Singlegeneration experiments

Given these problems, the alternative 'laboratory' approach, especially with plants (although the methods have occasionally been used with animals), has generally been to follow populations over just a single generation, comparing 'inputs' and 'outputs'. A number of experimental designs have been used.

In 'substitutive' experiments, the effect of varying the proportion of each of two species is explored whilst keeping overall density constant (de Wit, 1960). Thus, at an overall density of say 200 plants, a series of mixtures would be set up: 100 of species A with 100 of species B, 150 A and 50 B, 0 A and 200 B, and so on. At the end of the experimental period, the amount of seed or the biomass of each species in each mixture would be monitored. Such replacement series may then be established at a range of total densities. In practice, however, most workers have used only a single total density, and this has led to considerable criticism of the design since it means that the effect of competition over several generations - when total density would inevitably alter - cannot be predicted (see Firbank & Watkinson, 1990).

None the less, replacement series have provided valuable insights into the nature of interspecific competition and the factors influencing its intensity (Firbank & Watkinson, 1990). An early, influential study was that of de Wit et al. (1966) on competition between the grass Panicum maximum and the legume Glycine javanica, which often form mixtures in Australian pastures. Panicum acquires its nitrogen only from the soil, but Glycine acquires part of its nitrogen from the air, by nitrogen fixation, through its root association with the bacterium Rhizobium (see Section 13.10.1). The competitors were grown in replacement series with and without an inoculation of Rhizobium, and the results are given both as replacement diagrams and as 'relative yield totals' (Figure 8.18). The relative yield of a species in a mixture is the ratio of its yield in the mixture to its yield alone in the replacement series, removing any absolute yield differences between species and referring both to the same scale. The relative yield total of a particular mixture is then the sum of the two relative yields. It is fairly clear from the replacement series (Figure 8.18a)

field and laboratory experiments substitutive experiments

Panicum A Glycine

- Rhizobium

+ Rhizobium

Floral Diagram Panicum Maximum

--- Rhizobium o Nitrogen yield

• Dry matter yield

4P 0G

Figure 8.18 A substitutive experiment on interspecific competition between Panicum maximum (P), and Glycine javanica (G), in the presence and absence of Rhizobium: (a) replacement diagrams; (b) relative yield totals. (After de Wit et al., 1966.)

that both species, but especially Glycine, fared better (were less affected by interspecific competition) in the presence than in the absence of Rhizobium. This is clearer still, however, from the relative yield totals (Figure 8.18b), which never departed significantly

Figure 8.19 An 'additive design' competition experiment: the yield of cotton produced from stands planted at constant density, infested with weeds (either sicklepod or redroot pigweed) at a range of densities. (After Buchanan et al., 1980.)

from 1 in the absence of Rhizobium, but consistently exceeded 1 in its presence. This suggested that niche differentiation was not possible without Rhizobium (a second species could only be accommodated by a compensatory reduction in the output of the first) and that niche differentiation occurred in its presence (the species yielded more between them than either could alone).

A second popular approach in the past has been the use of an 'additive' additive experiments design, in which one species (typically a crop) is sown at a constant density, along with a range of densities of a second species (typically a weed). The justification for this is that it mimics the natural situation of a crop infested by a weed, and it therefore provides information on the likely effect on the crop of various levels of infestation (Firbank & Watkinson, 1990). A problem with additive experiments, however, is that overall density and species proportion are changed simultaneously. It has therefore proved difficult to separate the effect of the weed itself on crop yield from the simple effect of increasing total density (crop plus weed). An example is shown in Figure 8.19, describing the effects of two weeds, sicklepod (Cassia obtusifolia) and redroot pigweed (Amaranthus retroflexus), on the yield of cotton grown in Alabama (Buchanan et al., 1980). As weed density increased, so cotton yield decreased, and this effect of interspecific competition was always more pronounced with sicklepod than with redroot pigweed.

In substitutive designs the proportions of competitors are varied but total density is held constant, whilst in

Zoladex Injection Procedure

Figure 8.19 An 'additive design' competition experiment: the yield of cotton produced from stands planted at constant density, infested with weeds (either sicklepod or redroot pigweed) at a range of densities. (After Buchanan et al., 1980.)

response surface analysis

Potbelly Competitive Analysis

Figure 8.20 The response surface of competition, as indicated by seed production per pot, between (a) Phleum arenarium and (b) Vulpia fasciculata sown alone and in mixtures over a range of densities and frequencies. x1 and x2 are the sowing densities of Phleum and Vulpia, respectively. (After Law & Watkinson, 1987.)

Figure 8.20 The response surface of competition, as indicated by seed production per pot, between (a) Phleum arenarium and (b) Vulpia fasciculata sown alone and in mixtures over a range of densities and frequencies. x1 and x2 are the sowing densities of Phleum and Vulpia, respectively. (After Law & Watkinson, 1987.)

additive designs the proportions are varied but the density of one competitor is held constant. It is perhaps not surprising, therefore, and certainly welcome, that a 'response surface analysis' has been proposed and applied, in which two species are grown alone and in mixtures at a wide range of densities and proportions (Figure 8.20) (Firbank & Watkinson, 1985; Law & Watkinson, 1987; Bullock et al., 1994b; although the last of these deals with clones of the same species). Overall, these studies suggest that good equations for describing the competitive effect of one species (A) on another (B) are, for mortality:

and for fecundity:

which can both be seen to be related to Equation 5.17 (see Section 5.8.1 - basic model of intraspecific competition) and Equation 5.12 (see Section 8.4.1 - incorporation of interspecific competition). Thus, Ni A and NiB are the initial numbers of species A and B; NA and NB are the numbers of species A and B after mortality; YA is the yield (seeds or biomass) of species A; m and a are susceptibilities to crowding; P and a are competition coefficients; RA is the basic reproductive rate of species A (and hence, NaRa is the yield in the absence of competition); and b determines the type of density dependence (assumed equal to 1 for mortality - perfect compensation). Data like those shown in Figure 8.20, obtained over a single generation, can thus be used to fit values (by computer program) to the parameters in Equations 8.16 and 8.17, and the equations in their turn can be used to predict the outcome of competition between the species over many generations - which is not possible with either substitutive or additive designs.

On the other hand, Law and Watkinson (1987) found that they could obtain an improved fit to their response surfaces, especially for one of their species, if they used an equation in which competition coefficients were not fixed, but varied with both frequency and density - although the meaning of this in terms of 'plant behavior' is not clear. Hence, response surface analyses, in revealing the potential complexities in interactions between competing species, also reveal that knowing or predicting dynamical outcomes may be only part of the story. It may also be necessary to understand the underlying mechanisms (see Section 8.10).

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