untitled

the growth increment. Hence, the rate of plant growth is influenced by both rainfall

and plant biomass at the beginning of the period.

Figure 12.4 is a graphical representation of a regression analysis that estimated the

relationship between growth increment in kg / ha over 3 months (∆) on the one hand

and starting biomass (V) and rainfall in mm (R) on the other:

∆=−55.12 −0.01535V−0.00056V^2 +3.946R

Unlike the logistic model, plant growth in the Australian study was highest at low

levels of abundance, rather than at intermediate levels of abundance (see Chapter 8).

This is probably due to there being an ungrazeable plant reserve below ground. At

low levels of plant abundance, rapid regrowth is enabled by translocation from these

below-ground tissues. Such an ungrazeable refuge tends to lend a stabilizing influ-

ence to the interaction, as we shall shortly see.

Having established how fast the resource grows in the absence of grazing and brows-

ing, we now need to know what happens to it when a herbivore is present. The amount

a herbivore eats per unit time is a constant only when it is faced by an ad libitum

supply. Herbivores are seldom so lucky. The trend of intake against food availabil-

ity is therefore curved, being zero when the level of food is zero and rising with increas-

ing food to a plateau of intake. From there on no increase in food supply has any

effect on the rate of intake because the animal is already eating at its maximum rate.

Such a curve is called a functional responseor feeding response, the trend of intake

per individual against the level of the resource (see also Chapter 10). It can be

represented symbolically by an equation such as:

I=c[1 −exp(−bV)]

where Iis plant consumption, cis the maximum (satiating) intake, Vis the level of

the resource, and bis the slope of the curve, a measure of grazing efficiency. The

last has another meaning. Its reciprocal 1/bis the level of the resource Vat which

0.63 (i.e. 1 −e−^1 ) of the satiating intake is consumed.

Figure 12.5 shows the dry weight food intake (I) by a red kangaroo at various

levels of pasture biomass when it is grazing annual grasses and forbs interspersed

with scattered shrubs (Short 1987). The equation for a 35 kg kangaroo is:

I=86[1 −exp(−0.029V)]

The satiating intake is 86 kg / 3 months, occurring when pasture biomass exceeds

300 kg / ha.

Short (1987) estimated these two functional responses by allowing high densities

of kangaroos and rabbits to graze down pasture in enclosures, the offtake per day

being estimated as the difference between successive daily estimates of vegetation

biomass corrected for trampling. Daily intake could be estimated for progressively

lower levels of standing biomass because the vegetation was progressively defoliated

during the experiment. We scale up this daily intake rate to intake per 3 months to

maintain a similar time frame as for the plant growth data.

Although the functional response has been discussed here in the context of a

plant–herbivore system, all of that discussion carries over to prey–predator systems.

CONSUMER–RESOURCE DYNAMICS 201

12.5.2The functional
response of
kangaroos to plant
abundance