A Systems Approach to Wolf Reintroduction
A case study from a Systems Thinking for Global Engineers course from my graduate studies at the University of Colorado Boulder, co-authored with SJ Miranda.
Background
In 2020, Colorado voters approved legislation to reintroduce wolves to Colorado, west of the continental divide, by the end of 2023.1 Wolf existence and reintroduction has long been a contentious issue, particularly between livestock managers and conservationists2. Wolves, native to Colorado, were intentionally eradicated in the 1940s to benefit the livestock industry.2 The absence of this apex predator has disrupted ecosystems, especially those with large elk populations.3
Wolf reintroduction in Yellowstone National Park (YNP), is one of the best studied examples of predator reintroduction. Wolves were reintroduced here in the mid-1990’s, likely resulting in both ecological and economic benefits.2,4,5 The presence of wolves here is hypothesized to have had far-reaching effects across trophic levels in the ecosystem - even affecting riverbeds and the landscape itself. This will be explored in further detail later in the report, but briefly wolf reintroduction altered the movement patterns of elk, preventing overgrazing in riparian areas, and allowing for increased plant growth, less erosion, more biodiversity, and a more balanced ecosystem.6 Reintroduction also led to an economic boom in the area as visitors pour in from around the world to visit wolves. In 2008, YNP reported that 94,000 people came to the park specifically to see wolves, resulting in around $35 million in revenue. The cost of wolf reintroduction since the 1990’s totaled only $10.3 million as of 2008.4
In Colorado, there was already some interest due to a natural migration of wolves from Wyoming to Northern Colorado in 2020.7 Colorado also has an abundance of elk, which are wolves’ preferred prey.6 In fact, Colorado has the largest elk herd in the United States at 294,000 as of 2022.2 This elk herd has been over the state-recommended capacity of Colorado for several years. In Rocky Mountain National Park (RMNP), rangers fenced off areas to prevent elk overgrazing and erosion.6 Additionally, in RMNP and elsewhere, the State Government of Colorado has hired or utilized volunteer sharpshooters to cull elk in overpopulated areas.8 In theory, wolf reintroduction could alleviate overgrazing and overpopulation while boosting local tourism. Another factor in favor of reintroduction in Colorado is that the elk herd has a high prevalence (40%) of Chronic Wasting Disease (CWD).6 This is a prion disease similar to Mad Cow that sickens elk and renders the meat unfit for human consumption because of the risk of the disease “jumping” to humans.6 As wolves preferentially prey on the old, young, and sick there is the reason to believe that wolf reintroduction may reduce the presence of CWD within the elk herd of Colorado.
Colorado has a number of other conditions that suit it well for reintroduction. WildEarth Guardians propose that five key factors are needed for suitable wolf habitat: forested area, prey availability, public ownership, low human density, and low road density.2 These factors are based on their analysis of wolf packs and territory in Oregon, and they identified 12 suitable territories for wolf reintroduction within Colorado, primarily on the Western Slope.
Our interests in this area were sparked by a desire to understand how wolves affect ecosystems they exist in and to understand the arguments for and against wolf reintroduction. As the Colorado reintroduction has not been started, nor the reintroduction plan finalized, we decided to use Yellowstone National Park as a case study to see what reintroduction may mean in Colorado. The YNP case study has 30 years of data post-reintroduction, and populations in the Park appear to have stabilized giving us a strong background to compare our model to.
We started with a literature review, examining sociological, ecological, and governmental systems related to wolves. Next we created problem and solution trees, as well as a causal loop diagram (CLD), taking a wide-angle look at the ecosystem as a whole. In these models we aimed to demonstrate the broad effects of wolf reintroduction, the trophic cascade seen in YNP, and interactions with human systems like ranching and government bodies. Finally, we used Stella Architect to model the system dynamics between wolf and elk populations specifically.
For the Stella model, we chose to focus on wolf and elk populations because they are the leverage point of the proposed trophic cascade in YNP. It is wolves' effect on elk populations and movement that drives the rest of the observed changes. Elk are also the preferred prey of wolves, even when other populations or livestock are present, and wolves are historically the primary predator of elk.6 Ideally, we would have expanded the model to include the downstream effects of wolves on elk and the entire trophic cascade, but that would be beyond the scope of this project. Our goal was to use Stella to model the interactions between wolves and elk so that it could be expanded upon and used in a larger-scale model at a later date. We strove to replicate the dynamics between the wolf and elk populations seen in YNP post-reintroduction.
Problem and Solution Trees
We started with problem and solution trees illustrating the issues in YNP. The Problem Tree can be seen in Figure 1 and Solution Tree in Figure 2.
Figure 1: Problem Tree - Wolf absence and elk overgrazing in YNP
Without predators, elk started to overgraze, especially in riparian areas.2,9 This overgrazing had a number of implications. First, by eating the sapling aspen and willow trees, elk were robbing beavers of their natural habitat and building materials. Without beavers, whose tree-felling activity creates wetlands, nesting areas for songbirds started to disappear.2,5,6,9 Additionally, by overgrazing in riparian areas, elk damaged the root systems holding the stream sides together, causing erosion and widening of the stream.4 This widening slowed the flow of the water, increasing its temperature, and creating conditions unsuitable for some fish populations who required cold water.9
Figure 2: Solution Tree - Wolf reintroduction in YNP
In the solution tree, one can see how wolf reintroduction acts through effects on elk movement and activity to produce a trophic cascade.5,10,11 This increasing movement prevents overgrazing, as does a change to elk preferentially staying on high ground with the best visibility.4 This puts less pressure on the riparian vegetation and allows it to recover.10 It should be noted that the attribution of wolf introduction to being responsible for this has been debated in some studies, which argue that the change in vegetation was driven more by climatic variables than wolf reintroduction.13,14
Causal Loop Diagram (CLD)
We next used a CLD to illustrate feedback loops between the components of the ecosystems and other systems at play in Yellowstone- see Figure 3 below.
Figure 3: Causal Loop diagram showing the interactions of the eco-, social, agricultural, and governmental systems in YNP.
You can observe balancing loops between wolf and elk, as well as other animal populations within the ecosystem of YNP in B2-4. There is also an interesting reinforcing loop (R2) in which increased wolf populations lead to improved grass growth, higher elk population and thus higher wolf population. The wolf reintroduction also reached antelope and fox populations, as without the presence of wolves the coyote became the new top predator in the ecosystem, preferentially preying on antelope calves and small rodents. With wolf presence, coyote populations decreased, the antelope populations are able to grow, and there is more small rodent prey for other animals like foxes and raptors.11 It should be noted that our CLD does simplify wolf predation, assuming they prey only on elk. In reality, while wolves do preferentially prey on elk when available, they are adaptable and their diet can include other ungulates, small rodents, coyotes, and beavers.6,14 In fact, without an abundant elk population, wolves may be detrimental to a balanced ecosystem. In Minnesota, there have been reports of wolves wiping out beaver populations without elk to hunt.16
The CLD shows that the effects of wolf reintroduction reach further than simply the surrounding ecosystem, affecting social, agricultural, and governmental systems as well. The interactions with livestock is a particularly important one - as mentioned previously one of the primary drivers of forced extinction of wolves in Colorado was to benefit the livestock industry.2 There remains significant resentment and fear toward wolves and their potential to prey on livestock, indicated in the “Rancher anger” node.2 Ranchers typically prefer lethal management of wolves who prey on livestock, though evidence in favor of lethal management is mixed.2,17 Studies have shown that non-lethal management practices can be equally or even more effective, and ranchers do feel comfortable using them once they have seen success.2,17 The Center for Human-Carnivore Coexistence reports that ranchers were more likely to be in favor of non-lethal management and wolf reintroduction in general if they feel like they have the capacity to implement methods of non-lethal management.17 As seen in R1 and R1a there is a reinforcing effect of Wolf population, which increases tourism revenue, making governments and locals more likely to desire wolves in their communities, which reinforces a number of wolf friendly policies like farmer compensation for livestock loss and non-lethal management. However, there are likely delays between introducing wolves and recognizing tourism revenue, and further delays for actual policy implementation. There is a balancing loop B1 with far fewer delays, in which wolf population increases livestock death, increasing rancher anger, increasing lethal management, and ultimately decreasing the wolf population.
Stock and Flow Model
We next attempted to model the reintroduction of wolves, and impact on elk population in Yellowstone National Park using Stella Architect software. From our literature review, we knew we had the following initial conditions:
Initial wolf population: 41 wolves18
Initial Elk Population: 19,00019
Average Wolf Litter Size: 2-5 pups2,13
Average Lifespan in YNP: 5 years15
Wolf Pup Survival Rate: 30-60% (likely 60% in Yellowstone due to lack of hunting and trapping)2
Average Prey requirement per wolf: 3,650 pounds per year20
Average mass per Elk: 500 pounds2
YNP area: 8990 square kilometers21
Average Elk Lifespan: 13 years22
Elk birth rate: 70% (35% of total elk population assuming a 50/50 male-female split)23
Average Breeding pairs per pack: 1.25 (typically 1 breeding pair per pack, but 25% of packs are polygamous)2
We started with an average litter size of 5 pups, a life expectancy of 5 years, and pup survival rate of 60%. Average pack size was a little trickier to determine. It is typically reported to be 4-7 wolves, however in Yellowstone the recent average pack size is over 10 wolves.2,15 We started with a pack size of 6, since the Yellowstone data is just from recent years, and may well have been different earlier on in reintroduction. Similarly, the territory needs of wolf packs range from around 100 to 1100 depending on the wolf pack and area.2 WildEarth Guardians hypothesize that this could be due to prey density or habitat quality.2
Since wolf reintroduction in YNP is so well studied, we also knew the trends up to the present, around 30 years post-introduction. YNP experienced a sharp initial increase in wolves, to around 200, followed by a sharp decline in elk population and then wolf population - a classic overshoot and collapse archetype.19 The populations likely experience subsequent oscillations throughout the years., and have stabilized at around 100 wolves and 10,000 to 20,000 elk.22 As mentioned previously the current average pack size in Yellowstone is over 10, and their average range is around 500 square kilometers per pack.2,15
Using these parameters, we adapted the Predator-Prey-LevelC Stella Architect model provided by Professor Amadei. The resulting model is seen in Figure 4 below.
Figure 4: Overview of Stella Architect Wolf-Elk system dynamics model
We have two primary feedback mechanisms affecting the wolf population. The first is a relationship between the elk and wolf populations, where wolf predation decreases the elk population, but if the elk population gets too low, wolves are not able to eat enough per year and their lifespan therefore decreases. The second is related to the pack density and acceptable area for each pack. In YNP, wolf on wolf kills are the leading cause of their death, indicating that pack proximity factors strongly into wolf death rates.15 Presumably this effect does depend on prey availability, as wolves may feel they are able to survive in a smaller territory and avoid conflict. In this case, an “Acceptable Wolf Density” converter was defined, using the range of wolf pack territories reported by WildEarth Guardians.2 As elk density decreases, the acceptable territory per pack increases. This is compared to the current pack territory, and there is an additional converter which lowers the life expectancy of wolves if the packs are too dense, accounting for interpack conflicts.
The initial run of our model yields encouraging results, as seen in Figure 5. We see the expected initial spike in wolf population, collapse in elk population, and continued oscillations between the species. The wolf and elk populations do have higher peaks and lower valleys than in reality, indicating that there are other feedback mechanisms in the natural world that our model does not account for.
Figure 5: Elk and Wolf Populations over 50 years using initial, baseline conditions of the model
We next varied a few parameters that were given as ranges in the literature: litter size and pack size. The pack size was varied from 4 to 10 wolves per pack, while the litter size was varied from 2 to 5, each using an incremental distribution and a step of 1 wolf. Figures 6 and 7 show the effects of the wolf pack size variation, and Figures 8 and 9 show the effects of varying the litter size.
Figure 6: Effect of varying the wolf pack size from 4 to 10 on Elk Population. Run 1 has a pack size of 4 and run 7 has a pack size of 10.
Figure 7: Effect of varying the wolf pack size from 4 to 10 on Wolf Population. Run 1 has a pack size of 4 and run 7 has a pack size of 10.
When varying the wolf pack size, we see a delay in the oscillations of wolf to elk populations as the pack size increases. We believe this is because our model assumes violent wolf-wolf conflicts based on pack density rather than wolf density, and higher wolf densities are assumed to be tolerated for longer periods of time. This is likely not entirely true, in future models we would like to explore a feedback mechanism between elk/prey density, seasonal conditions, topography and pack size. It is entirely possible that the pack size should be a dynamic parameter, and the YNP website does mention that pack size can depend on prey availability.15 Run 1 results in data most similar to that seen in YNP.
Figure 8: Effect of varying the wolf litter size from 2 to 5 on Elk Population. Run 1 has a litter size of 2 and run 4 has a litter size of 5.
Figure 9: Effect of varying the wolf litter size from 2 to 5 on Wolf Population. Run 1 has a litter size of 2 and run 4 has a litter size of 5.
When varying the litter size, you can observe a unique trend in Run 1 as, due to the lower rate of wolf replication, the population grows quite slowly over time, also allowing elk populations to remain high. There is a similar effect of delaying the overshoot and collapse in the system at lower litter sizes.
Overall, the model does a nice job of demonstrating the trends seen after the reintroduction of wolves in YNP. The initial spike in population is there, as is the subsequent collapse of the elk population and then collapse of the wolf population. It also shows appropriate oscillations between the two populations over time, though the swings are larger than seen in YNP, and the wolf populations in particular are higher on average than they were in Montana. We expect there are additional feedback loops to be added to the model, perhaps strengthening the effect of pack density on wolf deaths.
Next Steps: Model Expansion
Ecology and Climate
Wolves’ impact on ungulate movement is a particularly interesting interaction that we were not able to model. In future models or if we were to expand further on ours, we would like to include this interaction and the effects on vegetation growth and other trophic levels. This would be an especially important next step as it is the leverage point sparking the rest of the trophic cascade seen in YNP.
Climatic variables including particularly harsh winters or droughts would also be interesting to add to the model. Studies that refute claims that wolf reintroduction caused the trophic cascade often point out that reductions in elk population could have been due to climatic conditions instead.13,14 Additionally, most elk living in YNP over the summer migrate out in the winter and it would be interesting to model this seasonal flux and how that might affect wolf populations and the true carrying capacity of YNP.22
Livestock Interactions and Social Systems
We would also like to see the model expanded to include livestock and wolf interactions. This would be our highest priority in adding to the model, as we believe this is where the biggest misunderstanding of wolf reintroduction lies. Wolves have only killed around 0.01% of cattle, compared with a loss of 8.37% from other causes such as disease, even though there are about 4x as many cattle as elk in Northern Rockies states.6,24 Around YNP specifically, only 256 sheep and 41 cattle were killed between 1995 and 2003.18 We think it would be really interesting to model this in two ways, one assessing the efficacy of lethal vs. non-lethal management and the other assessing the economic impact of compensation for loss of livestock vs. new income from tourism. There are possible dynamics to explore between the length of time wolves have been on the landscape and rancher views, as ranchers newer to wolf management tend to prefer lethal management options.17
Societal perceptions of wolves would be fascinating to explore here as well. From one author’s experience in living in Montana, wolf predation on livestock has resulted in extremely pejorative perceptions of wolves and a society that appears to glorify wolf culling, which could endanger wolf populations particularly before they can become established. On the other hand, the other author had a different experience in Colorado Springs, seeing the popularity of the Wolf and Wildlife Center and great potential for social acceptance. Different stakeholders within a society tend to have differing views as well. The general population, for example, tends to have a much more favorable view of wolves and reintroduction than ranchers and farmers.17 Native American communities tend to be more accepting of wolf populations on their lands than even the general population.17 Hunters are another group who tend to have a lower opinion of wolves than the general population, in part due to fears that wolves will take away their opportunity to hunt by over hunting elk and other large game.6,17 Interestingly, this has not been the case in Montana and Wyoming, as hunter success rates have actually increased since wolf reintroduction.6
Next Steps: Adapting the Model for Colorado
Colorado is estimated to have adequate space and prey to support at least 150 packs, with a population of 600-1500 wolves at any given time.2 While the official reintroduction plan has not been released yet, Wild Earth Guardians has recommended releasing one breeding pair in 12 different areas in Colorado.2 One could adapt our model by varying the initial numbers of wolves and elk specific to each region, as well as the available area. An interesting challenge would be in modeling the connectivity, the ability for these different populations to interact. Connectivity is important to maintain genetic diversity and ultimately survival.
Additionally, a Colorado population would need to consider wolf hunting. Hunting is not allowed at all in Yellowstone, and human-caused deaths of wolves in Yellowstone are not common. In Colorado, wolf management is proposed to have 3 phases - Reintroduction, Establishment, Viability, and a possible 4th stage post-Viability ,during which wolves could be hunted.2 The third stage, Viability, is able to be reached if wolf populations are at least 750 for four years and if both the elk populations themselves and the prevalence of CWD in them are halved.2
CWD would also be a necessary adaptation for a Colorado model, especially as this seems to be a government priority in terms of the benefits of wolf reintroduction.2 We imagine that in a Stella model, a converter capturing the percentage of elk deaths due to wolf predation could be created. This could connect to a second converter, which would describe a relationship in which as the percentage of elk death due to wolves increases, CWD prevalence decreases. If this were to be added to our model, it would be important to understand more about how CWD spreads among the elk population.
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