INSECT ECOLOGY  ENTOMOLOGY/BIOLOGY 127
LECTURES 3 and 4 GEOMETRIC & EXPONENTIAL GROWTH
POPULATION GROWTH
I. Processes affecting population growth
A. Fundamentally four processes affect population growth and decline, but we will
concentrate on just two for now:
birth and death.
IF we assume that the population is closed (no migration) and population growth is continuous,
then we can model population growth for infinitesimal small periods of time.
Population growth rate:
Δ
N/
Δ
t = dN/dt = B  D
B =
b
⋅
N, where
b
is the
instantaneous birth rate
of births individual
1
unit time
1
; a per capita
rate => per individual
D =
d
⋅
N, where
d
is the
instantaneous death rate
of deaths individual
1
unit time
1
; a per capita
rate => per individual
(NOTE: dN
≠
d
⋅
N)
dN/dt = (
b

d
)N; assumes
b
and
d
are constant and not affected by population size
=
r
N;
r
is the
instantaneous rate of increase
,
r
is also called the
intrinsic rate of natural
increase
.
B. The rate of change of size of a population is the difference between birth and death rates:
r
= rate of population size change = instantaneous birth rate – instantaneous death rate
dN
–– = rN
dt
C. This fundamental relation summarizes all development of descriptions about population
growth and dynamics.
Starting point for more complex models
.
II. Describing population growth:
A. Populations can grow in two distinct ways. These are:
Discrete generations:
 nonoverlapping generations
e.g., insects that reproduce annually: a single generation per year
Continuous generations:
Lecture 3 and 4, page 1
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