(x*/x)v when winds are light but it weakens as winds start to exceed 3 ms-1, disappearing altogether at U > 5 m s-1. The work on Ceratium in Esthwaite Water (Heaney, 1976; George and Heaney, 1978; Heaney and Tailing, 1980a, b) points consistently to the development of horizontal patchiness only at wind speeds < ~4 m s-1.

Apart from illustrating the link between vertical behaviour of phytoplankton and its horizontal distribution in small lakes, confirmed in the statistical interaction of horizontal and vertical patchiness shown in Fig. 2.31, the information considered in this section helps to establish a general point about the confinement of water motion to a basin of defined dimensions. It is that once a critical level of forcing is applied, a certain degree of uniformity is reimposed. It is not that the small-scale patchiness disappears - all the causes of its creation remain intact - so much as that the variance at the small scales becomes very similar at larger ones: small-scale heterogeneity collapses into large-scale homogeneity.

Large-scale patchiness

Nevertheless, the relationship does have a time dimension, the horizontal mixing time, and this may accommodate other sources of change. For instance, if a constant wind of 4 ms-1 induces a surface drift of the order of 400 md-1 across a 1-km basin, the probable mixing time is 5d. If, in the same 5 d, a patchy population is recruited through one or more successive doublings, then the same probability of its achieving uniformity requires stronger forcing or a shorter mixing time. This relationship between transport and recruitment becomes increasingly prevalent in larger lake basins where the role of the return current in establishing uniformity is progressively diminished: maintenance of large-scale patches (kilometers, days) needs persistent spatial differences in recruitment rate. The latter might be due directly to a local enhancement in organismic replication (because of warm or shallow water, or a point source of nutrient) or to consistently enhanced removal rates by local aggregations of herbivorous animals. However, to be evident at all, the patch must give way to the concentrations in a surrounding larger stretch of water, through diffusion and erosion by hydraulic exchanges at the periphery. Several publications have considered this relationship. Two of these, in particular (Skellam, 1951; Kierstead and Slobodkin, 1953), have given us the so-called KISS explicative model, relating the critical size of the patch to the interplay between the rates of reproductive recruitment and of horizontal diffusivity. Specifically, Kierstead and Slobodkin (1953) predicted the radius of a critical patch (rc) as:

where Dx is the horizontal diffusivity and kn is the net rate of population increase or decrease. Interpolating values for kn appropriate to the generation times of phytoplankton (the order of 0.1 to 1.0 doublings per day) and for typical wind-driven diffusivities (Dx ~ 5 x 10-3 to 2 x 10-6 cm2s-1: Okubo, 1971), critical radii of 60 m to 32 km may be derived. This 3-order range spans the general cases of large-scale phytoplankton patches in the open ocean considered by (for instance) Steele (1976), and Okubo (1978), with

Figure 2.31

Relationships between horizontal and vertical patchiness of Microcystis (•, Figures 2.23, 2.30) and of Daphnia populations (o) in Eglwys Nynydd reservoir, as detected by George and Edwards (1976). Redrawn from Reynolds (1984a).

the most probable cases having a critical minimum of ~1 km (review of Platt and Denman, 1980; see also Therriault and Platt, 1981).

Even under the most favourable conditions of low diffusivities and localised rapid growth, patches smaller than 1 km are liable to rapid dispersion. Moreover, wind-driven diffusivity may be considerably enhanced by other horizontal transport mechanisms, including by flow in river channels (see Smith, 1975), tidal mixing in estuaries (data of Lucas et al., 1999) and, in stratified small-to-medium lakes, by internal waves (Stocker and Imberger, 2003; Wuest and Lorke, 2003). In spite of this, some instances of small patch persistence are on record. Reynolds et al. (1993a) reported a set of observations on an intensely localised explosive growth of Dinobryon in Lake Balaton, following a mass germination of spores disturbed by dredging operations. The increase in cell concentration within the widening patch was overtaken after a week or two, partly through dispersal in the circulation of the eastern basin of the lake and into that of the western end but, ultimately, because the rates of Dinobryon growth and recruitment soon ran down.

At the other end of the scale, satellite-sensed distributions of phytoplankton in the ocean reveal consistent areas of relatively high biomass, covering tens to hundreds of kilometres in some cases - usually shallow shelf waters, well supplied by riverine outflows, or along oceanic fronts and at deep-water upwellings (see review of Falkowski et al., 1998). The size and long-term stability of these structures are due to the geographical persistence of the favourable conditions that maintain production (shallow water, enriched nutrient supply) relative to the rates of horizontal diffusivity in these unconfined locations.

Such behaviour is observable in larger lakes, especially where there are persistent gradients (chiefly in the supply of nutrients) that survive seiching. Enduring patchiness was memorably demonstrated by Watson and Kalff (1981) along a persistent nutrient gradient in the ribbonlike glacial Lake Memphrémagog (Canada/USA). Persistent gradients of phytoplankton concentration are evident from long-term surveys of the North American Great Lakes (Munawar and Munawar, 1996, 2000). Of additional interest in large, northern continental lakes is the vernal patchiness of phytoplankton attributable to the early-season growth in the inshore waters that are retained by horizontal temperature gradients associated with the centripetal seasonal warming - the so-called 'thermal bar'. This phenomenon, first described in detail by Munawar and Munawar (1975) in the context of diatom growth in Lake Ontario, has been reported from other large lakes: Issyk-kul (Shaboonin, 1982), Ladozhskoye, Onezhskoye (Petrova, 1986) and Baykal (Shimarev et al., 1993, Likhoshway et al., 1996).

In general, it is fair to say that the KISS model is illustrative rather than deterministic, and it is only imprecisely applicable to a majority of small lakes subject to internal circulation and advec-tion. Here, the predictive utility of the later general model derived by Joseph and Sendner (1958) is sometimes preferred. The fitted equation is used to predict critical patch radius as a function of the advective velocity, us:

If kn is one division per day and us = 5 x 10—3 m s—1 (roughly what is generated by a wind force of 4 m s—'1), rc ~ 1.6 km. At five times the rate of horizontal advection (us = 25 x 10—3 ms—1), the critical radius is increased to ~8 km. Again, the actual values probably have less relevance than does the principle that patchiness in phytoplank-ton developing in lake basins less than 10 km in diameter is likely to be temporally transient and not systematically persistent.

Relevance of patchiness

Many of the mysteries of patchiness that concerned plankton scientists in the third quarter of the twentieth century may have been cleared up, but the issue remains an important one, for two main reasons. One, self-evidently, lies in the design of sampling strategies. If the purpose is merely to characterise the community structure, much information may be yielded from infrequent samples collected at a single location (Kadiri and Reynolds, 1993) but, as soon as the exercise concerns the quantification of plankton populations and the dynamics of their change, it is essential to intensify the sampling in both time and space. Sampling design is covered in many methodological manuals (see, for instance, Sour-nia, 1978) but it is often useful to follow specific case studies where temporal and spatial variability needed to be resolved statistically (Moll and Rohlf, 1981).

The second reason is the perspective that is required for the ecological interpretation of information on the structure and distribution of planktic communities in nature. This is crucial to the ideas to be developed in subsequent chapters of this book. It is not just a case of defining the confidence intervals of quantitative deductions about organisms whose distribution has long been regarded as non-random, and over a wide range of scales (Cassie, 1959; McAlice, 1970). In order to sort out the multiple constraints on the selection, succession and sequencing of natural phytoplankton populations, it is always necessary to distinguish the dynamic driver from the starting base. The assemblage that is observed in a give parcel of water at given place and at a given time is unrelated to the present conditions but is the outcome of a myriad of processing constraints applying to a finite inoculum of individual organisms of historic and probably inexplicable provenance.

In this chapter, the focus has spanned the dissipation of a fortuitous and localised recruitment of algae in a relatively small, shallow lake through to the relative uniformity of the plankton composition of an oceanic basin. The one may depend upon the rapidity of growth in relation to diffusivity (Reynolds et al., 1993a); the other upon the extent of a single and possibly severe growth constraint over an extensive area of open ocean (Denman and Platt, 1975). Thus, it is important to emphasise that although the entraining motions and horizontal diffusivity of pelagic water masses influence profoundly the distribution of phyto-plankton, they do not confine organisms to a fixed position in relation to the motion. Transport in the constrained circulation of a small lake or passage in an open ocean current each sets a background for the dynamics of change and variations in composition. The various outcomes arising from differing relative contributions of the same basic entraining processes are remarkably disparate. On the one hand, we can explain the seasonal formation of cyanobacterial plates in deep alpine lakes (Bright and Walsby, 2000). On the other, there is no conceptual objection to the inability of McGowan and Walker (1985) to demonstrate any significant variation in the rankorder of species abundances in the North Atlantic at spatial scales up to 800 km, despite strong small-scale spatial and interseasonal and inter-annual heterogeneity. This is attributable to the large-scale coherences in the basin-scale forcing functions (direct measurements of the mid-depth circulation of this part of the Atlantic Ocean have been given by Bower et al., 2002). Analogous relationships among planktic components have been shown to be widespread through extensive circulation provinces of the tropical and subtropical Atlantic Ocean (Finenko et al., 2003), despite significant intracompartmental variability in abundance and considerable intercompart-metal structural differences. The observations demonstrate the nature of the interaction of population dynamics with the distinguishable movements of the water masses in shaping the species structures of the pelagic.

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