Myers et al. (2000, Nature)
Biodiversity hotspots for conservation priorities

What they did:

• Identified regions with:
  • 🌿 High biodiversity (endemism)
  • ⚠️ High threat (habitat loss)
• Found:
  • 44% of plant species
    
  • in just 1.4% of Earth’s land

👉 Focus conservation on these hotspots

• What do we conserve?

• ❌ No constraints (area, cost)
  
• ❌ No decision rule
  
• ❌ No complementarity
  
• ❌ No selection of specific areas

👉 It identifies important places
👉 But does not make a decision

• Define an objective
• Define decision variables
• Define constraints
• Use spatial data
• Compare efficient alternatives
• Evaluate and interpret solutions

👉 SCP is about choosing where to act

Now you are the planner.

You must: - choose areas - justify your choice - revise it as new information arrives

• 52.44% of area protected (Half earth)
• 71,461.48 square kilometers

• Grasslands

• https://www.menti.com/ code 8306 9647

Choose 2 areas using only:

• richness, the map

🧭 Based only on biodiversity information:

• Choose 2 areas to protect
• Use the Menti code 8306 9647 to vote

• with this new information select 2 areas

“Now that you know that some habitats are already protected, would you change your decision?”

“Now that you have seen the percentages, would you change your decision?”

🌍 Considering carbon stocks, would you change your decision?

• Conservation priorities change as we add new layers of information
• We may have biases (e.g., forests vs. grasslands, charismatic species)
• Decisions involve trade-offs between:
  • Biodiversity
  • Ecosystem representation
  • Feasibility and constraints

🤔 Would your original choices still be your final ones? Why or why not?

How do we convert agricultural land into new nature so that we jointly improve:

• biodiversity, carbon, spatial cohesion while still meeting real planning constraints?`

We want to maximize:

• biodiversity
• carbon benefits
• contiguity

👉 In SCP, the first question is: What are we trying to optimize?

\[ \text{maximize CI} = \color{#d7191c}{W_B \times \text{Biodiversity}} + \color{#7b3294}{W_C \times \text{Carbon}} + \color{#2c7bb6}{W_Q \times \text{Contiguity}} \]

• Biodiversity
  • Species richness
    
  • Phylogenetic diversity
    
  • Rarity
• Carbon
  • Aboveground carbon sequestration
    
  • Belowground carbon sequestration
    
  • Avoided emissions through rewetting of carbon-rich soils
• Contiguity
  • Rewards adjacent restored cells of the same nature type
    
  • Promotes larger and more cohesive habitat patches
• pareto edge design
  • Biodiversity weight fixed at 1
    
  • Carbon weight varies from 0 to 1.4

\[ CI = \sum_{l}^{L} \sum_{c}^{C} \left( X_{l,c} \cdot \left( \frac{Richness_{l,c} + PD_{l,c} + Rarity_{l,c}}{3} \right) \cdot CanChange_{c} \right) \]

+

\[ \sum_{l}^{L} \sum_{c}^{C} \left( X_{l,c} \cdot PC_{l,c} \cdot CanChange_{c} \right) \]

+

\[ CB \cdot \sum_{i,j}^{E} \sum_{l}^{L} \left( C_{l,i,j} \cdot CanChange_{i} \cdot CanChange_{j} + EN_{l,i} \cdot X_{l,i} \cdot CanChange_{j} \right) \]

CI is the Conservation Index, which is being optimized in this case.

L and l represents different land uses (in this case nature types).

C and c represents the cells of the study area.

X_l,c is the decision variable, which the model can vary to get the optimal solution. There is a decision variable for each nature type in each cell, and it is either 0 (choosing to not restore to this nature type) or 1 (choosing to restore to this nature type).

Richness_l,c, PD_l,c and Rarity_l,c represent the three biodiversity metrics used here.

CanChange represents whether a cell is available for agriculture-to-nature conversion.

PC_l,c is the potential carbon (made up of both aboveground and belowground carbon).

CB is the contiguity bonus.

C_l,i,j represents contiguity. If two cells (i and j) have the same nature type l, there is contiguity between these two cells.

EN_l,i represents whether nature type l already exists in cell i.

For each agricultural cell:

• change or not?
• if it changes, into what?

Options: - wet / dry - open / forest - poor / rich

👉 SCP needs explicit decisions, not just priority maps

Biodiversity

• species richness
• phylogenetic diversity
• rarity

Carbon

• future sequestration
• avoided emissions

👉 Good SCP depends on how objectives are measured

Biodiversity

Carbon

We do not ask for one answer.

We vary the carbon weight and generate:

👉 a Pareto frontier of optimal trade-offs

The Pareto frontier gives many optimal solutions.

We then identify elbows:

• strong biodiversity retained
• carbon improves
• diminishing returns after that

👉 SCP does not always produce one “best” answer 👉 It can define the best possible choices

Optimization used a scalable biodiversity proxy.

Afterward we evaluated solutions with:

• species persistence
• β-diversity
• alternative biodiversity dimensions

👉 Optimization and evaluation are not always the same thing

• Most biodiversity gains occur near biodiversity-focused solutions
• Constraints compress the solution space
• Hydrology matters more than forest/open shifts
• Some areas are stable across solutions, others are flexible

👉 The result is not just a map 👉 It is an interpretable decision space

Using the Patagonia example, define an SCP problem.

You have:

• species richness
• carbon storage
• habitat representation
• existing protected areas

In small groups, define:

1. Decision variable
   What are we choosing?

2. Objective function
   What are we maximizing?

3. Constraint(s)
   What limits the decision?

4. Trade-off
   What could conflict with what?

• Resilience
  • Contiguity (Area)
  • Stochastic components and Global Change Vulnerability
  • Network stability (Trophic and/or mutualistic)*
  • Ecosystem Functioning*

\[\max_{\text{ObjectiveFunction}} \sum_{i, j} \text{DecisionVariable}_{l, i} \cdot \text{DecisionVariable}_{l, j} \cdot \text{Bonus}\]

• More area can keep more species
• Example for animals in Danish forest

\(\begin{align*} \text{Maximize} & = \text{Biodiversity} + \text{Resilience} \cdot \text{bonus}\end{align*}\)

• Trade-off

\(\begin{align*} \text{Maximize} & = \text{Biodiversity}_c + \text{Resilience}_c\cdot \text{bonus}\end{align*}\)

• How we deaæ with expert knowledge in sdm?

• Here is the link for the following exercises

• There are 5 Species

Which landuse would you pick for each cell

• Constraint you can only change 3 landuse cells

• Constraint 1: you can only change 3 landuse cells
• Constraint 2: No species can go extinct

Let \(x_i = 1\) if we protect area \(i\), otherwise \(0\).

\[ \max \sum_i x_i \left( w_1 \cdot \text{Richness}_i + w_2 \cdot \text{Carbon}_i + w_3 \cdot \text{RepresentationBonus}_i \right) \]

subject to

\[ \sum_i x_i = 2 \]

where:

• \(\text{Richness}_i\) = biodiversity value
• \(\text{Carbon}_i\) = carbon storage
• \(\text{RepresentationBonus}_i\) = bonus for underrepresented habitats