Population Dynamics of Gray Wolf (Canis lupus) in Northern Rocky Mountain Region,
United States
LYNNLEE KIRKESSNER1, Undergraduate Student, Department of Ecosystem Science and
Management, The Pennsylvania State University, University Park, PA, 16802, USA
JOE REBERT2, Undergraduate Student, Department of Ecosystem Science and Management,
The Pennsylvania State University, University Park, PA, 16802, USA
KRYSTAL STEFANICK3, Undergraduate Student, Department of Ecosystem Science and
Management, The Pennsylvania State University, University Park, PA, 16802, USA
IAN R. WHITE4, Undergraduate Student, Department of Ecosystem Science and Management,
The Pennsylvania State University, University Park, PA, 16802, USA
ABSTRACT The gray wolf (Canis lupus) has been a difficult carnivore species to track over
time due to its unusual breeding patterns. As an attempt to distinguish a viable harvest for gray
wolves in the Northern Rocky Mountains region, a Leslie matrix model was created based upon
known survival and fecundity rates throughout the region. The model takes into account three
separate harvest scenarios: no harvest, which implies no wolves be taken at any time, limited
harvest, implying a certain percentage of the population be harvested each year, and an unlimited
harvest, which allows wolves to be taken without restriction. Based upon the assumptions of our
model, the ideal harvest rate should be set at 28% of age classes 2 through 7 in order to keep a
stable wild population. A higher take percentage led to an overall decline in the population
leading towards extirpation of the gray wolf in the region and possible enlistment and protection
under the Endangered Species Act once again. An unlimited harvest would similarly lead to the
extirpation of the wild gray wolf population in the Northern Rocky Mountain region.
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KEY WORDS Northern Rocky Mountains, Leslie matrix, Gray Wolf, population dynamics,
harvest
The gray wolf (Canis lupus) was once a highly abundant carnivore throughout much of the
United States, with numbers ranging from 250,000 to 500,000 in the wild. Through organized
human eradication efforts, by 1960, the gray wolf population was estimated to have as little as
300 wild wolves left in the natural population. Later, in 1974, gray wolves were placed on the
Endangered Species list and offered protection through federal laws. Between 1995 and 1996, 54
Canadian gray wolves were reintroduced into the Northern Rocky Mountain Region (Figure 1)
(White 2013). Since then, wolf populations have been on the incline within the reintroduced
areas and populations were seen as abundant. As of August 31, 2012, gray wolves have been
removed from the Endangered Species Act and their protection is enforced through statewide
management plans in the region (U.S. Fish and Wildlife 2012). With the current implement of
harvest seasons throughout the Northern Rocky Mountain region, the question of endangering
the gray wolf population comes back to existence.
Our research looks into the current survival and fecundity rates of the wolf populations
throughout the Northern Rocky Mountain Range. Our paper discusses the effectiveness of three
management alternatives concerning the population of interest. We analyzed the current
management plan implemented in the region, which is no commercial harvest. We then explored
two other alternatives which included limited fixed effort harvest and unlimited harvest. After
testing the alternatives, we determined that the best management plan for the studied wolf
population was a fixed effort limited harvest.
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METHODS
To model the population of wolves in the Northern Rocky Mountains, we chose to construct an
age-based Leslie matrix model. We chose to only use female wolves in the construction of this
model. Our matrix had 7 age classes, with class 7 containing all individuals age 7 and older. To
determine survival of wolves we took information from two papers on wolves from the Northern
Rocky Mountains (Massey 2011; Smith et al. 2010). Each of these papers had conducted surveys
on wolf populations in several recovery areas in the Northern Rocky Mountains. These recovery
areas are as follows; Central Idaho (CID), the Greater Yellowstone Area (GYA), Northwest
Montana (NWMT), and Wyoming (WYO) (Smith et al. 2010).
To determine the survival for use in our model we calculated the mean of the survivals
from each recovery area for both of the two studies. The survivals were; 0.680 NWMT, 0.771
GYA, 0.789 CID with a mean annual survival of 0.747 (Smith et al. 2010), and 0.629 WYO,
0.671 GYA, 0.645 CID with a mean annual survival of 0.648 (Massey 2011). We then calculated
the average of these two values, which gave us an estimate of overall average annual survival of
0.674 for wolves in the Northern Rocky Mountain area. We used this as a constant value of
survival for all age-classes of wolves in our matrix. Though this method may be somewhat of an
oversimplification, we believe that it represents wolf survival accurately (Miller et al. 2001).
In our matrix we chose to begin reproduction at age-class 2 since wolf pups cannot breed.
Determining how to represent fecundity in our model was difficult due to the hierarchal pack
structure of wolves. In the end we chose to use a constant fecundity to represent all age-classes
after age 1. This fecundity was taken from another study conducted on wolves of the Northern
Rocky Mountains and the value was 1.070 (Miller et al. 2001). After all these values were
finalized we entered them into Microsoft Excel to build our Leslie matrix (Table 1). We began
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by starting with an even age distribution of wolves. Since this is likely an unrealistic
representation of wolf age-distribution, we only used these values to determine what actual agedistribution might look like. After simulating this population out for 100 years we determined
percentages for age-distribution of wolves (Table 2) and then multiplied those percentages by
1,614 to find a more realistic starting age-distribution for our model. 1,614 was the number of
wolves in the Northern Rocky Mountains in 2010 according to government surveys from of the
three wolf recovery areas (Sime et al. 2011).
Once starting age-distribution for Northern Rocky Mountain gray wolves was
determined, we used Excel to simulate our population out for the next 100 years. From this
simulation we determined population growth rate to stabilize at a λ of 1.251. To confirm the
accuracy of this growth rate we calculated population growth rate using actual numbers of
wolves in the Northern Rocky Mountains for the past twenty years, and we found that our
growth rate was a fair representation of actual population growth rate for Northern Rocky
Mountain wolves (Sime et al 2011).
RESULTS
We had three different management objectives to test based on our population model for
Northern Rocky Mountain wolves. These were the effects of no harvest, a limited commercial
harvest, and an unlimited harvest. The no harvest scenario would simply be the results of our
original model. From this scenario we can see that the population growth rate is at a λ of 1.251,
meaning that the population of wolves is increasing by about 25 percent every year. In our
limited commercial harvest model we simulated various numbers of harvests on the wolf
population. For this scenario we only considered harvesting individuals at age 2 or older, which
we defined as the adult population. Using this model we determined that 28 percent of the adult
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population of wolves in the area can be harvested while maintaining the population at a stable
level, and that any percentage of harvest under 28 percent will result in an increasing population.
In our unlimited harvest scenario we included harvest on all age-classes. In our simulation we
determined that harvesting anything more than 20 percent of the entire population of wolves
would cause the population growth rate to drop below 1.000 which would cause a decline in the
number wolves in the Northern Rocky Mountains.
DISCUSSION
Upon creation of our Leslie matrix model, there were some model uncertainties. We chose to use
a constant survival rate for all age classes which we obtained from averaging the survival rates
from two previous studies. We chose this value due to the limited information on survival rates
per age class. We also, used a constant fecundity rate which was provided in a third study. An
attempt was made to calculate our own fecundity rate by multiplying the number of breeding
pairs × pup survival × number of female wolfs pup per litter. The calculation resulted in an
unreasonably low rate and was therefore omitted. If these uncertainties had not occurred, our
decisions may have been different. Had we noticed a lower survival rate in a particular age class,
we would have decided to limit harvest on that age class. Similarly, had we noticed higher
fecundity rates in older age classes, we may have chosen to limit harvest on those age classes.
Analysis of our control, no harvest, always results in an increasing population. This is the
method being implemented currently and the population is growing rapidly (Figure 2).
Overpopulation is a possibility with this current management plan. It should be noted that the
vital rates within our no harvest model include pest control of problem individuals. Therefore,
the two variations of harvest models demonstrate additional harvest beyond the control of
problem individuals. The alternative considering unlimited harvest on all age classes will result
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in a stable population when the harvest rate is 20 percent. If less than 20 percent of the total
population were to be harvested each year, the population would increase. If greater than 20
percent of the total population were to be harvested, the population would decline. The issue
with this alternative is the probability of more than 20 percent of the population being harvested.
With no limits or regulations, there is much likelihood of the population being over-harvested
and driven to extirpation.
Our chosen alternative, limited harvest, would require buying tags for all age classes over
age class 1. Harvest of age class 1 would not be permitted. With limited harvest, harvesting 28
percent of age classes 2 through 7 would result in a sustainable population. Harvesting less than
28 percent would result in an increased population and harvesting greater than 28 percent would
result in a decline. This is the most manageable alternative depending on the objectives of the
region. Even if the population is overharvested in one year, it would be easy to re-evaluate and
correct the issue in the following year by decreasing the amount of tags sold. If the goal is to
sustainably decrease the population, a greater number of tags could be sold in order to increase
the percent of individuals harvested.
An additional alternative we could have considered is the use of a harvest with a yearly
based quota. This method would be effective for the same reasons our commercial limited
harvest would be effective. Each year an analysis could be done to evaluate the appropriate
number of individuals to harvest in order to meet the stakeholders’ needs.
LITERATURE CITED
Massey, J. 2011. Survival of an exploited grey wolf population in the Northern Rocky
Mountains: density dependence and licensed hunting. Thesis, Imperial College London,
London, UK.
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Miller, D.H., A. L. Jensen, and H. H. James. 2001. Density dependent matrix model for gray
wolf population projection. Ecological Modeling 151: 271-278.
Mission Wolf: Education vs. Extinction [MW]. 2013. MW homepage.
<http://www.missionwolf.org/>. Accessed 9 Apr 2013.
Sime, Carolyn A., V. Asher, L. Bradley, N. Lance, K. Laudon, M. Ross, A. Nelson, and J.
Steuber. 2011. Montana gray wolf conservation and management 2010 annual report.
Montana Fish, Wildlife & Parks. Helena, Montana, US.
Smith, D. W., E.E. Bangs, J. K. Oakleaf, C. Mack, J. Fontaine, D. Boyd, M. Jimenez, D. H.
Pletscher, C. C. Niemeyer, T. J. Meier, D. R. Stahler, J. Holyan, V. J. Asher, and D. L.
Murray. 2010. Survival of colonizing wolves in the Northern Rocky Mountains of the
United States, 1982-2004. Journal of Wildlife Management 74(4):620-634.
U.S. Fish and Wildlife Service [FWS]. 2012. Gray wolves in the Northern Rocky Mountains.
<http://www.fws.gov/mountainprairie/species/mammals/wolf/>. Accessed 9 April 2013.
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Table 1. Leslie matrix for female production and survival of all gray wolf (Canis lupus)
individuals in the Northern Rocky Mountain Range, based on data from two studies in three
areas within the range.
1
0
0.674
0
0
0
0
0
2
1.07
0
0.674
0
0
0
0
3
1.07
0
0
0.674
0
0
0
4
1.07
0
0
0
0.674
0
0
5
1.07
0
0
0
0
0.674
0
6
1.07
0
0
0
0
0
0.674
7+
1.07
0
0
0
0
0
0.674
Table 2. Distribution of wolf individuals across age classes based on a stable age population
calculated using total wolf population in the Northern Rocky Mountain Range.
1
2
3
4
5
6
7+
TOTAL
744.1807 401.055 216.1371 116.481 62.77409 33.83031 39.53181
1614
0.461079 0.248485 0.133914 0.072169 0.038893 0.020961 0.024499
1
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Figure 1. Map outlining the three gray wolf (Canis lupus) recovery areas present in the Northern
Rocky Mountain Range. The map shows the borders of the three states included in the
range, Idaho, Montana and Wyoming, as well as the borders of the three recovery areas
as they are different than the state borders. Map from Sime et al. 2010.
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1800
Population Size
1600
1400
1200
1000
800
600
400
200
0
1990
1995
2000
2005
2010
Time (Years)
Figure 2. Graph depicting the actual population change from 1990-2010 of gray wolves (Canis
lupus) in the Northern Rocky Mountain Range. The average lambda of the changing
population is 1.215 during this time span. Data from Sime et al. 2010.