To be developed.

An animal population is a group of animals of the same species (i) in a place (x, y, z) during a period (t).

N_{i, x, y, z,t}

The individual animal is:

i_pqrsxyzt

where p is sex; q is age class or stage; r is dominance, behavioral, or health coefficient; x is a pregnancy coefficient (including zero); xyz is location in 3-D space; and t is time.

One model is:

N_t+1 = N_t + N_tr

N_t+1= N_t + N_t(B-D)

= N_t (1 + r) (difference equation)

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

N_t+1 = N_t + M_t migration unit M added each year

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

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

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

N_t+1 = N_t + rN_t ^(1-(Nt/K)) (sigmoid)

N_t = N_o^ert (logistic)

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

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