## Info

G. H. M. Jaworski (unpublished data)

Dinophyta

Ceratium hirundinella

0.2l

G. H. M. Jaworski (unpublished data)

a Rate extrapolated to 20 °C. b Unicellular culture. c Colonial culture.

generally excellent (Reynolds, 1988a, 1997a). Where there has been a significant departure, as there is in the case of the two entries for Microcystis, it is attributable to the difference between working with a colonial strain and, as is common among laboratory cultures, one in which the colonial habit had been lost. This turns out to be an important observation, for it provides the clue to the robust pattern that accounts for a large part of the variability in organis-mic replication rate, which relates to organismic morphology. The apparent dependence of growth rate on algal size and shape, suggested by earlier analyses (Reynolds, 1984a) was convincingly confirmed when the replication rates (r20) were plotted against the surface-to-volume ratio (sv-1) ratio of the life-form, regardless of whether it was a unicell, coenobium or mucilage-bound colony (Reynolds, 1989b). The relationship, between the replication rates shown in Table 5.1 (save the entry for Dinobryon that was not available to the 1989 compilation) and the corresponding species-specific surface-to-volume ratios noted in Table 1.2, is reproduced in Fig. 5.2. The regression line fitted to points plotted in Fig. 5.2 is:

where s is the approximate area of the algal surface (in |im2) and v is the corresponding volume (in |im3). Both dimensions were estimated from microscope measurements and the compounding of relevant geometric shapes (Reynolds, 1984a). The coefficient of correlation is 0.72; thus, 52% of the variability in the original dataset is explained.

The outcome is instructive in several ways. First, it is satisfying that surface-to-volume

Figure 5.2

Maximum growth and replication rates of phytoplankters in continuously light- and nutrient-saturated media at constant temperatures of 20° C, plotted against their respective surface-to-volume ratios. The algae are: An flo, Anabaena flos-aquae; Aphan, Aphanizomenon flos-aquae; Ast, Asterionella formosa; Cer h, Ceratium hirundinella; Chlo, Chlorella sp.; Cry ov, Cryptomonas ovata; Eud, Eudorina unicocca; Fra c, Fragilaria crotonensis; Mic, Microcystis aeruginosa; Monod, Monodus sp.; Monor, Monoraphidium sp.; Pla ag, Planktothrix agardhii; Ste h, Stephanodiscus hantzschii; Syn, Synechococcus sp.; T fl, Tabellaria flocculosa; Volv, Volvox aureus. The fitted least-squares regression is r2o = 1.142 (s/v) 0 325. Redrawn with permission from Reynolds (1997a).

### Figure 5.2

Maximum growth and replication rates of phytoplankters in continuously light- and nutrient-saturated media at constant temperatures of 20° C, plotted against their respective surface-to-volume ratios. The algae are: An flo, Anabaena flos-aquae; Aphan, Aphanizomenon flos-aquae; Ast, Asterionella formosa; Cer h, Ceratium hirundinella; Chlo, Chlorella sp.; Cry ov, Cryptomonas ovata; Eud, Eudorina unicocca; Fra c, Fragilaria crotonensis; Mic, Microcystis aeruginosa; Monod, Monodus sp.; Monor, Monoraphidium sp.; Pla ag, Planktothrix agardhii; Ste h, Stephanodiscus hantzschii; Syn, Synechococcus sp.; T fl, Tabellaria flocculosa; Volv, Volvox aureus. The fitted least-squares regression is r2o = 1.142 (s/v) 0 325. Redrawn with permission from Reynolds (1997a).

should provide such a strong allometric statement about the capacity of the alga to fulfil its ultimate purpose. The empirical relation between these two attributes is, of course, not constant, even among individual spherical cells. Rather, it diminishes with increasing diameter (d), with a slope of exactly 2/3. The unit in which (sv-1) is expressed, (^m2/^m3 =) ^m-1, has the dimension of reciprocal length and conveys the idea that the decline in assimilation and growth efficiency might be primarily a function of the intracellular distance that metabolites must be conducted within the cell. The implication is that small spherical cells are metabolically more active than large ones. If there is to be an advantage in being larger, it must either be at the expense of the potential for rapid growth, or it should invoke a simultaneous distortion in shape. As the sphere is bounded by the least possible surface enclosing a given three-dimensional space, any distortion from the spherical form increases the surface area relative to the enclosed volume. It was pointed out first by Lewis (1976) that the morphologies of marine phytoplankton, despite embracing a range of sizes covering 6 or 7 orders of magnitude, are such that many of the larger ones are sufficiently non-spherical for the corresponding surface-to-volume values to vary only within 2. He deduced that this conservatism of (sv-1) was not incidental but a product of natural selection. When Reynolds (1984a) attempted the analogous treatment for a selection of freshwater phytoplankton, nearly 3 orders of magnitude of variation in (sv-1) were found, against over 9 orders of variation in the corresponding unit volumes (see 1.7). The cytological relationship of cell surface to cell mass is clearly a relevant factor in cell physiology.

The second interesting feature of Fig. 5.2 is the slope of r20 on (s/v): the exponent, 0.325 agrees closely with Raven's (1982) theoretical argument for growth conforming to a model relationship of the type, r = a constant x (cell C content)-0 33. Raven's supposition invoked the slower increase of surface (as the square of the diameter) than the volume (as its cube) of larger-celled organisms. Assuming, for a moment, carbon content to be a direct correlative of protoplasmic volume (as is argued in Section 4.2), and the surface area to be a 2/3 function of increasing volume, then the arithmetic of the indices to (s/v) clearly sum to 1/3. Raven's (1982) derivation differs from the more frequently quoted deduction of Banse (1976), namely r = a constant x (cell C content)-0.25, which had been based upon marine diatoms. Reynolds' (1989b) equation (i.e. that in Fig. 5.2) is not necessarily at odds with Banse's findings, as the assumption of a constant relationship of C to external cell volume does not hold for the (larger) diatom cells characterised by large internal vacuolar spaces.

A further satisfaction about the relationship comes from the fact that the scatter of points shown in Fig. 5.2 becomes a cluster at the end of the regression line fitted by Nielsen and Sand-Jensen (1990) to the growth rates of higher plants as a function of their surface-to-volume ratios. The slopes of the two regressions are almost identical. Presumably, small size, the consequent relatively high surface-to-volume ratio, structural simplicity and the exemption from having to allocate resources to the production of mechanical and conducting tissues provide the main reasons for the high rates of specific biomass increase among planktic microalgae relative to those of littoral bryophytes and angiosperms. The ability of the plankter to exchange materials across and within its boundaries is a key determinant of its potential physiological performance. That ability is strongly conditioned by the ratio of its surface to its volume.

### 5.3.2 The effect of temperature

Sourcing from the various literature compilations mentioned in the previous section, Reynolds (1984a) deduced that, with the exception of acknowledged cold-water stenothermic and thermophilic species, most laboratory strains of planktic algae and cyanobacteria then tested achieved their maximal specific rates of replication in the temperature range 25-35 °C. A few (like the Synechococcus of Kratz and Myers, 1955) maintain an accelerated function beyond 40 °C but, exposed to their respective supra-optimal temperatures, the replication rates of most of the species considered here first stabilise and, sooner or later, fall away abruptly. From 0 °C to just below the temperature of the species-specific optimum, the replication rates of most plankters in culture appear, as expected, to increase exponentially as a function of temperature. However, the degree of temperature sensitivity of the division rate is evidently dissimilar among plank-ters. In some, growth rates vary by a factor of ~2 for each 10 °C step in temperature, as Lund (1965) recognised; for others, the temperature dependence of growth rate is more sensitive and the slope of r on temperature is steeper.

Seeking some general expression to describe the sensitivity of algal replication rates to temperature, Reynolds (1989b) used the same data compilations to identify sources of relevant information on growth performances. What was needed were the maximum rates of replication of named algal species maintained in culture under constant, photosynthesis-saturating light conditions and initially growth-saturating levels of nutrients but at two or (ideally) more constant temperatures. Data satisfying this criterion were found for 11 species. For the purpose of comparative plotting (Fig. 5.3), data were normalised by relating the logarithm of daily specific replication rate at the given temperature, log(r¿), to the given temperature (9 °C) rendered on an Arrhenius scale. The latter invokes the reciprocals of absolute temperature (in kelvins). Thus, 0 °C (or 273 K) is shown as its reciprocal, 0.003663. For manipulative convenience, the units shown in Fig. 5.3a are calculated in terms of A = 1000 [1/(9 K)]. The thousand multiple simply brings the coefficient into the range of manageable, standard-form numbers.

In this format, the temperature-response plots reveal several interesting features. These include interspecific differences in the temperature of maximum performance, ranging from appearing at a little over 20 °C (a little under 3.42 A) in Apha-nizomenon flos-aquae and Planktothrix agardhii (original data of Foy et al., 1976) but somewhere >41 °C (<3.19 A) in the Synechococcus of Kratz and Myers (1955). The differences in the normalised parts of the species-specific slopes reflect interspecfic differences in sensitivity to variation in temperature. Thus, the slope fitted to the data for Synechococcus, for example, has the value ¡3 = -3.50 A-1. Cast in the more traditional terms of the Qjo expression for the factor of rate acceleration over a 10- ° C step in customary temperature (usually that from 10 to 20 °C), the normalised response has a Qjo of ~2.6. In contrast, the slope for colonial Microcystis, ¡ = -8.15 A-1 (Qj0 ~ 9.6), reveals a relatively greater temperature sensitivity. The slopes, of course, reflect interspecific differences in the sum of metabolic responses to temperature fluctuation, some of which are themselves differentially responsive to thermal influence. Whereas, for instance, photosynthetic electron transfer has a Qj0 of approximately 2 over a 30 °C Range (see Section 3.2.1) and both light-saturated photosynthesis and dark respiration carry Qj0 values in the range 1.8-2.25 (Section 3.3.2), protein assembly has a Q10 said to exceed 2.5 (Tamiya et al., 1953). Whereas the rates of growth of the plankters whose (relativly gentler) slopes appear towards the top of Fig. 5.3a might reflect temperature constraints on individual assembly processes, the (steeper) slopes towards the bottom of the figure refer to larger, low (s/v) forms and coenobial Cyanobacteria whose responses

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