Just as a Start:
http://www.globalchange.umich.edu/gl...predation.html
The Lotka-Volterra Equations detail a rather detailed relationship between types of predation, of both predator and prey-populations:
https://en.wikipedia.org/wiki/Lotka–Volterra_equations
And aside from the Generalized Lotka-Volterra Equations, there is the issue of Mutualism between a predator and prey population when modeling the population sizes and relationships:
https://en.wikipedia.org/wiki/Mutual...tical_modeling
In the latter example, this is where the two populations share one or more traits, or functions in the environment.
All of these are dependent upon a Carrying Capacity of the Environment:
https://en.wikipedia.org/wiki/Carrying_capacity
...and the Lotka-Volterra Equations show the interrelationships of these Carrying Capacities.
Also important is the "Impact of Human Activity on the Environment" described by Dr. Paul Erlich's I = PAT equations:
https://en.wikipedia.org/wiki/I_%3D_PAT
In terms of Middle-earth, this is a very important term, as that of Humanity and Elves (or Hobbits) needs to be greater than that of Orcs, lest you wind up with a world where the Orcs quickly destroy the Carrying Capacity of the entire "planet" (or habitable regions of the world with which we are concerned).
I = PAT
is:
Impact = Population * Affluence * Technology
In Middle-earth, this impact is nearly non-existent save for in the regions of:
• The Shire.
•*Dale/Erebor
•*Mordor
•*Gondor
•*Rohan
•*And likely in Harad and Rhûn as well, since we are told these areas are fairly highly populated.
But given that 'A' and 'T' are so low, the Impact isn't very great, and thus the effect upon Carrying Capacity isn't hugely affected (which is not to say that it is not affected at all - over time the
Impact can be cumulative).
I=PAT, though, can really only be significantly considered once you have an idea of GDP of an area.
This can be estimated in Middle-earth based upon Medieval Data about what was required for a typical person to live, and then estimating the populations of the regions based upon the population models created by the Lotka-Volterra models
Do you need anything else?
If you have your own Foundational Postulates and Coherent Metaphysical and Theological Systems upon which Middle-earth operates, please feel free to elaborate.
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