the term 'pre-normal vegetative period' divides the life history into the following series of successive stages: auxospore, initial cell, pre-normal vegetative cell, and normal vegetative cell.
Uniparental initial valve period: The time between the first-generation valve from the initial cell and the termination of initial valves' division. There are two types of frustule: one is composed of an initial epivalve and a non-initial hypovalve (the newly formed valve), the other is of one initial hypovalve (as epivalve in the first-generation frustule) and a non-initial hypovalve (the newly formed valve). Both the structure of the initial epivalve and initial hypovalve can be maintained for a few generations.

Initial frustule
The first initial frustule is illustrated in Figs 79-84. It is cylindrical and twisted from pole to pole (Fig. 79). The virgae and vimines are almost flush to each other, with the virgae relatively wide with respect to the vimines (Figs 80-84). The central area is an area completely (or almost) silicified, with no appreciable distinction between virgae and vimines; even ghost striae are not evident, nor is a sternum (Fig. 80; Fig. 81, arrow; Fig.  Figures 60-65. Hannaea inaequidentata, normal vegetative valves, external view, SEM 60 displaced frustule 61 detail of Fig. 60, showing well-developed virgae and vimines (arrows), spines mostly located between two adjacent virgae, sometimes situated on virgae (arrowheads) 62, 63 apex details of Fig. 62 showing rimoportula configuration in two valves forming a cell: each cell with two rimoportulae, located diagonally at both apices of each cell (two arrows, respectively) 64, 65 another two apices showing a regular ocellulimbus and areolae occluded internally by hymens. Scale bars: 10 μm (60), 2 μm (61-63), 1 μm (64, 65). 83, arrow). There are two girdle bands (Figs 82, 84, labelled B1 and B2); the incunabular scales are disc-shaped, slightly dendritic (cf., "dendroid scales (dendroid spine scales)", Kaczmarska et al. 2013, p. 283;see Fig. 83, curved arrow, Fig. 84, arrow). The perizonium plate cannot be detected because it tightly covers the valve surface. The second initial frustule is illustrated in Figs 85-90. It is cylindrical and twisted (Fig. 85). The central area is an area completely (or almost) silicified, with some noticeable distinction between virgae and vimines; ghost striae are evident, but a sternum is not (Fig. 86, two arrows). The longitudinal perizonium plate covers the valve surface, but no transverse perizonium bands were observed (Figs 87-89, arrows). Plaques are present, more spaced out than on the normal vegetative valves (Fig. 87, arrowheads). There are two girdle bands (Fig. 87, labelled B1 to B2). There is a cluster of small poroids on the valve margin giving the appearance of a pore-field or ocellulimbus (Fig. 89, curved arrow); the ocellulimbus occurs at the poles (Fig. 90). The longitudinal perizonium plate approaches a corrugated appearance at one pole (Fig. 90, arrow).    The third initial frustule is illustrated in Figs 91-96. It is cylindrical and slightly twisted (Fig. 91). The virgae and vimines are almost flush to each other and the longitudinal perizonium plate can be observed from the centre to the pole (Figs 92-96, arrows): the two valves and one girdle band are all covered by the longitudinal perizonium plate and band (Fig. 92, three arrows). One initial valve has two rimportulae, one at each pole (Figs 95, 96, two curved arrows).
Overall, the three examples illustrate the changes exhibited from a relatively disorganised structure to a more conventional and regular vegetative valve (see Table 2).

Pre-normal frustule/valve
an undulating appearance (Figs 74,76), others slightly sigmoid with constrictions at the central margins (Figs 73,74). Some have an expanded central area on one side of the valve (e.g. Figs 77, 78), others with the central area across the whole valve from margin to margin (e.g. Figs 73-76), some partially across valve surface (e.g. Fig. 77), and others with central area on one side of the valve but having a distinctly arcuate outline (e.g. Fig. 78).

Pre-normal frustule with uniparental initial epivalve
Using SEM, we illustrate two pre-normal frustules with uniparental initial epivalves. The first is illustrated in Figs 97-102. It is cylindrical with a constriction at its centre (Fig. 97). The longitudinal perizonal plate can be observed from centre to pole (Figs 98-102). There are six girdle bands (Figs 101, 102, labelled B1 to B4 and B1 to B2). One new-born hypovalve has a central sternum (Fig. 102, two arrows) and a more conventionally structured ocellulimbus.
The second is illustrated in Figs 103-106. It is cylindrical with an expanded central part (Fig. 103). The longitudinal perizonal plate can be observed (Fig. 104, two ar-  (Figs 104-106). There are four girdle bands (Fig. 106, labelled B1 to B4). The hypovalve has spines (Fig. 106,  arrows) indicating that the initial epivalve may have passed a few generations.

Pre-normal frustule composed of new-born epivalve and hypovalve
Using SEM, we illustrate six frustules in external view (Figs 107-112) to document how the pre-normal vegetative frustules gradually develop into normal vegetative  Fig. 107 showing deflexed sternum (two arrows) and central area 114 detail of middle illustrated in Fig. 108 showing sternum (two arrows) and central area 115 detail of middle illustrated in Fig. 109 showing sternum (two arrows) and central area 116 detail of middle part illustrated in Fig. 110 showing developed virgae and vimines 117 detail of middle part illustrated in Fig. 111 showing developed spines 118 detail of middle part illustrated in Fig. 112 showing well-developed virgae, vimines and spines. Scale bars: 5 μm (113-118).
virgae and vimines occur on the same plane (Figs 113-115), with the virgae becoming raised away from the vimines (Figs 116-118), and the ocellulimbus gradually become more regular in its structure (Figs 119-124). Using SEM, we illustrate six pre-normal vegetative valves in internal view (Figs  125-130). These valves have different outlines: a twisted, rounded valve (Fig. 125); an arcuate valve with swollen centre (Fig. 126); a valve with sternum and swollen centre (Fig. 127); a valve with bi-constricted centre area and a central sternum (Fig. 128); a slightly arcuate valve with parallel centre and central sternum (Fig. 129); and a nearly  Fig. 126 showing two rimoportulae per valve (two arrows) 133 middle part detail of Fig. 127 showing swollen central area and ghost striae 134 detail of Fig. 128 showing the bi-constricted middle part and ghost striae 135, 136 two apices of Fig. 130 showing two rimoportulae per valve. Scale bar: 2 μm (131-136).
normal valve (Fig. 130). Internally, as noted above for the external view, the virgae and vimines first occur on the same plane, with the virgae becoming raised away from the vimines and the lateral sternum becomes central (Figs 131-136). As with the initial valve, some pre-normal new-born valves also have two rimoportulae per valve (Figs 131,132,135,136, two arrows respectively).

Summary of morphological features changing
The morphological features that change during the life circle of Hannaea inaequidentata are summarised in Table 2. From initial frustule/valve, via pre-normal vegetative frustule/valve, to normal vegetative frustule/valve, the colony, girdle band numbers, valve outline, valve apex, sternum, central area, virga and vimine, linking spines, rimportula number per valve, and ocellulimbus all gradually become normal ( Table  2). The valve plaques are a constant feature, occurring in the initial valve, pre-normal valve, and normal valve.

Discussion
We noted above that Hannaea is usually characterised as having valves "asymmetrical to the apical axis, usually with a small, unornamented tumid area on one side of the center of the valve" (Liu et al. 2019, p. 42) -four groups have been recognised, based on a combination of striae structure and rimoportula number: one group has uniseriate striae and a single rimoportula, another has biseriate striae and two rimoportulae, one at each pole; these two groups are both asymmetrical about the apical axis. The additional two groups are those that have either poorly developed asymmetry to the apical axis or with parallel margins (cf. Liu et al. 2019, p. 42). These latter two groups are those possibly related to Fragilaria Lyngbye.  (Williams 2001) and in a species of Ulnaria (Kützing) Compère, Williams and Metzeltin noted that the auxospore/initial cells were rather large (in excess of 250 μm), curved along their length, with an irregular basal siliceous layer and the valve outline sometimes interrupted by undulations or a central inflation (Williams and Metzeltin 2004, see also Sato et al. 2004 for further comparisons).  Krammer and Lange-Bertalot (1991, p. 134, as a shape variant, 'Umrissvariation') and implied in Genkal and Kharitonov (2008, p. 17, pl.1, fig. 8). Many of currently valid taxon names may turn out to be simply stages in individual life-cycles, e.g. Ceratoneis arcus f. trigibba C. Zimmermann (Zimmermann 1915: 36, pl. 4, fig. 10) and the various valves illustrated in Meister (1919) (see Van de Vijver and Ector 2020 for illustration and discussion).

Structure and ontogeny
The 1979 terminology paper defined the central area as "an expanded or otherwise distinct portion of the axial area midway along its length" (Ross et al. 1979, p. 518). This definition related more to raphid diatoms than 'araphid' diatoms. Bixby et al., in their study of Hannaea, suggested some useful additional terms that help describe more accurately the structure of the central area. In valves of Hannaea superiorensis Bixby and Edlund (in Bixby et al. 2005, p. 231), internal views shows that the central area is demarcated by a central swollen portion of the valve with an area demarcated by buttressing (as in: "buttressed central inflation", Bixby et al. 2005, p. 235, p. 234, fig. 11). In Hannaea superiorensis, the "buttressed central inflation" extends up to the sternum. The buttresses are effectively a pair of heavily silicified virgae situated either side of the demarcated central area enclosing a series of "ghost striae", the latter being a more heavily silicified set of virgae and vimines but with each visible (Bixby et al. 2005, p. 234, fig. 11). Most species of Hannaea have this kind of central area construction, but not all -see Hannaea tibetiana, for example, which has a simple plain area demarcated by the virgae and vimines being more silicified in this area (Liu et al. 2019, p. 46, fig. 3; figure 3B is of the 'plain' internal view). The buttressing is less obvious in species such as Hannaea arcus and H. inaequidentata. Here we noted that in the normal vegetative valves, H. inaequidentata has a central area on the ventral side of the valve with faint ghost striae, and transversely raised virgae are evident. Further, in the initial cells, the central area appears without any obvious distinction between virgae and vimines, hence ghost striae and the sternum are not evident. In the 'pre-normal frustule/valve', the central area varies in shape, from slightly sigmoid, expanded on one side of the valve, extending across the whole valve, margin to margin, often with varying shapes. Finally, the central area occupies one half of the valve and the ghost striae become evident. The implication is that the virgae in the central area being laid down later emerge from the silica basal layer rather than forming first with the vimines and then being filled in. Thus, while the structure called the 'central area' is obviously composed of various parts of the valve structure and is now better known, its relevance to taxon relationships remain less than obvious.

Relationships
At present, it is not clear if Hannaea, consisting of all the various groups of species, is monophyletic, in spite of the conclusions offered by Bixby et al. (2005). As we noted above, Bixby et al. (2005) based its monophyly on a combination of the presence of a unilateral inflation, the lack of striae in that inflation, and a valvocopula with an ad valvar crenate margin. None of these characters appear unique (synapomorphic) to Hannaea as currently formulated. For example, the asymmetrical valve shape can be found elsewhere in freshwater 'araphid' diatoms currently included in Fragilaria (e.g., Fragilaria flexura Hoff and Lange-Bertalot in Hoff et al. 2011, which is admittedly an unusual species of Fragilaria) and, as we noted above, the "small, unornamented tumid area" is also found in a few other species (e.g., Synedra mazamaensis Sovereign 1958 (as the current definition of Synedra refers to a marine genus, this species clearly does not belong there -it is probably not a species of Fragilaria sensu stricto either, but that requires further investigation, see Williams & Karthick, In Review, for comments on the name Synedra; other species to consider might be Fragilaria bidens Heiberg and its relatives). It is also not clear if the four sub-groups noted above are themselves monophyletic or just 'convenience' groups to aid identification.

Final comments
The diversity of species in Hannaea is currently recognised by the array of names available, some 30+ for Ceratoneis arcus alone, for example. Many of these may turn out to be definable taxa, but others will simply be stages in the individual life cycles, e.g., Ceratoneis arcus f. trigibba (see Van de Vijver and Ector 2020). Schmid (1997) suggest-ed that species in Hannaea may simply be teratological forms of Fragilaria, in a similar fashion to the tri-radiate cells of Centronella M. Voigt. This is certainly a possibility but the work of Van de Vijver and Ector (2020) suggests that while there are shape changes to the valves, they should not be considered teratological forms but natural. That viewpoint is supported here. Nevertheless, it would seem essential at this stage to perform life-cycle studies where possible to ascertain not just how valves form and how exactly valve characters emerge, but to utilise this information to establish evidence for the relationships of taxa at all ranks.