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Reynolds (1984a)
°Asterisks indicate experiments on diatones killed prior to measurement of sinking rates, to overcome vital interference (see Section 2.5.4).
rates increase with increasing chain length. However, Walsby and Reynolds (1980) argued that the linear expression is misleading as increasing chain length should tend to a finite maximum. The sinking velocity of the chain (say wc) is linked to the sinking rate of the sphere of similar volume (ws), through wc = ws/^r. According to Stokes' equation (2.16), ws a (ds/2)2, where ds is the diameter of the equivalent sphere. However, ds/2 a b033, so ws a b067, i.e. ws does not increase linearly, as Hutchinson's equation predicts, neither does it fall asymptotically to zero as implied.
Cylinder elongation and cylindrical filaments
This theory is upheld by the data of another set of observations presented by Reynolds (1984a) for filaments of Melosira italica (now Aulacoseira subarctica). This freshwater diatom comprises cylindrical cells joined together by the valve ends, effectively lengthening the cylinder in a linear way. In Reynolds' experiments, the mean length of the cells was hc = 19.0 ¡m, the mean diameter (dc) was 6.3 ¡m. The external volume of the cylindical cell was calculated from n(dc/2)2 hc ~592 ¡m3. The ratio hc/dc, a sort of index of cylindricity, is 3.0 and the diameter of the sphere (ds) of the same volume is ~10.4 ¡m. Adding another cell doubles the length, volume and cylindricity, but the area of mutual contact between them means that the surface is not quite doubled but the diameter of the equivalent sphere is increased by about a third, to 13.1 ¡m. The sinking rates (ws) of individual filaments of a killed suspension of an otherwise healthy, lateexponential strain of Aulacoseira (excess density ~251kgm3) were measured directly and grouped according to the number of cells in the filament. The measurements were compared directly with the rates calculated for spheres of equivalent volume and excess density (ws calc) in Fig. 2.11; equivalent values of (as ws calc/ws) are also included.
The plot is instructive in several ways. Lengthening increases size as it does ws. Filament formation does not decrease sinking rate with respect to single cells. On the other hand, the increments become smaller with each cell added, with an asymptote (in this instance) of about 15 ¡m s1, reached by a filament of 1112 cells in length
Figure 2.11
Plot of sinking rates (ws) against length (as cells per filament) of Aulacoseira subarctica filaments compared with the sinking rates calculated for a spheres of the same volume and density (ws calc). The ratio, 0r = (ws calc)/ws, is also shown against the horizontal axis. Redrawn from Reynolds (1984a)
Figure 2.11
Plot of sinking rates (ws) against length (as cells per filament) of Aulacoseira subarctica filaments compared with the sinking rates calculated for a spheres of the same volume and density (ws calc). The ratio, 0r = (ws calc)/ws, is also shown against the horizontal axis. Redrawn from Reynolds (1984a)
(200220 ¡m, hc/dc ~ 30, ~ 4.5). This velocity is, moreover, about the same as that calculated for a sphere of similar density and of diameter equivalent to only 1.2 cells. Thus, the sacrifice of extra sinking speed is small in relation to the gain in size and where the loss of surface area is probably insignificant.
It is, of course, a feature of many pennate diatoms in the plankton to have finely cylindrical cells. On the basis of a small number of measurements on a species of Synedra and treating the essentially cuboidal cells as cylinders (hc = 128±11 ¡m, greatest dc ~ 8.9 ¡m, hc/dc 1316), Reynolds (1984a) solved (as ws calc/ws) ~ 4.1. For the shorter individual cuboidal cells of Fragilaria crotonensis, whose length (~70 ¡m) exceeded mean width (3.4 ¡m) by a factor of over 20, was determined to be about 2.75. In the experiments with single cells of Asterionella
Figure 2.12
Plot of sinking rates (ws) against the number of cells of killed Fragilaria crotonensis colonies compared with the sinking rates calculated for a sphere of the same volume and density (ws calc). The ratio, 0r = (ws calc)/ws, is also shown against the horizontal axis. Redrawn from Reynolds (1984a).
Figure 2.12
Plot of sinking rates (ws) against the number of cells of killed Fragilaria crotonensis colonies compared with the sinking rates calculated for a sphere of the same volume and density (ws calc). The ratio, 0r = (ws calc)/ws, is also shown against the horizontal axis. Redrawn from Reynolds (1984a).
formosa (length 66 ¡m, mean width 3.5 ¡m) the form resistance was found to fall in the range 2.3 to 2.8. Compared with the squat cylindrical shapes of the centric diatoms Cyclotella and Stephanodiscus species for which measurements are available, the impact of attenuation on form resistance is plainly evident (see Table 2.5).
Colony formation
Of course, both Fragilaria and Asterionella are more familiarly recognised as coenobial algae, the cells in either case remaining tenuously attached on the valve surfaces, in the central region in Fragilaria (to form a sort of doublesided comb) and at the flared, distal end in Asterionella.
These distinctive new shapes generate some interesting sinking properties. In Fig. 2.12, mea sured sinking rates of killed coenobia of Fragilaria crotonensis are plotted against the numbers of cells in the colonies and compared with the curve of (ws calc) predicted for spheres of the same volumes. Whereas, once again, Stokes' equation predicts a continuous increase in sinking rate against size, coenobial lengthening tends to stability at 1620 cells, not far from the point, indeed, at which the lateral expanse exceeds the lengths of the component cells and the coenobium starts to become ribbonlike. It is not unusual to encounter ribbons of Fragilaria in nature exceeding 150 or 200 cells (i.e. some 500700 ¡m in length) but it is perhaps initially surprising to find that they sink no faster than filaments onetenth their length! A further tendency that is only evident in these long chains is that the ribbons are not always flat but are sometimes twisted, with a frequency of between 140 and 200 cells per complete spiral. The extent to which this secondary structure influences sinking behaviour is not known.
The secondary shape of Asterionella coenobia is reminiscent of spokes in a rimless wheel, set generally at nearly 45° to each other. When there are eight such cells, they present a handsome star shape (alluded to in the generic name), although the mutual attachments determine that the colony is not flat but is like a shallow spiral staircase. Cell no. 9 starts a second layer; in cultures and in fastgrowing natural populations, coenobia of more than eight cells are frequently observed (although, in the author's experience, chains of over 2024 cells are in the 'rare' category). Following a similar approach to that used for Aulacoseira and Fragilaria, Reynolds (1984a) plotted measured sinking rates of killed coenobia against the numbers of cells in the colony and, again, compared them with corresponding curve (ws calc) for spheres of the same volumes (see Fig. 2.13). Now, although the observed sinking rates, ws, suggest the same tendency to be asymptotic up to a point where there are 610 cells in the coenobium, it is equally clear that higher numbers of cells make the colony sink faster, with no further gain in after ~4.0. Reynolds (1984a) interpreted this result as demonstrating the advantage to form resistance of creating a new shape, from a cylinder to a spoked disc,
Colony volume I \imi X 10 3
Colony volume I \imi X 10 3
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T... i ▼ ...I* ; / 

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