Biology Reference
In-Depth Information
Where Mq is mortality, Mp metabolic costs, z0 background mortality, z is mortality rates
determined by resources, G is growth of biomass, H and C are the Carnivore intake rates
influenced by Herbivore biomass. Both z0 and z are curve fitting constants.
This is simplified into the formula: G-Mp - Mq = (1/H)dH/dT
Thus, each component is dependent on environmental influences, namely Growth is
dependent on resources, metabolic costs on environmental conditions such as temperatures,
and Mortality is dependent on the environmental predation but also interacts with resources
and senescence. Clearly, the biomass rate of change, dH/dT, is dependent on these four GMM
components of the equation. If one then looks at the individual animals in the population that
make up the biomass, their food intake is an important factor. Herbivores spend time grazing or
browsing foraging for food, travelling, resting, ruminating and socializing. Thus food intake is
given by the equation: Id = If (1- tr, - tmis)
Where If is food intake minus tr time resting and tmis time for miscellaneous activity. For
medium sized ungulates, most of the feeding is during the day but rhino and elephants continue
to feed during the night and buffalo for a variable amount of time. Small ungulates feed mostly
at night. Cattle, in contradistinction only can feed for about 13-14 hours a day, even when food
resources are poor and they are starving. Kudus spend 91% of the day feeding. The rate of
food intake from an area varies for animals and sheep consume 11g of vegetation per square
meter whereas bison eat 90g per square meter and for kudu only 3g/m2. For cattle half -
saturation is 40g/m2 so the food intake rate would be higher. Clearly, vegetation mass rate of
growth is also dependent on the rate of grazing of herbivores in a closed environment that in
turn feeds back on the herbivore population dynamics.
The formula for this is: dV/dT = gvV(1-V/vmax)
Where the rate of change of Vegetation biomass above ground is equal to the maximum
growth rate (gv) vmax is the maximum biomass that the vegetation can attain.
The rate of vegetation consumption by herbivores is given by the formula: I = imF/(f1/2 + F)
Where I is the relative intake rate, im is the potential maximum intake rate, F is the
vegetation Forage biomass, and f1/2 the half - saturation biomass. The vegetation biomass is
not quite the same as the Forage biomass because not all vegetation will be available. Using
the GMM formula from above one can then calculate the rate of change of Herbivore biomass
change by the formula: dH/dT = (G-Mp - Mq) H
From this one can then also work out the Growth of herbivore biomass dependent on the
conversion of the vegetation biomass into Herbivore biomass. The formula is given as:
G = c im {F/ (g1/2 + F)}
Where c is the conversion coefficient represented in a maximum conversion environment
with high forage biomass, and g1/2 represents half saturation herbivore biomass gain but this
may change and f1/2 represents the rapidity of biomass quality decline with biomass
consumption. The parameters usable for these models are known so that calculations can then
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