NRES 310: Wildlife Ecology and Management
Ricker Model lecture
13 October 2008
McCullough Model -- George Reserve Deer Herd 1979, University of
Michigan Press.
Population of white-tailed deer was reduced to few animals and then increased to
high density over a 15-year period. George Reserve population was reduced to
about 10 adult females. When removing animals in autumn became difficult to
differentiate fawns from adult females because so big and growing so fast. Very
high plane of nutrition.
At K
Populations at K are characterized by:
Poor Physical Condition (intense intraspecific competition for resources)
Low ovulation rates
Reabsorption or abortion of fetuses
Stillborn or weak young
Failure of does to care for young
Not all does reproduced (single offspring)
No yearling females or female fawns reproduced (age at first reproduction
became older)
But, as population was killed back the above conditions were reversed
because there was reduced competition for resources and thus a higher
nutritional plane.
Most does gave birth to twins  then triplets
Yearling females and female fawns began to reproduce
Low Density
 twins common, even from fawns
 triplets in females > 1.5 years
 few females failed to breed
 # of embryos per pregnant female increased rapidly as population size
declined.
NRES 310: Wildlife Ecology and Management
Ricker Model lecture
13 October 2008
K need not be
known in advance
K/2
Recruitment Rate
(Young / adults)
K
Population Size
a = rmax for that environment (r changes all along the
line, but models assume r is constant, need to use
rmax).
Regression Line
Recruitment
Rate
(No. Young / No.
Adults
Rate x Population Size = Number
K/2 or MSY
K
Extremely high rate
of reproduction
Population Size
From this example K and a can be calculated with simple regression.
Regression line calculated as Y = a + bX
Where b = slope
a = y-intercept, basically rmax for that environment, constant at x=0.
K = intercept at Y = 0,
These are nutritional models:
 As population size increases
 nutrition per individual decreases.
 young fostered / adult also decreases
NRES 310: Wildlife Ecology and Management
Ricker Model lecture
13 October 2008
As push population size away from K
 body condition increases as intraspecific condition decreases
 age first reproduction decreases
 higher conception and ovulation rates
 low density, fawns begin reproducing and often have twins

very low density does begin having triplets  animals in
phenomenal shape!
Cannot assess populations in different areas using the same criteria. K differs
between populations so you cannot directly compare them! (same population
size is different density with respect to K).
For example:
Population Size
200
300
400
K
200
300
400
No. Dying
20
30
40
10 % dying. When plot
mortality rate v. population
size. You would conclude
populations are density
independent, although in
reality all are at K and showing
strong density dependence
Mortality
Rate
Population Size
May compare populations that show density independent growth.
Changes in mean generation time, litter size etc.  things that are relatively
fixed in density dependent organisms.
So then we graph number of adults against recruitment number.
NRES 310: Wildlife Ecology and Management
Ricker Model lecture
13 October 2008
highest number of recuits into the
MSY population because relatively
high r and larger number of
animals producing offspring.
FRY
Number of
Fawns
K
Population Size
High reproductive rate, but
very small population size
High population size,
but low reproductive
rate with very few
young
MSY  maximum sustained yield – maximum harvest that you can remove from
the population without leading to extirpation. Basically this is an interaction
between population size and per captia recruitment.
FRY  fixed removal yield – NOT mathematically determined. Difficult to
precisely measure MSY so when setting harvest back off MSY to FRY on the
right size of the parabola (if on left can lead to extirpation of the population).
Where people push harvest to MSY the effort to "bag " an animal increases (I.e.
more time is required because don't see many animals running around). So
hunter satisfaction drops (too much work) often public perception is more
important which is another reason to be between FRY and K.
 closer to K see more animals running around.
Effects in density dependent systems are very different from density
independent.
Discuss male v. female harvest to where populations are, on this curve, with
respect to K and how you are going to affect growth of populations by harvest
single or both sexes.
NRES 310: Wildlife Ecology and Management
Ricker Model lecture
13 October 2008
Harvest determines the
surplus and varies
uniquely with it.
MSY
Number of
Fawns
Additive
mortality
Compensatory
mortality
Population Size
K
Management works well from
MSY to K, not between 0 and
MSY.
Density independent (draw)  IF mortality is compensatory  surplus
determines the harvest.
Some environmental
perturbations causes the
population to crash
Compensatory
Mortality
Surplus – Leopold termed the
"harvestable surplus" – true if
mortality is compensatory. So
the amount number of animals
above the refuge line can be
harvested (i.e. surplus)
N
Refuge Effect
T
NRES 310: Wildlife Ecology and Management
Ricker Model lecture
13 October 2008
Ricker Curve
K
45 Line of no
population growth
MSY
Nt+1
Equal increments on
X and Y axes
Nt
Nice way to project population growth between one year and next. In
McCulloughs models Nt is "prehunt population" and Nt+1 is post hunt population.
Directly determine recruits and harvest of population.
NRES 310: Wildlife Ecology and Management
Ricker Model lecture
13 October 2008
Characteristics of Population
Pop.
Pop
No
Not
@
@
Diff.
enough
MSY
K
info
Population with highest recruitment of
√
fawns
Population with largest no. of animals
√
Average size of animals will be smaller
√
Age at first breeding, of females, will be
√
younger
√
Individuals more vulnerable to predators
√
Highest breeding potential
√
Best management
Availability of food greatest
√
NRES 310: Wildlife Ecology and Management
Ricker Model lecture
13 October 2008
AGE STRUCTURE AND POPULATION DENSITY
5–6
M
SY
4–5
3–4
1–2
Number of
female Fawns
K
0–1
EXPANDING
Population Size
Size
5–6
4–5
3–4
RR
1–2
K
0–1
STATIONARY
5–6
4–5
3–4
1–2
0–1
DECLINING
Population Size