2 Ecological and biological background
In this form the ingestion rate as a function of food concentration can be written as
Gmax=Qmax + c
where Gmax is the maximum ingestion rate and Qmax the maximum clearance rate that
determines the maximum slope of the function (gure 2.2 A). The ratio Gmax=Qmax
denes a characteristic concentration, to which the organism is adapted and where it
reaches half of the maximum ingestion rate. Above that concentration the function
levels o and thus there is little additional gain from higher concentrations.
The growth rate of an individual describes the individual rate of mass increase (as
opposed to the population growth rate). For comparison of dierent organisms one
can measure a maximum growth rate that is independent of prey concentration such
as the maximum ingestion rate Kirboe and Hirst, 2013. Growth of course increases
with increasing prey ingestion.
Finally with the respiration rate, i.e., the amount of oxygen respired per time, one
can measure the energy expenditure per time (metabolic rate) of animals, which is used
for basic maintenance (basal respiration rate) and for foraging (dynamic respiration
rate) Schmidt-Nielsen, 1997. In many cases the dynamic rate is neglected and the
total respiration rate is measured as proxy for the basal rate. Ingestion, growth, and
respiration rates can be converted to energy per time and the prey concentration in
carbon mass per volume can be converted to an energy density (gure 2.2). The
clearance rate generally has the dimensions of a volume ow rate (volume per time).
Intuitively it is clear that, integrated over the average lifetime, the total gained
energy by ingestion needs to balance growth, respiration, predation mortality, and
reproduction Litchman et al., 2013. There are several hypotheses and theories on
the scaling of rates with body size, where the metabolic rate is often seen as the most
important measurable characteristic of the organism performance that the scalings of
other rates depend on Brown et al., 2004. Vital rates (in dimensions of gained or lost
mass, energy or volume per time) are found to scale linearly or less than linearly with
carbon mass and energy content, thus with an exponent k = 1. The deviation from
linear scaling can be more easily seen, when considering mass- or energy-specic rates,
which have the exponent k 1 = (gure 2.2 B, C). A common hypothesis assumes
so-called allometric scalings of all rates, with quarter powers = 1=4 (i.e., k = 3=4).
This was rst suggested by Kleiber and the quarter power was reasoned for by theories
on optimal branching of transport networks Kleiber, 1932; West and Brown, 2005.
Since measured scaling exponents are often closer to 1=4 than 1=3 (an exponent
suggested from a surface law) the quarter power scaling is widely accepted. However,
the theory behind this exponent and its universal applicability are still subject to
debate Hulbert, 2014.
Mass- or energy-specic metabolic as well as maximum clearance rates across speciesoverarching
size ranges exhibit values ranging between an upper and lower `universal'
constant, while the allometric scaling is only conserved within similar species groups
(only the coecient shifts across groups) Makarieva et al., 2008. Maximum ingestion
and maximum growth rate, however, apparently do not have such bounds and exhibit a