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B. How do populations change; "the motion picture" (population dynamics)

  3. Regulation of populations

From a previous lecture
 Nt+T (erT) * Nt

 dN/dt= rN

What does  this model of population growth assume?


Bacteria innoculated in a broth  (N0=100)
Bacteria double every 20 min (r=1.035 min-1)
population size after 36 hours = e1.035(36*60)* 100  =  2 X 1034
or enough bacteria to cover the entire earth 1 ft deep!


What really happens to natality and mortality as a population grows beyond a certain size?  Why?

Resource = "environmental component used by an organism" e.g. food, shelter, light, space.

The population size at which population growth rate is zero (no slope,  dN/dt=0) is the 'carry capacity' or 'equilibrium population density' (K).  It is the maximum number the environment can support indefinitely.  At some point, something has to limit population growth.

There are numerous ways that limitations to population growth can be modelled and the most appropriate model for a given population would be a function of the type of factors that most affect that population.  Two general types of models:

Deterministic models - The population density at a future time can be predicted based on present density.  These models should work best for populations in which intrinsic or density-dependent factors dominate.  That is, the density of the population directly determines the rate of births and/or deaths.   For example:
Stochastic models - Such models incorporate processes that affect density which are unpredictable.  These models should work best for populations in which extrinsic or density-independent factors dominate.   That is, the affects on births and/or deaths will be similar regardless of whether the population is large or small.  For example:

Here are two examples of these models:
A simple deterministic model of population growth

Note that such time delays can be added into this model by substracting a time delay term from the time N is evaluated relative to K (see text) (click on here to run a simulation).

A closer look at factors limiting population size in nature
Why might an ecologist be biased one way or the other?

Four species of moths in a German pine forest.