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?

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

If you integrate then this changes into:

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?

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.

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**.

**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.

- role of technology.
- population density and disease vectors.
- food producing capacity.
- many others.

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.