Introduction: characterising growth

Whereas the previous two chapters have been directed towards the acquisition of resources (reduced carbon and the raw materials of biomass), the concern of the present one is the assembly of biomass and the dynamics of cell recruitment. Because most of the genera of phyto-plankton either are unicellular or comprise relatively few-celled coenobia, the cell cycle occupies a central position in their ecology. Division of the cell, resulting in the replication of similar daughter cells, defines the generation. On the same basis, the completion of one full replication cycle, from the point of separation of one daughter from its parent to the time that it too divides into daughters, provides a fundamental time period, the generation time.

Moreover, provided that the daughters are, ultimately, sufficiently similar to the parent, the increase in numbers is a convenient analogue of the rate of growth in biomass. The rate of increase that is thus observed, in the field as in the laboratory, is very much the average of what is happening to all the cells present and is net of simultaneous failures and mortalities that may be occurring. The rate of increase in the natural population may well fall short of what most students understand to be its growth rate. It is, therefore, quite common for plankton biologists to emphasise 'true growth rates' and 'net growth rates'. In this work, 'growth rate' (represented by r) will be used to refer to the rates of intracellular processes leading to the completion of the cell cycle, net or otherwise of respiratory costs as specified. 'Increase rate' (presented as rn) will be used in the context of the accumulation of species-specific biomass, though frequently as detected by change in cell concentration. The potential increase in the biomass provided by the frequency of cell division and the intermediate net growth of the cells of each generation will be referred to as the biomass-specific population replication rate, signified by r'. In each instance, the dimensions relate the increment to the existing mass and are thus expressible, in specific growth units, using natural logarithms. In this way, the net rate of increase of an enlarging population, N, in a unit time, t, is equivalent to:

where N0 is a population at t = 0 and Nt is the population at time t; whence, the specific rate of increase is:

Then, the replication rate is the rate of cell production before any rate of loss of finished cells to all mortalities (rL), so r = rn + rL

Replication rate is net of all metabolic losses, not least those due to respiration rate (R). Where the computation of cytological anabolism (r) is before or after respiration and other metabolic losses will be stated in the text.

On the above basis (Eq. 5.2), one biomass doubling is expressed by the natural logarithm of 2 (ln 2 = 0.693) and its relation to time provides the rate. Growth rate may be expressed per second but growth of populations is sometimes more conveniently expressed in days. Thus, a doubling per day corresponds to a cell replication rate of 0.693 d-1, which is sustained by an average specific growth rate of not less than 8.0225 x 10-6 s-1, net of all metabolic and respirational losses.

The present chapter is essentially concerned with the growth of populations of planktic algae, the generation times they occupy and the factors that determine them. It establishes the fastest replication rates that may be sustained under ideal conditions and it rehearses their susceptibility to alteration by external constraints in subideal environments. In most instances, information is based upon the observable rates of change in plankton populations husbanded in experimental laboratory systems, or in some sort of field enclosures or, most frequently, on natural, multi-species assemblages in lakes or seas. They are expressed in the same natural logarithmic units. Their derivation necessarily relies upon the application of rigorous, representative and (so far as possible) non-destructive sampling techniques, to ensure that all errors due to selectivity or patchiness of distribution are minimised.

Estimating the numbers or the biomass of each species in each of the samples provides a further problem. To use such analogues as chlorophyll, fluorescence, light absorption or scatter is convenient but each compounds the errors of sampling through misplaced assumptions about the biomass equivalence. They also lose a lot of species-specific information. There really is no substitute for direct counting, using a good microscope and based on a pre-validated subsam-pling method, subject to known statistical confidence (Lund et al., 1958). However, the original iodine-sedimentation/inverted microscope technique (of Utermohl, 1931) has largely given way to the use of flat, haemocytometer-type cells (Young-man, 1971). With the advent and improvement of computer-assisted image analysis and recognition, algal counting is now much less of a chore. Properly used, the computerised aids yield results that can be as accurate as those of any human operator.

Results accumulated over a period of algal change can be processed to determine the mean rate of population change over that period. Often it is convenient to find the least-squares regression of the individual counts for each species ln(N1), ln(N2)... ln(Ni), on the corresponding occasions (t1, t2 ... ti). The slope of ln(N) on t is, manifestly, equivalent to rn. Much of the information to be presented, in this and subsequent chapters, on the net rates of change in algal populations and the rates of growth and replication that may be inferred, is based on this approach. Modifications to this technique have been devised in respect of colony-forming algae, such as Micro-cystis and Volvox (Reynolds and Jaworski, 1978; Reynolds, 1983b).

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