  The Tilman model of consumers competing for resources has some aspects that
appear counterintuitive. Within the standard Tilman model for a single consumer
and a single resource, when a very efficient consumer rapidly eats all
available food, the resource density becomes zero, but if there is no food, how
can the consumer survive? The paradox can be lifted by realising that on the
short term indeed rapid consumption may lead to starvation and a decline in the
consumer population, but in the long term a finite resource and consumer
density remain. A single consumer living on two essential nutrients leaves the
density of the non-limiting nutrient above its critical level, so what is done
with the extra food? We explain that this does not imply extra food is
consumed, just for fun, but that in fact the food is left untouched because
there is no use for it. For a model with two consumers competing for a single
nutrient one of the consumers will eventually disappear, even if the food
economics of the surviving one is worse and there is still much food wasted.
Both are inherent aspects of the model, and the paradox can be avoided if the
difference between the consumers is small, in which case it will take very long
to reach equilibrium. We argue that in general an extended stability analysis,
in which not only the asymptotically stable state is considered, but also the
unstable steady states and all time scales involved in the transient dynamics,
can help in avoiding apparent contradictions in ecological models, or accepting
them.
