A unit of Lasting Forests Sustained forests; sustained profits evolving since March 30, 1999

N _{x, y, z, t}

The individual animal is:

a _{p, q, r, s, x, y, z, t}

where p is sex; q is age class or stage; r is a dominance, behavioral, or health coefficient; x is a pregnancy coefficient (including zero); x,y,z is location in 3-D space (z expressing the timely quality of the map location for the animal); and t is time.

A population is the sum of the individuals.

A population resource is the population products or services aided or hampered by the number and characteristics (size, health, fur primeness) of the animals in the population. Thus, if n is the observed population, and f is a coefficient expressing enhancement due to density of animals and positive (or negative relations), then the population resource is:

N_t+1 = n + nf or n(1.0 + f)

Fundamental or basic models of population dynamics or change are:

N_t+1 = N_t + N_tr

N_t+1 = N_t + N_t(B-D) (B-D = birth minus death)

N_t+1 = N_t (1 + r) (difference equation)

N_t+1 = N_t + M_t (migration unit M each year)

N_t = N_o (1 + r)^t (exponential)

Note that r, a rate of population change, may be considered to be B - D.

Plot the values of N over time. Plot an upper and lower constraint. Low numbers may be "minimum viable population."

N_t+1 = N_t +c_t^(B-D) (allometric model)

compare the above equation to S = a + CA^z (the species-area curve)

N_t+1 = N_t + r N_t (1-(N_t/K)) (sigmoid)

N_t = N_oe^rt (logistic)

The previous population is a very key element of any population analysis.

A fundamental model recommended for use by managers, one highlighting negative feedback and one closely related to adaptive management, is:

N_t+1 = N* - (1-K)(N_t - N*)

Where K is the level of managerial control over the difference between where the system is now (N)and where it ought to be (N*) (the desired population based on stated objectives).

This Web site is maintained by R. H. Giles, Jr.
Last revision January 17, 2000.