How Old-Growth Forest Conservation Policies
Support Caribou Recovery in British Columbia
Thompson Rivers University
Abstract
This research examines the critical policy intersection between old-growth forest
preservation and caribou conservation strategies in British Columbia. Caribou depend heavily on old-growth
forests for lichen, their primary food source. In response, British Columbia has implemented policies aimed at
protecting old-growth ecosystems, thereby indirectly safeguarding caribou habitats. While alternative methods
such as predator control (e.g., wolf reduction) and maternal penning provide short-term conservation gains,
long-term caribou recovery requires substantial protection of old-growth forests. However, expanding
conservation efforts entails significant opportunity costs, particularly the loss of logging revenues that
remain vital to the provincial economy. To explore these dynamics, this study applies a simple extinction model
to evaluate the impact of different forest management scenarios on caribou population trajectories.
Through a
comprehensive review and critical analysis of current forest preservation policies, the study identifies key
gaps and proposes strategic enhancements to strengthen conservation efforts. The findings emphasize that
preserving old-growth forests not only supports caribou survival but also enhances British Columbia’s ecosystem
services and long-term ecological resilience.
Keywords: caribou population, policy review, old-growth forest, British Columbia, economics of conservation
British Columbia (BC) encompasses a total land area of 95 million hectares, of which approximately 64% is forested (Government of British Columbia, 2016). Among these forested lands, about 11.1 million hectares—or roughly 20%—are classified as old-growth forests (Ministry of Forests, 2024). Old-growth forests are critical habitats for woodland caribou, a species increasingly threatened by human disturbances, such as forestry operations and pipeline expansions (Cichowski et al., 2022).
Forest harvesting and linear fragmentation disrupt caribou habitats in several ways. First, logging destroys key food sources, particularly lichens, which are vital for caribou survival (Cichowski et al., 2022). Second, reduced forest density creates open landscapes that make caribou more vulnerable to predation (James & Stuart-Smith, 2000). Additional disturbances, including noise pollution and the increase of linear features like roads and pipelines, further intensify risks to caribou populations (Maher et al., 2020; Maltman et al., 2024).
Several recovery strategies have been proposed to mitigate these impacts and support caribou conservation. Key interventions include minimizing habitat alteration, enhancing nutrition through maternal penning, and reducing predator populations such as wolves and moose (Maher et al., 2020). Johnson et al. (2019) demonstrate through their caribou-moose-wolf model that wolf population control is the most cost-effective short-term strategy for recovering the Chinchaga herd in British Columbia. However, for populations like the Charlevoix herd in Quebec, maternal penning proves more effective, highlighting the importance of tailoring conservation strategies to local demographic and ecological conditions.
Although predator-prey dynamics have often been emphasized, Ehlers et al. (2016) argue that in areas of low population density, such as those affected by extensive logging, direct encounters between caribou and wolves are relatively rare. Short-term interventions like wolf culling have shown success, but they are not sustainable in the long term (McNay et al., 2022). A more enduring solution lies in conserving old-growth forests, which provide both abundant lichen resources and the dense forest cover necessary for caribou to evade predators.
To address habitat loss, southern British Columbia has implemented sustainable forest management practices, particularly in second-growth forests (Stevenson, 1990). Strategies such as partial harvesting are designed to minimize impacts on wildlife habitat. Moreover, because caribou prefer high-elevation forests that offer refuge from predators, selective logging and careful forestry planning are critical for maintaining viable habitats (Newsome et al., 2016).
Provincial policy further mandates collaboration between wildlife experts and foresters during forestry planning processes (Government of British Columbia, 2025). This collaboration seeks to establish clear boundaries for caribou habitat reserves and create buffer zones that enhance habitat quality. Innovative planning tools, such as Cumulative Risk or Bow-tie Risk Assessment frameworks, also offer promising approaches to monitoring habitat dynamics and guiding conservation policy decisions (Winder et al., 2020, Hervieux et al., 2020).
Conserving old-growth forests offers additional benefits beyond caribou protection, particularly for Indigenous communities. Programs such as the First Nations Caribou Recovery Implementation Fund and the Caribou Recovery Program provide financial support, offering alternatives to the economic reliance on old-growth logging (Watt, 2024). These initiatives facilitate Indigenous-led conservation projects that integrate traditional ecological knowledge with scientific research, leading to more holistic and culturally grounded recovery strategies (Kutz & Tomaselli, 2019).
This research aims to evaluate current caribou conservation policies in British Columbia and assess their effectiveness in practice. Relying primarily on secondary sources from government publications and peer-reviewed studies, this project seeks to develop a balanced understanding of existing approaches and identify opportunities for improvement. In the next section, a theoretical model will be introduced to illustrate the relationship between caribou populations and old-growth forest conservation, providing a foundation for analyzing large-scale conservation outcomes.
Taylor and Weder (2024) developed a simple yet powerful model to illustrate the economics of extinction. In this section, we apply their framework to analyze the survival dynamics of caribou populations in British Columbia's old-growth forests. As outlined in the introduction, caribou are increasingly threatened by a combination of wolf predation, habitat degradation from human activities, and direct harvesting through hunting. Effective management and conservation require a clear understanding of how these factors interact and cumulatively affect caribou population trajectories.
To illustrate let \(C(t)\) represent the caribou population at time \(t\). The population dynamics can be captured by a modified logistic growth function: $$dC(t)/dt=gC(t)(1-C(t)/K(L) )((C(t)-M)/M)-H(C(t)) ........... (I)$$
where:
\(g\) is the constant growth rate of the caribou population, reflecting natural reproductive capabilities.
\(K(L)\) represents the natural carrying capacity of the caribou in the presence of logging where increases in logging reduce the carrying capacity K, \(dK/dL <0\)
M represents the minimum number of caribou below which it becomes extinct.
\(H(C(t))=cC(t) \) represents the hunting of caribou assumed to be a linear function of the number of caribou, where c is a constant rate.
Also note that the following condition holds: \(0 < M < K(L)\).
Let \(v(t)= M/K(L) \) as the fraction of the carrying capacity below which extinction occurs, even without active harvesting.
In the caribou model, the vulnerability parameter \(v(t)= M/K(L) \) summarizes how fragile the population is by comparing the minimum viable population \(M \) to the carrying capacity \(K(L) \) under logging pressure. A higher \(v\) means that caribou require a larger share of their potential habitat capacity to avoid slipping below the threshold, so the “safe zone” between collapse and carrying capacity becomes narrower. Ecologically, this makes the population much less resilient: the peak of biological growth falls, the unstable threshold shifts upward, and the buffer against hunting or predation shrinks. Because logging reduces \(K(L) \) while \( M\) remains relatively fixed, habitat loss automatically increases \(v \), raising extinction risk even if hunting effort is unchanged. In this way, \(v \) operates as a combined indicator of how both ecological requirements and habitat degradation interact to determine the likelihood of collapse.
This model captures several critical ecological dynamics. In the absence of logging, predation, and hunting, the caribou population would naturally converge with K, the undisturbed carrying capacity, through logistic growth. However, logging reduces \(K(L) \), diminishing available habitat and increasing predator encounters, thereby accelerating population decline toward extinction thresholds. The harvesting function \(H(C(t)) \) captures mortality from both traditional subsistence hunting and natural predation. The harvest function is increasing linearly as the caribou population increases.
Figure 1 depicts a theoretical model of caribou population dynamics under harvesting and no logging, incorporating logistic growth with a threshold, \(M \), and a linear harvest function. The green curve represents population growth \(G(C(t)) \), and the red line represents harvest losses \(H(C) = cC(t) \). The intersections of these functions define five key equilibria. The point \(C = 0 \) represents extinction and is a conditionally stable equilibrium: if the population begins below the \(C_L \) threshold, it will decline toward zero. At \(C_L = 500 \), net growth is zero, but the equilibrium is unstable; small downward shifts lead to extinction, while upward shifts trigger recovery. The upper interior equilibrium at \(C_H = 2,600 \) is the only stable equilibrium; if populations reach this level, they will persist unless strongly disturbed (See Appendix III). Finally, the carrying capacity at \(K=3,000 \) is unstable under harvest pressure; growth ceases while harvesting continues, leading to a net decline. Altogether, the model defines a bistable system in which long-term survival depends on maintaining populations above critical thresholds to avoid collapse. A summary is provided next:
In the absence of human activities, extinction risks persist due to natural predation or extreme environmental events. If \(C(t) \) falls below \(M \), even without human interference, extinction follows. However, if the caribou population remains above \(C_L\), natural predator-prey dynamics allow the population to stabilize around \(C_H \).
Figure 1: Illustration of the caribou in Itcha-Ilgachuz with the minimum viable threshold population of caribou at 100 herds, a carrying capacity of 3,000, a growth rate of 0.3, a harvest slope of 1, and no logging results in an approximate lower unstable equilibrium (CL) of 500 caribou and a CH of 2600. See Appendix I for the derivations. The other equilibrium is the extinction of the caribou if the herd falls below 100. Logging impact is absent in the above figure. Image Description
Predation exerts downward pressure on growth rates, often forcing caribou to migrate toward higher-elevation, denser forests that offer better refuge and food resources. Without logging or excessive hunting, these movements help maintain a stable ecosystem balance.
Logging has a huge impact on the caribou due to the creation of open space and increased success rate of predators. Logging reduces the carrying capacity and the viability of the caribou population. At the carrying capacity of \(K=3,000 \), the model shows a lower unstable threshold and an upper stable equilibrium, allowing for potential recovery if populations remain above the critical level of \(C_L \). However, by the time K declines below \(K=1,537 \) (See Appendix IV), the model crosses a tipping point: the growth function G(C) lies entirely below the harvest function H(C). In this regime, caribou populations are certain of extinction regardless of initial size (Figure 2, bottom right).
Hence, introducing logging into the model alters the system's dynamics by the vulnerability parameter \(v(t)= M/K(L) \) for the caribou. As logging progresses and available habitat shrinks, \(K \) declines from its initial value of 3,000 according to a degradation rate linked to cumulative logging effort. This reduction of carrying capacity causes the population growth curve \(G(C) \) to shift leftward, reducing the maximum sustainable population size. As a result, \(C_L \), the lower unstable equilibrium, and \(C_H \), the upper stable equilibrium, begin to converge (Figure 2). If logging continues unchecked, these equilibria eventually merge and vanish, eliminating the system’s capacity to stabilize at any positive population level. Beyond this tipping point, no population size above extinction can be sustained, and collapse becomes inevitable regardless of initial conditions. Thus, logging-induced habitat loss not only reduces the long-term ecological potential of the environment but also erodes the caribou population’s resilience to harvesting and other pressures. One of the assumptions is that the hunting function remains unchanged, which is most likely not true since hunters can more easily detect their prey. Hence, increased logging leads to a higher hunting rate, which could drive extinction even faster than shown in the illustration.
Figure 2: Simulated caribou population dynamics under varying carrying capacities K, with growth G(C) and harvest H(C) functions. At K = 1,527, the two interior equilibria CL and CH merge, and a tipping point occurs around 814 herds (See Appendix II and IV). Below this threshold, no positive equilibrium exists, and the population collapses to extinction. Image Description
In the next section, evidence from the Cariboo region of BC is shown. First, regions showing consistent population declines over time are identified. Then, micro-level analyses of specific study blocks are conducted by applying the model to predict future population trends under both regulated and unregulated harvesting scenarios. This approach aims to evaluate the model’s practical utility and inform conservation policy decisions.
While caribou populations are distributed across eight regions of British Columbia, this study focuses on the Cariboo region, which historically supports some of the province's highest caribou numbers. The Cariboo region is home to five distinct herds: Barkerville, Wells Gray North, Itcha-Ilgachuz, Rainbows, and Charlotte Alplands (Figure 3). These subpopulations are managed separately but may involve overlapping survey counts (Government of British Columbia, 2025).
Figure 3: Cariboo region in BC (Credit: Government of
British
Columbia,
n.d.) Image Description
This map was created using ArcGIS® software by
Esri.
Population data were retrieved from the Wildlife Species Inventory Survey Summary (Government of British Columbia, n.d.). Although the dataset includes multiple species such as elk, sheep, moose, and goats, only caribou data were extracted for this analysis. To ensure data credibility, only records with the "best parameter" designation were included, as this classification indicates the highest survey reliability according to the Government of British Columbia (n.d.).
To further refine data quality, the dataset was filtered based on survey methodology. Priority was given to methods with higher accuracy, including:
According to Conns et al. (2017), model-based corrections and expert knowledge approaches are more credible than raw total counts. Nonetheless, limitations remain as inconsistent survey coverage across years resulted in missing data points for some subpopulations. To aid visualization and analysis, caribou population counts were transformed using natural logarithms.
Figure 4 depicts notable population changes over time across the five herds.
Figure 4: Caribou in the Cariboo region of BC. Image Description
Given the dramatic decline of the Itcha-Ilgachuz herd, this subpopulation serves as the primary case study for applying the extinction model outlined previously. Simulations will explore whether observed population trends align with theoretical predictions under different management regimes, including regulated and unregulated harvesting.
Further insights are drawn from a controlled field experiment conducted by Waterhouse and Armleder (2005) in the Itcha-Ilgachuz Provincial Park. Five blocks, each spanning 60 to 80 hectares, were designated as treatment and control groups.
Baseline conditions were established in 1995 when the park was created. Subsequent surveys in 1998, 2000, and 2004 assessed lichen abundance, the primary winter food source for caribou. The results were stark:
These findings highlight the long-term ecological impacts of forest harvesting, even under selective logging practices. They highlight the critical importance of preserving old-growth forests to maintain essential habitat conditions for caribou survival, particularly in vulnerable herds like the Itcha-Ilgachuz.
Building upon the historical analysis of the Itcha-Ilgachuz herd, this section applies the extinction model introduced earlier to simulate potential future population trajectories and recommend conservation actions.
Historically, the Itcha-Ilgachuz caribou population exhibited robust growth, rising from approximately 711 individuals in the 1980s to a peak of 2,861 in 2004. However, from 2006 onward, the herd began a continuous and dramatic decline, falling to just 185 individuals by 2019. Although there was a minor recovery in 2009, the population ultimately plummeted by over 90% within a decade.
One major factor contributing to this decline was the mountain pine beetle outbreak. According to the Government of British Columbia (2009), red-stage infestations—where trees are fatally attacked—affected 358,000 hectares in 2008 and 199,730 hectares in 2009, with the Itcha-Ilgachuz region suffering particularly severe losses. While direct causal research is limited, the importance of forest health to caribou survival is well-established; caribou depend heavily on lichen that grows on mature trees (Fortin et al., 2017). Extensive tree mortality likely disrupted critical food sources and exacerbated population pressures.
Applying the extinction model (Equation 1) from Taylor and Weder (2024), Figure 5 presents three simulated scenarios based on varying levels of old-growth forest protection:
Figure 5: Itcha-Ilgachuz population at risk. Image Description
These projections emphasize the acute sensitivity of caribou populations to human activities such as logging and hunting, as well as to indirect ecological effects like predator dynamics. The simulations reinforce the urgent need for proactive and stringent conservation measures.
Moreover, the three scenarios are benchmarked against key biological thresholds: passing the recovery target level (Environment Canada, 2014), maintaining genetic diversity (Frankham et al., 2014), ensuring a minimum viable population size (Shaffer, 1981; Traill et al., 2007), and avoiding extinction (Lande, 1988). Only the high-regulation scenario meets all of these criteria.
The only viable policy path for recovering the Itcha-Ilgachuz herd is to impose strict protection of old-growth forests, thereby minimizing human interference. The next section will explore available regulatory frameworks and conservation policy options to implement this strategy.
Recognizing the critical relationship between old-growth forests and caribou habitat, forest development deferral has emerged as a mainstream conservation strategy (Parks Canada, 2023; Gorley & Merkel, 2020; Government of British Columbia, 2025). Development deferral involves postponing commercial logging activities in designated areas, subject to future reassessment (Government of British Columbia, 2025).
The Government of British Columbia (2025) identifies three primary types of development deferrals:
Applying the extinction model (Equation 1), development deferrals effectively increase the carrying capacity \( K(L)\) for caribou populations by eliminating logging pressures. For example, in Upper Seymour Provincial Park, 2,640 hectares (Cox, 2022) of a total 10,672 hectares (BC Parks, n.d.) are protected under regulation-based deferrals, while an additional 3,070 hectares are safeguarded through voluntary agreements.
However, as Cox (2022) highlights, these deferrals are closely tied to caribou population status. If the herds were to disappear, protected areas could revert to commercial logging eligibility, demonstrating the mutually reinforcing relationship between caribou conservation and old-growth forest protection.
Parks Canada (2023) further underscores the ecological consequences of logging, noting that post-harvest landscapes create open spaces that increase predator access to prey such as caribou (James & Stuart-Smith, 2000). In the absence of human disturbance (i.e., \( H(C) = 0\) ), natural predator-prey dynamics stabilize. To restore disturbed habitats, reforestation efforts and forestry road deactivation are critical (Central Chilcotin Rehabilitation Ltd., 2025). Reversing the effects of industrial seismic lines and replanting access roads can restrict predator movement and help reestablish natural forest density.
Together, proactive development deferral and habitat restoration provide the foundation for effective caribou conservation through integrated forest landscape planning.
Indigenous-led conservation projects have played a transformative role in safeguarding old-growth forests (Government of British Columbia, 2024). A landmark example is the creation and expansion of Twin Sisters (Klinse-Za) Provincial Park, led collaboratively by the West Moberly and Saulteau First Nations in partnership with the Government of Canada.
The park's size expanded by nearly 1,000%, from 2,700 hectares in 2020 to approximately 200,000 hectares by 2024 (Cruickshank & Wood, 2024). This dramatic growth aims to conserve critical ecosystems for at-risk species, including caribou, grizzly bears, and bull trout.
Supporting this initiative, the Government of Canada and British Columbia committed $46 million in financial compensation to forestry stakeholders affected by logging restrictions. To further offset economic impacts, the South Peace Mackenzie Economic Diversification and Stabilization Trust was established, providing an initial $1 million to support local economic diversification (Government of British Columbia, 2022).
Additionally, the Province of British Columbia invested $300 million to launch a new Indigenous-led conservation program (Verde, 2023). This initiative supports the broader goal of protecting 30% of British Columbia’s old-growth forests by 2030.
The funding enhances Indigenous stewardship capacities, empowering First Nations to lead conservation policy development, implement protection measures, and pursue economic alternatives to old-growth logging.
Organizations like the Ancient Forest Alliance (n.d.) have endorsed these measures, emphasizing that financial support not only compensates for foregone logging revenues but also builds Indigenous capacity for conservation planning and governance. Moreover, the Alliance advocates for expanding second-growth commercial forestry to meet wood product demand while minimizing further impacts on remaining old-growth ecosystems.
Collectively, these policy measures illustrate a paradigm shift toward Indigenous leadership, sustainable economic development, and the long-term protection of critical wildlife habitats, including those needed by caribou populations.
Despite considerable efforts to recover caribou populations, significant challenges remain. Biologist Clayton Lamb, in an interview with Rochefort (2024), noted that predator management strategies have led to only a 60% recovery of South Mountain caribou herds over a decade. Lamb cautions that predator control is unsustainable in the long term, as it disrupts broader ecosystem balances. He advocates for habitat regeneration, although he acknowledges it is a slow and uncertain process (Rochefort, 2024).
Additional critiques highlight inconsistencies in British Columbia’s conservation policies. Lindsay (2024) reports that despite substantial financial commitments to caribou recovery, commercial logging persists within critical caribou habitats. For instance, BC Timber Sales and Pacific Woodtech proposed clear-cutting 620 hectares of old-growth forests within the Seymour River watershed—an area vital for the Columbia North caribou—overlapping old-growth deferral zones initially set aside for conservation.
Similar shortcomings are observed elsewhere. In Ontario, the government has failed to meet agreed-upon standards for forestry management in critical habitats, falling short of species-at-risk commitments (CPAWS Northern Alberta, 2024).
Gorley and Merkel’s (2020) review of old-growth conservation in British Columbia further identifies key gaps:
Moreover, some areas designated for conservation were poorly chosen, sometimes lacking significant old-growth stands or being prone to wildfires. Resource constraints have limited the government's capacity to address these systemic weaknesses (Gorley & Merkel, 2020).
Overall, the lack of comprehensive monitoring and adaptive management undermines the effectiveness of existing caribou conservation policies, signaling an urgent need for stronger, better-enforced measures.
The Itcha-Ilgachuz herd provides a microcosm of broader trends. Following a peak population in 2004, the herd suffered a dramatic decline, likely due to logging pressures and the mountain pine beetle outbreak. The critical dependence of caribou on old-growth forest ecosystems, particularly lichen-rich habitats, has been well-documented (Waterhouse & Armleder, 2005). Applying the extinction model developed by Taylor and Weder (2024) reveals clear outcomes under different management scenarios:
The model highlights the vital importance of immediate, effective interventions. Moreover, logging not only reduces habitat area but also creates open landscapes that increase predator access, further stressing vulnerable caribou populations. Strategies such as forestry road deactivation and habitat restoration are crucial to mitigating these effects.
To safeguard caribou populations in British Columbia, several strategies emerge from the analysis:
Strengthen the enforcement of voluntary, regulation-based, and directed deferrals. Ensure deferrals are resilient to fluctuations in caribou population status. Without effective intervention, the decline of caribou populations may result in the removal of conservation protection and ultimately lead to the opening of commercial logging. It is recommended that further development deferral programs be expanded to advance caribou habitat conservation and to strengthen enforcement laws under the Forest Act, thereby preventing unauthorized logging activities.
Build on successful models such as Twin Sisters Park. Increased funding for Indigenous stewardship programs can foster regionally focused, culturally informed conservation strategies while supporting economic diversification in affected communities. Expanding Indigenous-led conservation initiatives and consulting with Indigenous communities will further Truth and Reconciliation efforts while helping restore people’s relationship and connection with the land.
Implement periodic, landscape-scale reviews of old-growth conservation effectiveness. Address resource gaps that have historically limited monitoring and enforcement capacities. According to Gorley and Merkel (2020), the lack of formal review and monitoring of old-growth forest areas makes it difficult to assess policy effectiveness. In addition, the implementation of old-growth forest conservation has been criticized for poor site selection, with some protected areas containing few old trees or being at higher risk of wildfire.
Promote forestry road deactivation, seismic line restoration, and reforestation in critical caribou habitats. Logging also impacts predator-prey dynamics, as clear-cutting creates open landscapes that increase predator access to caribou and decrease the caribou’s carrying capacity. Implementing forestry road deactivation, habitat restoration, and old-growth forest preservation is essential to mitigate these impacts. Collaboration with local communities can support monitoring efforts and help design regionally focused caribou recovery strategies.
Extend financial support to communities transitioning from logging economies and invest in second-growth forestry as a sustainable alternative. By balancing ecological priorities with economic considerations, policymakers can improve caribou survival while promoting rural economic growth and community well-being.
Caribou conservation efforts in British Columbia have combined maternal penning, predator control, and habitat interventions. While some short-term successes have been achieved, long-term sustainability demands a renewed focus on habitat conservation. The Itcha-Ilgachuz case study vividly demonstrates the stark consequences of inaction and the potential for recovery under strong regulation. A holistic strategy must integrate Indigenous leadership, expand habitat protections, enforce logging regulations more rigorously, and balance ecological priorities with economic considerations. By embracing these approaches, policymakers can foster a future where caribou populations survive and thrive, promoting both ecological resilience and community well-being across British Columbia. Immediate, decisive and effective action is essential to reverse the threat of caribou extinction.
I would like to express my deepest gratitude to all those who supported and guided me throughout the development of this research. I am especially grateful to the Adams Lake Indian Band for their invaluable insights in identifying the research gap in the economics of conservation, with a focus on caribou. I also wish to thank Professor Stefania Strantza for her mentorship, encouragement, and guidance in refining the data set and moving the project forward. Finally, I owe profound thanks to Dr. Peter Tsigaris, whose trust and unwavering confidence in the value of this research enabled me to complete this research project. His expertise and guidance also provided me with technical and analytical skills that exceeded my expectations as an undergraduate student. Finally, I would like to acknowledge that this research paper used the assistance of ChatGPT (OpenAI, GPT-4) for code generation, figure creation, and some text editing, all under the author’s direct supervision. All theoretical development, analysis, interpretation, and extended discussion were conducted solely by the author. The author independently paraphrased academic materials as part of responsible scholarship, ensuring proper synthesis and citation of all sources.
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Figure 1 Image Description: A graph illustrates caribou population growth dynamics using two functions: G(C) and H(C). The x-axis represents caribou population size (C), and the y-axis represents population growth rate. The (G(C)) curve rises, peaks, and then declines, showing natural growth patterns with density dependence. The (H(C)) line is linear and increasing, representing external pressures (e.g., harvesting or mortality). The two curves intersect at two points: a lower equilibrium point (CL) and a higher equilibrium point (CH). At very small population sizes (below M), growth is negative and populations trend toward extinction. At populations above CL but below CH, caribou can persist and grow until they stabilize near CH. The carrying capacity is marked as K. The arrows along the axis show direction of population change depending on starting population size.
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Figure 2 Image Description: This figure compares four scenarios of caribou population dynamics.
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Figure 3 Image Description: A map of part of British Columbia showing designated caribou ranges and regions.
The map shows how these ranges are geographically grouped, with western herds (Rainbows and Itcha-Ilgachuz) highlighted separately from central and eastern ranges such as Wells Gray and Columbia. Boundary lines indicate regional divisions, while highlighted overlays identify specific herd ranges.
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Figure 4 Image Description: A line graph tracking caribou population trends across five regions of British Columbia between the early 1980s and 2019, shown on a natural log scale.
Overall, most herds declined, with the sharpest losses seen in the Itcha-Ilgachuz and Rainbows populations.
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Figure 5 Image Description: A line graph shows the population trends of the Itcha-Ilgachuz caribou herd from the early 1980s to 2019, with projections under different regulation scenarios extending to 2060.
[Back to Figure 5]
Trang Phan is an Economics major at Thompson Rivers University with a strong academic focus on applied econometrics, environmental economics, and natural resource management. His research explores how economic tools and data-driven analysis can be leveraged to address real-world challenges, particularly those affecting environmental sustainability and rural community development. Currently, Trang serves as a Socioeconomist for the Adams Lake Indian Band, where he conducts economic research on cumulative environmental effects and contributes to policy analysis in forestry development.
Trang has also demonstrated leadership through various roles, including Conference Coordinator for the TRU Economics Students' Association and Financial Manager for the TRUSU Dance Club. Looking ahead, Trang plans to pursue graduate studies in environmental economics and indigenous studies, aiming to deepen his quantitative expertise and advance evidence-based research and policy evaluation.
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import fsolve
# Parameters
M_val = 100.0
K_val = 3000.0
r_val = 0.3
h_slope = 1.0
# Domain
C = np.linspace(0, K_val, 4000)
# Functions
def G(C):
return r_val * C * (1 - C / K_val) * (C / M_val - 1)
def H(C):
return h_slope * C
# Intersection function
def intersection(x):
return G(x) - H(x)
# Roots for reference
C_L = float(fsolve(intersection, 500.0))
C_H = float(fsolve(intersection, 2600.0))
# Curves
G_vals = G(C)
H_vals = H(C)
maxG = float(np.max(G_vals))
# Figure
plt.figure(figsize=(12, 7))
plt.grid(True, color='black', linestyle='-', linewidth=0.5, alpha=0.2)
plt.plot(C, G_vals, color='green', linewidth=3)
plt.plot(C, H_vals, color='red', linewidth=3)
# Axes lines
plt.axhline(0, color='k', linewidth=1.5)
plt.axvline(0, color='k', linewidth=1.5)
# Set y-limits to include requested y coordinate if needed
lower_extra = -round(maxG * 0.1, 1)
upper_limit = max(maxG * 1.05, 2281 * 1.05)
plt.ylim(lower_extra, upper_limit)
# Labels
plt.xlabel('Caribou Population (C)')
plt.ylabel('Population Growth Rate')
# Place G(C) at exact coordinates
x_gc = 1000
y_gc = 2281
plt.text(x_gc, y_gc, 'G(C)', color='green', fontsize=14, fontweight='bold')
# H(C) label
x_h = K_val * 0.55
y_h = H(x_h) + maxG * 0.05
plt.text(x_h, y_h, 'H(C)', color='red', fontsize=14, fontweight='bold')
# X-axis labels positioned in the gap
label_y = lower_extra * 0.4
plt.scatter([M_val, K_val, 0], [0, 0, 0], color='black', s=50)
plt.text(M_val, label_y, 'M', ha='center', va='top', fontsize=14, fontweight='bold')
plt.text(K_val, label_y, 'K', ha='center', va='top', fontsize=14, fontweight='bold')
plt.text(C_L, label_y, 'C$_{L}$', ha='center', va='top', fontsize=14, fontweight='bold')
plt.text(C_H, label_y, 'C$_{H}$', ha='center', va='top', fontsize=14, fontweight='bold')
# Dotted lines and points
plt.scatter([C_L], [G(C_L)], color='black', s=50)
plt.scatter([C_H], [G(C_H)], color='black', s=50)
plt.plot([C_L, C_L], [G(C_L), 0], color='black', linestyle='dotted', linewidth=1.5)
plt.plot([C_H, C_H], [G(C_H), 0], color='black', linestyle='dotted', linewidth=1.5)
# Direction arrows using sign of G-H
ax = plt.gca()
narrow_props = dict(arrowstyle='->', color='black', lw=2)
regions = [0, C_L, C_H, K_val]
for a, b in zip(regions[:-1], regions[1:]):
x_test = a + 0.3*(b-a)
val = intersection(x_test)
num_arrows = 3
seg = np.linspace(a + 0.1*(b-a), b - 0.1*(b-a), num_arrows)
arrow_len = (b - a) / 15.0
for sx in seg:
if val > 0:
ax.annotate('', xy=(sx + arrow_len, 0), xytext=(sx, 0), arrowprops=arrow_props)
else:
ax.annotate('', xy=(sx - arrow_len, 0), xytext=(sx, 0), arrowprops=arrow_props)
# Clean bottom-most tick label if present
yt = ax.get_yticks()
yt_new = [t for t in yt if not (t == lower_extra)]
ax.set_yticks(yt_new)
# Ticks
ax.xaxis.set_major_locator(plt.MultipleLocator(500))
ax.yaxis.set_major_locator(plt.MultipleLocator(maxG/10.0))
plt.tight_layout()
plt.show()
import numpy as np
import matplotlib.pyplot as plt
# Parameters
r = 0.3 # intrinsic growth rate
M = 100 # minimum threshold
h = 1.0 # harvest slope
phi = 1.0 # linear harvest function
# Population range
C_dict = {
3000: np.linspace(0, 3100, 500),
2500: np.linspace(0, 2600, 500),
2000: np.linspace(0, 2100, 500),
1537: np.linspace(0, 1700, 500)
}
# Growth function with minimum threshold effect
def G(C, r, K, M):
return np.maximum(0, r * C * (1 - C / K) * (C / M - 1)) # prevent values below 0
# Harvest function
def H(C, h, phi):
return h * C**phi
# Carrying capacities
K_vals = [3000, 2500, 2000, 1537]
# Plotting
fig, axes = plt.subplots(2, 2, figsize=(12, 8))
axes = axes.flatten()
for i, K in enumerate(K_vals):
C = C_dict[K]
G_vals = G(C, r, K, M)
H_vals = H(C, h, phi)
axes[i].plot(C, G_vals / 1000, label='G(C) — Growth', color='green')
axes[i].plot(C, H_vals / 1000, label='H(C) — Harvest', color='red')
axes[i].axhline(0, color='black', linewidth=0.5)
axes[i].set_title(f'Carrying Capacity K = {K}')
axes[i].set_xlabel('Caribou Population (C)')
axes[i].set_ylabel('Rate of Change (×1000 caribou/year)')
axes[i].legend()
axes[i].grid(True)
plt.tight_layout()
plt.show()
Model parameters:
M = 100: Minimum viable population
K(L) = K = 3000: Carrying capacity without logging
g = 0.3: Intrinsic growth rate
c = 1.0: Harvest rate
The time path of the caribou over time is given by [1] in the manuscript:
$$ dC(t)/dt=gC(t)(1-C(t)/K(L) )((C(t)-M)/M)-H(C(t)) $$
Equilibrium requires \(dC(t)/dt = 0\) and given the above parameters we have
$$ 0.3C^* (1-C^*/3,000)((C^*-100)/100)-C^*= 0 $$
Where is the stationary equilibrium. Factoring out yields:
$$ C^* [0.3(1-C^*/3,000)((C^*-100)/100)-1]= 0 $$
Hence 1 equilibrium is extinction \(C^ *= 0\) and occurs if \(C(t) < 100\).
The other two equilibria are found by solving the following quadratic equation
$$ [0.3(1-C^*/3,000)((C^*-100)/100)-1]= 0 $$
After simple manipulations we get the following quadratic equation:
$$ 〖C^*〗^2-3,100 C^*+300,000=0 $$
Solving yields \(C_L^ *= 500\) and \(C_H^ *= 2,600\)
In general, the quadratic equation is: $$〖C^*〗^2-(K+M) C^*+(1+c/r)KM=0$$
Carrying Capacity (K) | Lower Equilibrium (CL) | Upper Equilibrium(CH) |
---|---|---|
3000 | 500 | 2600 |
2500 | 521 | 2079 |
2000 | 564 | 1536 |
1800 | 600 | 1300 |
1700 | 629 | 1171 |
1600 | 679 | 1021 |
1550 | 730 | 920 |
1527 | 804 | 823 |
1526.785 | 814 | 814 |
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https://publishing.bceln.ca/index.php/furture-earth/article/view/710.