General Stream Stoichiometry (GSS) Model
Breck Bowden, Carl Cappelletti, Alex Hackman, Maeve McBride
Objective: To simulate the influences of food quantity and quality on growth of organisms in a simple
stream food web.
Intent: This model is intended to explore theoretical relationships between food quantity and, especially,
food quality (stoichiometry) in a simplified stream food web. It is not intended to simulate all aspects of
food web dynamics in a complete food web.
Structure: One primary producer group, two primary consumers (invertebrates), on secondary consumer
(fish).
Spatial scale: A unit meter squared of ‘average’ stream bottom. This unit can be scaled to habitats or
entire reaches by simply multiplying by the desired area.
Temporal scale: simulation time step is 0.25 to 1 hour; total run time is 10,000 to 25,000 hours.
Units: Stocks are in mg/m2; flows are in mg/m2/h
Basic dynamics:
Photosynthesis is a constant input in this model, but can be varied as desired. In the future,
photosynthesis can be driven by key variables (light, temperature, nutrient availability). We have
constructed a module to do this, but it is not included in this version. Photosynthesis creates primary
producer biomass.
The quality of primary producer biomass is determined by a mean C:N (or C:P) ratio and a variance about
this mean.
The primary consumers have a maximum theoretical growth rate that is set by turnover time,
characteristic of the ‘species’. This maximum growth rate is modified by two factors: food quantity and
food quality. The effect of food quantity is controlled by a multiplier that varies from 0 to 1 and that
follows a cumulative, sigmoid curve as a function of food abundance. The half-maximum of this sigmoid
curve essentially defines the ease with which the ‘predator’ can find and eat the ‘food’. The form of this
function is the same for the primary and secondary consumers, though the defining parameters can be
varied at will. This multiplier is functionally similar to a feeding efficiency.
The effect food quantity is controlled by a multiplier that varies from 0 to 1 and that follows a one-sided
normal probability distribution. The shape of this special function is defined by the mean C:N (or C:P)
that the ‘predator’ needs and their ‘tolerance’ (variance) around this mean. If the ‘food” C:N (or C:P) is
less than this mean, then the quality multiplier is 1, by definition (i.e., the predator gets the maximum
benefit from eating the high quality (low C:N or C:P) food. If the ‘food’ C:N or (C:P) is greater than the
mean C:N (or C:P) required by the ‘predator’, then the quality multiplier decreases at a rate defined by the
‘tolerance’ (variance). Thus multiplier is functionally similar to an assimilation coefficient.
Actual growth is the product of the maximal growth and the quantity and quality multipliers. This
general structure is the same for both primary and secondary consumers. Primary consumers are
responsive on to the primary producer. The secondary consumer is responsive to both primary
consumers, independently. Feeding preferences can be controlled through choices for the ‘halfmaximum’ values of the ‘quantity multipliers’.
Under conditions in which the food quality is greater than that required by the predator, the excess N (or
P) is simply ‘lost’ from the organism (and the system). The model includes a provision to allow the
primary and secondary consumers to produce biomass with C:N (or C:P) ratios that are different from
what the primary and secondary consumers actually eat. This is to recognize that even though the
primary and secondary consumers eat foods with a particular quality (C:N or C:P) ratio, their own
physiology may be such that they produce tissues with a different C:N (or C:P) ratio.
Interface: The model includes an interface that allows the user to vary key parameters within set limits
and view the results of most variables.