I mean on a macro scale>picrel
Lokta Volterra is supposed to fit sometimes. Carrying capacity isn't one number because you can wipe out the predators to get more prey.
>>16536585No
Predicting the carrying capacity of a real ecosystem accurately is usually impossible. But it depends on the ecosystem and what you mean by "accurately".
>>16536585It depends on the specific field and notion of carrying capacity. Generally, these things don't lend themselves to being tractable problems to model. Here's a brief and incomplete list of the factors preventing "perfect" prediction of the carrying capacity of an ecosystem/economy:1) The actual dynamics of the system are imperfectly described by whatever differential/difference equation modeling they use. This is true both in the sense that systems are far less linear than our models tend to be, and that real world ecological factors tend to have mixtures of continuous and discrete variables at once (while the models are almost always simply continuous time diff eq or discrete time difference only rather than mixed). 2) The parameters of any dynamic systems model you use are not known (meaning they generally need to be estimated from data) and are also usually time-varying. 3) Organisms are not fungible/interchangable like variables in some mathematical system. Any two animals/people will have differences in the resources they consume/produce and this will happen at all levels of the model. There might be some statistical average behavior you can point to in a predator/prey type model (as an example) but particular animals will not generally be exactly like the average.4) Even if all of the qualitative factors end up working out in your favor (e.g., you have somehow found the only LTI population system in existence), you still need to accurately estimate a continuous variable from discrete observations. Even in ideal classroom settings that often requires asymptotically infinite sample sizes to get the "exact" answer.
