Optimizing Dam Removals: Balancing Ecology and Economy in Lake Erie

Lake Erie, the shallowest and most productive of the Great Lakes, faces significant environmental challenges. Decades of human activity, including the construction of thousands of dams on its tributary rivers, have altered the ecosystem. Many of these dams block fish migration routes, particularly impacting species like the native walleye (Sander vitreus) that need access to river habitats for spawning.

Removing old or unnecessary dams seems like a straightforward solution to restore these habitats. However, the reality is complex. Dam removal is expensive, and the ecological consequences aren't always purely positive. For instance, removing a dam might also open up habitat for invasive species like the parasitic sea lamprey (Petromyzon marinus). Furthermore, some dams still provide services like flood control or hydropower.

This leads to a challenging question: With limited resources, which dams should be removed to achieve the greatest overall benefit for the Lake Erie ecosystem, considering multiple, often conflicting, objectives?

The academic paper "Optimizing multiple dam removals under multiple objectives: Linking tributary habitat and the Lake Erie ecosystem" by Zheng, Hobbs, and Koonce (2009) tackles this problem using mathematical optimization. This page explores the core ideas of their approach, using interactive visualizations to build intuition.

The Core Challenge: Balancing Trade-offs

Dam removal decisions involve balancing competing factors. Let's consider the main ones highlighted in the paper:

• Ecological Benefit (Walleye): Removing dams can open up upstream spawning habitat for desirable native species like walleye. More habitat can potentially lead to larger, healthier populations.
• Ecological Harm (Sea Lamprey): Unfortunately, the same removal might also grant access to invasive sea lamprey, which prey on valuable fish species. Controlling lamprey requires costly chemical treatments (lampricides).
• Economic Cost: Removing a dam involves direct costs (demolition, sediment management) and potentially indirect costs (loss of services like hydropower). Adding lamprey control costs further increases the expense.

Quantifying the Impacts

To make informed decisions, we need to quantify these benefits and costs. The paper uses several modeling techniques:

1. Habitat Changes: How Much Space is Opened?

When a dam is removed, fish gain access to upstream river sections previously blocked. The paper uses Habitat Suitability Index (HSI) models combined with Geographic Information System (GIS) data. HSI models estimate how suitable a specific river reach is for a particular species (like walleye spawning or lamprey larvae) based on physical characteristics like water depth, velocity, and substrate type (e.g., gravel, sand, mud).

Removing dam $j$ potentially opens up a certain area or length of habitat upstream. Let's visualize this simply:

The actual calculation in the paper is more complex, considering the specific HSI values for different river reaches ($k$) upstream of dam $j$ and summing the suitable habitat area ($A_{k,s}$ for walleye, depending on substrate $s$) or length ($L_k$ for lamprey):

Walleye Spawning Habitat Area opened by removing dam $j$ (simplified concept):

Lamprey Nursery Habitat Length opened by removing dam $j$ (simplified concept):

Note: The paper also incorporates the *likelihood* ($V^{\text{walleye}}_j$, $V^{\text{lamprey}}_j$) that the species will actually successfully utilize this new habitat, based on expert judgment for different watersheds.

2. Ecosystem Response: From Habitat to Fish Populations

Simply opening habitat doesn't guarantee more fish. The link is complex, involving survival rates, food availability, and interactions within the ecosystem. The paper uses the Lake Erie Ecological Model (LEEM), a sophisticated simulation model representing the lake's food web and major fish species.

The key linkage is the estimated increase in Walleye Young-of-Year (YOY) recruitment ($\Delta YOY^{\text{walleye}}$) resulting from the increased egg production ($EP_j$) in the newly accessible spawning habitat:

LEEM is then used to estimate how this pulse of new walleye affects various ecosystem metrics ($x_1, ..., x_8$) like the ratio of walleye to other fish, overall fish productivity, and harvest levels. This is done using "impulse response" functions ($IR_{x_i}$), which estimate the change in metric $x_i$ per unit increase in walleye YOY:

This allows the model to connect a specific dam removal decision to its broader ecological consequences across the lake.

3. Economic Costs: Removal and Control

The paper estimates two main costs:

• Dam Removal Cost ($C^{\text{dam}}_j$): Estimated using a statistical regression model based on data from past removals. Larger dams (height, length) cost more, and dams serving important functions (like hydropower) have higher effective removal costs (due to lost services). Earthen dams are generally cheaper to remove than concrete ones.
• Sea Lamprey Control Cost ($C^{\text{lamprey}}_j$): If removing dam $j$ opens up suitable lamprey nursery habitat ($H^{\text{lamprey}}_j$), the cost of applying lampricide (TFM chemical) to that stretch of river is calculated. This cost depends on the length of habitat opened and occurs periodically (e.g., every 4 years).

The total economic cost ($x_9$) for a portfolio of removed dams (set $J_{removed}$) is the sum of individual removal and lamprey control costs:

Putting It All Together: The Optimization Model

The goal is to select a set of dams to remove ($J_{removed}$) that maximizes the overall ecological health of Lake Erie, subject to a budget constraint ($B$).

Defining "Ecological Health" - Multi-Criteria Value Analysis (MVA)

Since "ecological health" isn't a single number, the paper uses Multi-Criteria Value Analysis (MVA). This involves defining several specific criteria ($x_1, ..., x_8$) derived from the LEEM outputs (e.g., walleye biomass, native species ratio, fishery harvest levels). Each criterion $x_i$ is assigned a value function $V_i(x_i)$ (scaling its performance from 0 to 1, worst to best) and an importance weight $W_i$ (reflecting stakeholder priorities, elicited in workshops). The overall ecological health score ($z_1$) is the weighted sum:

The Optimization Framework: Mixed Integer Linear Programming (MILP)

The core of the paper is a Mixed Integer Linear Program (MILP). This is a mathematical technique for finding the best solution to a problem where some decisions are discrete (like yes/no for dam removal) and others are continuous (like the resulting ecological scores), subject to constraints.

Let $d_j$ be a binary decision variable: $d_j = 1$ if dam $j$ is removed, $d_j = 0$ otherwise.

The basic model formulation is:

Maximize: Ecological Health Score $z_1$

Subject to:

1. Budget Constraint: Total cost cannot exceed the budget $B$.
$$ x_9 = \sum_{j \in J} (C^{\text{dam}}_j + C^{\text{lamprey}}_j) d_j \leq B $$
2. Ecological Linkages: Changes in criteria $x_i$ depend on total walleye YOY increase, which depends on which dams $j$ are removed ($d_j=1$).
$$ x_i = x_i^{\text{base}} + IR_{x_i} \times \sum_{j \in J} (\Delta YOY^{\text{walleye}}_j \times d_j) $$ (Simplified; assumes linear value functions $V_i$ for the MILP)
3. Habitat Logic: An upstream dam $n$ cannot be removed ($d_n=1$) unless the immediately downstream dam $j$ is also removed ($d_j=1$).
$$ d_n \leq d_j \quad \text{for all } n \text{ directly upstream of } j $$
4. Binary Decisions:
$$ d_j \in \{0, 1\} \quad \text{for all dams } j $$

Interactive Mini-Optimization

Solving a full MILP is complex. Let's simulate the *idea* with a small set of hypothetical dams. Try to manually select dams to maximize the "Ecological Benefit Units" without exceeding the budget. Then see what the optimal solution is.

Results: The Efficient Frontier

Because there's a trade-off between cost ($x_9$) and ecological benefit ($z_1$), there isn't one single "best" solution. Instead, the MILP can identify a set of efficient or Pareto optimal solutions. An efficient solution is one where you cannot improve the ecological score without increasing the cost, and you cannot decrease the cost without worsening the ecological score.

Plotting these efficient solutions reveals the trade-off curve (also called the Efficient Frontier), showing the maximum ecological benefit achievable for any given budget level.

The shape of the curve is important. Often, initial investments yield large ecological gains (steep slope), but achieving further improvements becomes increasingly expensive (flattening slope) - demonstrating diminishing returns.

Sensitivity Analysis: What if Priorities Change?

The choice of which dams form the "optimal" portfolio depends heavily on the priorities assigned, particularly the balance between promoting walleye and avoiding sea lamprey habitat expansion.

The paper explores this by introducing a weight ($WL$) on a *negative* objective: minimizing the percentage of potential lamprey habitat opened ($z_3$). The objective function becomes a combination of maximizing ecological health $z_1$ and minimizing lamprey habitat $z_3$:

Changing the $WL$ weight dramatically alters the recommended dam removal strategy:

• Low $WL$ (Focus on Walleye/Overall Health): The model tends to remove dams in watersheds known for good walleye spawning (like the Sandusky River), even if some lamprey habitat is also opened (requires control). This corresponds to the results shown in the trade-off curve above.
• High $WL$ (Focus on Avoiding Lamprey): The model avoids removing dams that open significant lamprey habitat. It shifts focus to dams in watersheds considered less risky for lamprey invasion, even if the walleye benefits are lower. The total number of dams removed might even increase (as smaller, "safer" dams are chosen), but the overall ecological score ($z_1$) will be lower.

Impact of Lamprey Avoidance Weight (WL)

Adjust the slider to change the priority placed on avoiding sea lamprey habitat. Observe how the "recommended" strategy might shift (represented conceptually on the map and trade-off curve).

Lamprey Avoidance Weight (WL): 0.1

Conceptual Map (Inspired by Figures 3 & 5):

Summary: With low WL, removals focus on high-potential walleye areas. With high WL, removals shift to areas with minimal lamprey risk.

Map is purely illustrative. Marker positions and colors change based on WL to represent the strategic shift described in the paper.

Conclusions

Choosing which dams to remove is a complex environmental management problem with significant ecological and economic consequences. The approach detailed by Zheng, Hobbs, and Koonce provides a powerful framework for navigating these complexities:

• It explicitly links dam removal decisions to habitat changes and then to broader ecosystem effects using models like HSI and LEEM.
• It incorporates multiple objectives using MVA, allowing for the consideration of stakeholder priorities.
• It uses optimization (MILP) to systematically identify portfolios of dam removals that offer the best performance for a given budget, revealing the crucial trade-offs involved.
• It highlights the sensitivity of decisions to underlying priorities, such as the relative importance of enhancing native species versus avoiding invasive ones.

While the model relies on estimates and involves uncertainties (requiring site-specific studies before actual removal), it serves as a valuable screening tool. It helps managers understand the system-wide implications of different strategies and identify potentially cost-effective portfolios for restoring habitat and improving the health of the Lake Erie ecosystem.