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Notes: The volumes and surface areas are necessarily approximate. The values cited are those adopted and presented in Reynolds (1984a); some later additions taken from Reynolds (1993a), mostly based on his own measurements. The volumes given in brackets cover the ranges quoted elsewhere in the literature (see text). Note that the volumes and surface areas are calculated by analogy to the nearest geometrical shape. Surface sculpturing is mostly ignored. Shapes considered include: sph (for a sphere), cyl (cylinder), ell (ellipsoid), bicon (two cones fused at their bases, area of contact ignored from surface area calculation). Other adjustments noted as follows: a Cell visualised as two adjacent ellipsoids, area of contact ignored. b Cell visualised as two prisms and six cuboidal arms, area of contact ignored.

c Cell visualised as two frusta on elliptical bases, two cylindrical (apical) and two conical (lateral) horns. d Coenobium envisaged as 40 contiguous spheres, area of contact ignored. e Coenobium envisaged as four adjacent cuboids, volume of spines ignored f Coenobium envisaged as eight cuboids, area of contact ignored.

§ Each cell visualised as four trapezoids; area of contact between cells ignored. h Coenobium envisaged as a seies of cones, area of contact ignored j Coenobium envisaged as a discus-shaped sphaeroid.

k Coenobium envisaged as a chain of cylinders, area of contact between cells ignored. 1 Coenobium envisaged as a single cylinder, terminal taper ignored. m Filament visualised as a chain of spheres, area of contact between them ignored n Filament visualised as it appears in life, enveloped in mucilage, turned into a complete 'doughnut' ring, with a cross-sectional diameter of 21 |xm.

p Filament visualised as a chain of ovoids, area of contact between them ignored. q For the typical 'raft' habit of this plankter a bundle of filaments is envisaged, having an overall length of 125 |im and a diameter of 12.5 |xm. rThe volume calculation is based on the external dimensions.

s In fact the cells in the vegetative stage are located exclusively on the wall of a hollow sphere. This second volume calculation supposes an average wall thickness of 10 |im and subtracts the hollow volume.

independent but rather constitute a multicellular 'unit' whose behaviour and experienced environment is simultaneously shared by all the others in the unit. Such larger structures may deploy cells either in a plate- or ball-like coenobium (exemplified by the species listed in Table 1.2B) or, end-to-end, to make a uniseriate filament (Table 1.2C). Generally, added complexity brings increased size but, as volume increases as the cube but surface as the square of the linear dimension, there is natural tendency to sacrifice a high surface-to-volume ratio.

However, a counteractive tendency is found among the coenobial and filamentous units (and also among larger unicells), in which increased size is accompanied by increased departure from the spherical form. This means, in large-volume units, more surface bounds the volume than the strict geometrical minimum provided by the sphere. In addition to distortion, surface folding, the development of protuberances, lobes and horns all contribute to providing more surface for not much more volume. The trend is shown in Fig. 1.6, in which the surface areas of the species listed in Tables 1.2A, B and C are plotted against the corresponding, central-value volumes, in log/log format. The smaller spherical and ovoid plankters are seen to lie close to the (lower) slope representing the geometric minimum of surface on volume, s a v, but progressively larger units drift away from it. The second regression, fitted to the plotted data, has a steeper gradient of v0 82. The individual values of

Nominal u (jam3)

Figure 1.6

Nominal u (jam3)

### Figure 1.6

Log/log relationship between the surface areas (s) and volumes (v) of selected freshwater phytoplankters shown in Table 1.2. The lower line is fitted to the points (□) referring to species forming quasi-spherical mucilaginous coenobia (log s = 0.67 log v + 0.7);the upper line is the regression of coenobia (log s = 0.82 log v + 0.49) fitted to all other points (•). Redrawn from Reynolds (1984a).

s/v entered in Table 1.2B and C show several examples of algal units having volumes of between 103 and 105 |im3 but maintaining surface-to-volume ratios of >1. In the case of Asterionella, the slender individual cuboidal cells are distorted in one plane and are attached to their immediate coeno-bial neighbours by terminal pads representing a very small part of the total unit surface. The resultant pseudostellate coenobium is actually a flattened spiral. In Fragilaria crotonensis, a still greater s/v ratio is achieved. Though superficially similar to those of Asterionella, its cells are widest in their mid-region and where they link, mid-valve to mid-valve, to their neighbours to form the 'double comb' appearance that distinguishes this species from others (mostly non-planktic) of the same genus. Among the filamentous forms, there is a widespread tendency for cells to be elongated in one plane and to be attached to their neighbours at their polar ends so that the long axes are cumulated (e.g. in Aulacoseira, Fig. 1.4).

Again confining the argument to the planktic forms covered in Tables 2.2A, B and C, whose volumes, together, cover five orders of magnitude, these show surface-to-volume ratios that fall in scarcely more than one-and-a-half orders (3.6 to 0.1). This evident conservatism of the surface-to-volume ratio among phytoplankton was noted in a memorable paper by Lewis (1976). He argued that this is not a geometric coincidence but an evolutionary outcome of natural selection of the adaptations for a planktic existence. Thus, however strong is the selective pressure favouring increased size and complexity, the necessity to maintain high s/v, whether for entrainment or nutrient exchange or both, remains of overriding importance. In other words, the relatively rigid constraints imposed by maintenance of an optimum surface-to-volume ratio constitute the most influential single factor governing the shape of planktic algae.

Lewis (1976) developed this hypothesis through an empirical analysis of phytoplankton shapes. To a greater or lesser extent, departure from the spherical form through the provision of additional surface area is achieved by shape attenuation in one or, perhaps, two planes, respectively resulting in slender, needle-like forms or flattened, plate-like structures. Lewis

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