2014). Thus the growth rate H Au c − Rb is approximately equal for the observed strategies
that have approximately constant energy-specific 146 clearance rates Au.
The observations here illustrate that filter feeding strategies are characterized by combinations
148 of physiological and behavioral traits that are defined by a constant energy-specific clearance rate.
Flow speeds, however, are found to be insufficient to utilize either of the two optimum strategies,
150 thus we cannot explain the observed trait combinations by global optimization. This suggests
physical constraints on the flow speeds that the organisms can produce.
152 Limitations on body plan and flow speed
There are of course limits to the power and force that the flow-creating motor can generate and
these limits depend on the body plan. One natural constraint is found by assuming that the
maximum motor power scales linearly with the energy content of the organism. Such a scaling is
suggested by several studies on metabolic rates at high activity that found close to linear scaling
relations (Glazier 2014; Meyer-Vernet and Rospars 2016; Weibel and Hoppeler 2005). From this
we obtain a constant maximum limit Rmax to the energy-specific dynamic respiration rate Rf , as
has also been found for the energy-specific total respiration rate (Kiørboe and Hirst 2014). We
make the simplifying assumption that the maximum motor power is equal to the basal respiration
rate, i.e., in the extreme case the total consumption is divided equally into flow creation and basic
investment. Thus we have
k Au2 = Rf < Rmax = Rb. (10)
The larger the energy-specific filter area of an organism, the lower is the flow speed that the motor
can generate. With the power limit Rmax the flow speed is limited by a maximum
We further consider a maximum motor force. For complex motors of multicellular organisms
Marden and Allen (2002) have found that the maximum force scales linearly with the motor mass