Environmental Geology Lecture Outline - Population dynamics and environmental pressures.

What makes the human species distinct from other species (if anything)?

Why might an understanding of population dynamics be relevant in an environmental geology course?


The nature of geometric (exponential growth, unrestrained growth).

Malthus (1766-1834)

A specific case of doubling every generation. Take the case where every couple has 4 children which survive to parenthood and repeat their parents history, a doubling of population every generation. this would result in a sequence like: 2 -> 4 -> 8 -> 16 -> 32 -> 64 -> 128 -> 256 -> 516 -> 1032 -> 2064 -> 4128 ...... The general formula is y=2**t , where t = the number of generations (in years generation = average age of parent). This produces a J shape curve, and the number 2 can be considered as a growth constant.

The general case: We can describe an increment of growth with the following sentence: population growth (N) = # of reproducing units (N(i)) * growth constant (k) * time increment (t). The shorthand for this is below

N = N(i) * k * t

If you integrate then this changes into:

N(t) = N(0)* (e ** (k't )) or ln Nt = ln No + k't

where e=2.71 , where ln is the natural log (base e), N(0)=initial population at time 0, N(t) = population after time t. k' is a different growth rate. You can use this equation in plug and chug mode to predict unrestrained constant growth rate population histories (yet consider how likely is such a history to occur?).

Reiterative description. For successive generations imagine a series of numbers: N(0) - N(1) - N(2) - N(3) - N(4) - N(5) - N(6) ...- N(n). If N(n) is the population at present somewhere throughout this history, then the population in the next cycle (generation), N(n+1), is given by: N(n+1)=B*N(n) , where B is the equivalent of k, a growth constant. Notice by the way that there is no reason why B can't change with time.

Exponential population growth versus consumption rate, which is the real culprit?


Growth with a restraint term and this way to chaos.

What will happen as the population begins to reach a maximum population possible (N(max))? The growth constant must decline in value. Verhulst in 1845 came up with this equation for this situation: N(n+1)=B*N(n)*(1- N(n)/N(max)) . B is a inherent growth factor (reproduction rate when restraining factors are not significant). How does the last term behave as you approach or move away from N(max)? Simple rearrangement of the forumula may better show this behavior.

N(n+1)=B'*N(n) , where B'=B*(1- N(n)/N(max))

In this formula the growth 'constant' actually varies with time depending on how close or far away it is from some maximum. See the computer program for a visualization of this behavior. Can you think of some species whoes populations show chaotic and/or large fluctations, and whether their inherent growth rate is high or low? Remember that this is a model, and if it has a sound theoretical basis it informs of possibilities, not eventualities.



What will cause changes in growth "constant"?

Maintaining present behavior, how long till 1 person for every square meter?

Conclusion: present behavior can't be maintained and growth constant is not constant, but continuously changes and might be better thought of as growth factor or parameter. In this way the Verhultz equation is a more useful guide than standard depictions of exponential population growth.

Concept of carrying capacity and determinants of such capacity.

Have local carrying capacities been reached and what were/are the consequences?

What is the role between growth constant at any one time and environmental conditions? consideration of this also indicates that the carrying capacity changes with time and events.

Economics of growth vs. sustainable development; e.g. Daly, H. E., 1991, Steady-state Economics; Island Press, 300 p.


Population density map taken from CIESEN's web site. The more intense colored reds and purples represent higher population densities. What are the factors controlling this distribution?


Some web resources on population dynamics:

Population Index is a journal dedicated to population science.

Population Growth and Balance is an excellent educational resource with some real depth to it, and includes interactive computer models.

This is the homepage of a group which advocates negative population growth.

Paul Ehrlich and the population bomb - this is a PBS documentary.


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