Limits on population growth
Dismal theorems
If the only ultimate check on the growth of population is misery, then the population will grow till it is miserable enough to stop its growth.
- Kenneth Boulding
Moderately cheerful version:
If something else other than misery and starvation can be found which will keep a prosperous population in check, then the population does not grow till it is miserable and starves, and it can be stably prosperous.
Criteria to judge models
- Does it answer some clear causal questions? (of the type: “Under conditions A, X leads to Y.”) Or does it intend to make quantitative predictions?
- Is it sufficiently abstract (and therefore intelligible), and not loaded down with unnecessary details?
- Is it mathematically elegant (in a way that could contribute to building mathematical theories for their own sake)?
Approaches
- Process based, open ended “theory”
- Fitting a model to a specific dataset/ outcome.
Resources
- Vishvesh Guttal 2021 course: videos, canvas site.
Equilibrium
- At equilibrium, population size remains constant:
- Or \(f(x^) = x^\)
Stability
- An equilibrium is stable if any perturbation from the equilibrium dies down. Local extinction (N=0) is an unstable equilibrium - introduce a few individuals and population size starts approaching a different equilibrium N.