South Dakota's "2 + 2 = 5"
Mountain Lion Population
Estimate Error
Just
one of the many holes in
SDGF&P's 2010-2015 Mountain
Lion Management Plan you
could drive a bus through
By Amy Rodrigues
The South Dakota Department of
Game, Fish & Parks (SDGF&P) has
submitted its 2010-2015 Mountain
Lion Management Plan for public
review. The new plan calls for
reducing the state's mountain
lion population by about 80 to
100 cats in order to bring their
estimated population total down
from an approximated 251 lions
to only 150 to 170 mountain
lions. The current 251 estimate
includes kittens. Since mountain
lion kittens may not legally be
hunted, and
South Dakota
fails to recognize that killing
a mother lion often results in
her orphaned kittens starving to
death, their mountain lion
management plan ultimately calls
for the removal of 80 to 100
adult lions.

I'll be honest, I personally
believe this plan to decimate
the state's still-recovering
mountain lion population is
purely an early Christmas
present for the agency's hunting
pals, wrapped in a few fancy
equations and colorful graphs so
it looks like science. The plan
appears sneaky, is a waste of
taxpayer money, and
exterminating a species in the
pursuit of outdoor recreational
fun is morally disgusting.
However, I decided to give them
the benefit of the doubt and
objectively review their data
first to see if at least their
math was legit. (Spoiler Alert:
It's not!) Changing personal
opinions on how many mountain
lions
should be in the state is a
long and heated debate - still
very important - but fixing 2 +
2 = 5 is a much simpler and
obvious correction. Emotion
aside, let's just focus on the
numbers for now.
The SDGF&P's entire mountain
lion management plan is based on
the department's calculation of
the size of South Dakota's mountain
lion population. One seemingly
innocent "2 + 2 = 5"
miscalculation and the whole
house of cards comes tumbling
down.
The problem is often that
these "2 + 2 = 5" errors are
complicated and buried within
mathematical jargon . . . and of
course state agencies rarely
take the time to explain the
process and source data in plain
English. For the majority of
people who don't speak
statistics, it's common to just
take the state's word for it and
assume their lengthy
calculations for population
estimates are correct. Well, as
a zoologist fluent in
statistics, I'd like to show you
their mistakes and the reasons
why I (and math) believe
their own data indicates a
maximum of only 111 adult
mountain lions living in
South Dakota.
If I was able to catch this
error only a few minutes into my
first read, what other slip-ups
and poor judgments went into
creating this management plan?
SDGF&P is currently accepting
public comments through July 26th
on this plan. In addition to
your own critique, I encourage
you to point out the basic
errors made in their
calculations.
Let's begin . . .
The Population Information
section begins on page 4 of the
South Dakota
mountain lion management plan.
The data says it's from
2007-2009 harvest numbers. At
the end of that section it
happens to mention, "No
harvest occurred in 2008 due to
movement of the harvest season
to January 2009. Harvest data
for 2009 provided a similar
estimate of population size to
that of 2007." The three
years of harvest data used for
the population estimate is
actually just 2007's numbers,
which means they are
relying on only one year's data
to assume population trends.
SDGF&P justified this choice by
saying 2009 was "similar"
to 2007 and thus only needed to
use results from one of the
years. Their harvest data is
noted below.
|
|
2007
|
2008
|
2009
|
|
Females
|
16
|
No harvest
|
15
|
|
Males
|
3
|
No harvest
|
11
|
|
Total
|
19
|
0
|
26
|
|
Yes, female data was
similar (16 to 15) but male
harvest (3 to 11) increased
drastically!
That's up 267 percent .
. . how convenient to ignore the
higher harvest year.
If we overlook the fact that
they are only using one year's
data, and selecting their
favorite year to build upon,
they still screwed up their
calculations.
They use harvest rate to guess
population size, and "Harvest
rate was estimated using number
of radio-collared mountain lions
harvested divided by total
number of radio-collared
mountain lions available to be
harvested." Yes, this is a
legitimate scientific way to
estimate populations through
harvest (hunting) data.
It assumes what happens
to the radio-collared
"community" is exactly
proportional to what's happening
to all lions in the state. It's
certainly not 100 percent
accurate, but it can give a
ballpark estimate of the
population size.
As a hypothetic example of this
model: if I have 3 pet cats and
1 gets hit by a car, I would
assume 1 out of
every 3 pet cats (33
percent) in my region gets hit
by a car. If there are 300 pet
cats in my neighborhood, then
this technique would conclude
100 (33 percent of the total)
would be hit by cars.
This method gives a very
rough estimate of what's going
on with all the animals, but
it's only one of the tools used
by population biologists. The
more animals studied, the more
accurate the results.
If instead I had 20 pet
cats, and still only that 1 was
hit by a car, then now my data
tells me only 1/20 (or 5
percent) of pet cats are hit by
cars. That's a big drop from 33
percent in my first scenario.
These numbers are also subject
to wide interpretation because
they do not indicate whether I
live on a busy street, if the
cats live indoors/outdoors, if
older cats are more likely to
wander into the street,
distracted drivers, etc, and any
other factors that may lead to
cats being hit by cars. Multiple
mortality factors should always
be included when analyzing data
of this sort.
But let's continue with South Dakota's math.
In 2007, SDGF&P had 35
radio-collared lions.
Out of the 19 mountain
lions killed by hunters that
year, 6 were SDGF&P's
radio-collared research lions.
Here's a breakdown - for
reference - of the data from
2007 that will be used to
calculate the mountain lion
population:
|
Radio-Collared Females
|
20
|
|
Radio-Collared Males
|
15
|
|
Total Lions Radio-Collared
|
35
|
|
|
|
Radio-Collared Females Killed
|
5
|
|
Radio-Collared Males Killed
|
1
|
|
Total Radio-Collared Lions Killed
|
6
|
|
|
|
Total Females Killed
|
16
|
|
Total Males Killed
|
3
|
|
Total Lions Killed
|
19
|
|
|
Using the ratio
to calculate
total harvest,
we see:
If 6 out of 35 radio-collared
lions were killed (6/35 = 0.171
= 17 percent), that means 17
percent of the radio-collared
population was harvested in
2007.
We now make the
assumption (just like we did
with the pet cat roadkill
example) that 17 percent of all
adult mountain lions were killed
that year.
From the hunting data, we
see that 19 mountain lions were
killed. So those 19 lions are
believed to represent 17 percent
of the
South Dakota
population. That means according
to this technique, there could
be 111 adult mountain lions in
the state (19 is 17 percent of
111).
Remember, in their proposed
2010-2015 Mountain Lion
Management Plan, SDGF&P wants to
kill about 90 of those. If
accomplished, that would bring
the adult lion population down
to about 21 cats. For reference,
Florida only has about 100
panthers left and because of
this small population size, they
are federally protected,
considered critically endangered
and in jeopardy of going
extinct. Yet
South Dakota
could have about the same number
of lions and is pushing to
legally exterminate them . . .
Again!
Back to the math...
In their management plan, South
Dakota GF&P decided this 111
number was a little too small
for their liking, and decided
instead to focus on the female
portion of the mountain lion
population for their
calculations.
The text on page 5 reads,
"In
2007, estimates of population
size were generated for the
female segment of the population
only due to total harvest of 1
radio-collared male." This
makes sense. Only 1
radio-collared male was killed,
and just as we saw with my
hypothetic pet cat example,
assuming trends based on the
fate of one individual cat is
not good science.
So, SDGF&P calculated the female
portion of the population - and
this is where they really
tripped up!
Correct Math:
5 out of 20 radio-collared
female mountain lions were
killed (5/20 = 0.25 = 25
percent). 16 total female lions
were killed that year. If those
16 lions represent 25 percent of
the female population, then we
believe there are
64 female lions in the state
(16 is 25 percent of 64).
Wrong Math:
And I quote
from page 5 of the management
plan, "Harvest
rate for the female segment of
the population was estimated at
0.143 (5/35 = 0.143) where 5
radio-collared female mountain
lions were harvested of a total
of 35 available radio-collared
mountain lions. Total number of
females in the population was
then estimated by dividing total
number of females harvested (n =
16) by harvest rate (0.143),
which gave an estimate of 112
female mountain lions."
Do you see the problem? Whether
it was a convenient typo,
incapable employee, or honest
mistake,
SDGF&P used the wrong number.
They divided by 35 (the total
number of female
and male radio-collared
lions) rather than the actual 20
female collared lions. Diving by
35 (male + female) is okay, but
it means the final 112 number
also represents male + female.
The ratio stays the same: 5
collared females out of 35 total
(male + female) collared lions =
16 females out of 112 total
(male + female) lions. Or, 5 out
of 20 collared females = 16 out
of 64 total females. Either way,
their numbers only let them
assume 112 total lions or 64
females . . . not 112 females.
Had they looked at the whole
population or done the female
calculation correctly, they
would have concluded there are
approximately 111 or 112 adult
mountain lions in the state (and
that's still assuming hunting is
the only cause of death and
kittens are independent from
birth).
If they want 150 adults,
they are going to have to
INCREASE the population to get
there!!!
Another interesting point is
that SDGF&P assumes 70 percent
of the population is female (see
why this is probably an error,
too!). If there are
64 female lions, representing 70
percent of the population, this
means
there may only be 91 adult
mountain lions in the whole
state (64 females, 27 males).
I may actually be cutting them
some slack and overestimating by
saying there could be 112 adult
lions in South Dakota - but hey, I'm only using their
data!
The
South Dakota
mountain lion management plan
also uses other sketchy
assumptions like the number of
kittens and survival rates, and
even territory size shrinking
despite less food, that I
encourage you to challenge. All
the studies show that food
abundance dictates territory
size--the less food, the larger
the territory. Feel free to
include your personal opinions
about the management plan and
please see MLF's official
comments to the plan once they
are written and posted on the
South Dakota State Page, but if
nothing else, send them the
following corrections to their
Population Information section .
. . because if they haven't
learned 2 + 2 = 4 yet, they
shouldn't be trusted to manage
our wildlife.
While I may not agree with all
of their assumptions, the
following edits simply fix the
mathematical errors and give the
real version of the management
plan their biologists intended
to produce.
With my edits in bold,
page 5 of South Dakota's Management
Plan should read:
"During 2007-2009 when
sufficient radio-collared
female mountain lions were
available to estimate the
population post harvest, an
estimate of harvest rate was
generated for the female segment
of the population. Harvest rate
was estimated using number of
radio-collared mountain lions
harvested divided by total
number of radio-collared
mountain lions available to be
harvested (Skalski et al. 2005).
Estimates from 2007-2009 were
compared to those generated via
population reconstruction to
adjust temporal change in the
mountain lion population. In
2007, estimates of population
size were generated for the
female segment of the population
only due to total harvest of 1
radio-collared male. Harvest
rate for the female segment of
the population was estimated at
0.143 0.25 (5/35
20 = 0.143
0.25) where 5 radio-collared
female mountain lions were
harvested of a total of 35
20 available
female radio-collared
mountain lions. Total number of
females in the population was
then estimated by dividing total
number of females harvested (n =
16) by harvest rate (0.143
0.25), which gave an
estimate of 112
64 female mountain lions.
The following assumptions were
used to estimate reproduction:
1) 50 percent of females were
with kittens; 2) survival of
kittens was 0.67; and 3) litter
size was 3 kittens/litter (based
on field data collected over the
past 5 years [Thompson 2009, B.
Jansen, unpubl. data]). Thus,
the number of kittens added to
the population was 112
64 females multiplied by
0.5) which equals 56
32 females with kittens. The
56
32 females with kittens were
multiplied by 3 kittens/female
for a total of 168
96 kittens born. This number
was multiplied by the survival
rate of 0.67 to estimate total
number of kittens added to the
population or 113
64 kittens. The sex ratio of
the population was estimated at
70% females, based on observed
data and those from other
populations (Logan and Sweanor
2000), which provided an
estimate of adult and transient
males of 48
27. Thus, total number of
males and females was 160
91 and this estimate was
adjusted by multiplying by
survival rate for males and
females of 0.86 (Thompson 2009),
which gave 138
78 adult mountain lions.
Thus, total population was
estimated at 138
78 adults and 113
64 kittens or 251
142 mountain lions."
If South Dakota's plan to
kill 80 to 100 adult mountain
lions is approved, they could
exterminate the entire mountain
lion population!
They did it once before.
Through this mountain lion
management plan, all 78 adult
lions could be killed (if there
really are even than many to
begin with) and the 64 predicted
kittens listed above would all
be less than one year old and
unable to survive without their
mothers - despite what SDGF&P
thinks.
My only thought now is dear god
I hope the numbers are wrong and
there actually are more lions
out there . . . somewhere.
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