Some paradoxes in the Tilman model, how to avoid or accept them

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.