ekokrati / docs / EC(PC)

EC(PC) — Equivalent Connected Area

EC(PC) is the primary output metric of ekokrati.graph. It translates the dimensionless Probability of Connectivity index into a habitat area, making results directly interpretable to ecologists and planners.

1. Definition

$$ \text{EC(PC)} = A_L \cdot \sqrt{\text{PC}} $$

where $A_L$ is the total landscape area and PC is the Probability of Connectivity.

Equivalently, expanding the PC formula directly:

$$ \text{EC(PC)} = \sqrt{\sum_{i=1}^{n} \sum_{j=1}^{n} a_i \cdot a_j \cdot p^*_{ij}} $$

EC(PC) is expressed in the same area units as the input patch geometry — typically hectares or km².

2. Ecological interpretation

EC(PC) answers the question: how much well-connected habitat does this landscape effectively provide?

More precisely: EC(PC) is the area of a single, perfectly connected patch that would produce the same PC value as the actual fragmented landscape. A landscape where all patches are large and well-connected approaches a single intact habitat; a highly fragmented landscape of many small isolated patches has a much smaller effective area than its physical total would suggest.

Why this matters. Regulatory thresholds, conservation targets, and environmental assessments work in area units. Saying "this development reduces the equivalent connected habitat from 4 200 ha to 3 900 ha" is more actionable than "PC decreases from 0.087 to 0.081". EC(PC) enables direct communication with decision-makers who are comfortable with area but not with dimensionless indices.

3. EC(PC) and landscape area

EC(PC) is always at most $A_L$:

$$ \text{EC(PC)} \leq A_L $$

with equality only when the entire landscape is one connected patch ($\text{PC} = 1$). For any real fragmented landscape, $\text{EC(PC)} < A_L$.

The ratio $\text{EC(PC)} / A_L$ is a connectivity efficiency — the fraction of the landscape's theoretical connectivity potential that is realised. A value of 0.60 means the landscape provides 60% of the connectivity that a single intact habitat block of the same area would provide.

For comparison: a landscape consisting entirely of isolated patches (no edges) has $\text{EC(PC)} = \sqrt{\sum_i a_i^2}$, which is equal to the root-mean-square patch area. Large isolated patches dominate this expression; small isolated patches contribute little. Adding any connections between patches increases EC(PC) above this lower bound.

4. EC(PC) across dispersal distances

Running ekokrati.graph with multiple analysis distances produces an EC(PC) value for each distance. The EC(PC) distance profile shows how the landscape's effective connectivity depends on species dispersal ability:

  • High EC(PC) at short distances, declining steeply: the landscape has strong local connectivity (many small patches close together) but poor landscape-scale linkage. Species with limited dispersal ability are well-served; wide-ranging species are not.
  • Nearly flat profile: connectivity is similar regardless of dispersal distance — either the landscape is uniformly well-connected at all scales or uniformly fragmented.
  • Low EC(PC) at all distances: severe fragmentation; the landscape provides little functional connectivity for any dispersal scenario.

Monitoring EC(PC) over time at the same dispersal scenario reveals connectivity trends: a declining profile across monitoring periods signals accumulating fragmentation even if total habitat area is unchanged.

5. Using EC(PC) in conservation planning

Baseline assessment. EC(PC) at multiple dispersal distances provides a structured baseline against which future changes can be measured. A landscape with EC(PC) = 5 200 ha at $d = 1\,000$ m is that landscape's connectivity fingerprint under the chosen dispersal scenario.

Impact assessment. The ΔEC(PC)% metric (see Scenario analysis) quantifies the connectivity cost of removing habitat. Regulatory guidance in some jurisdictions (e.g. Swedish transport infrastructure planning) uses percentage change in connectivity metrics as part of environmental impact characterisation.

Restoration prioritisation. Adding candidate restoration patches to the network and computing ΔEC(PC)% ranks them by connectivity return on investment: which location gives the largest increase in effective connected area per hectare restored?

Reporting. When citing EC(PC) in publications or assessments, always include:

  • The dispersal distance(s) used
  • The dispersal probability parameter
  • The software and version (ekokrati.graph vX.Y.Z)
  • Whether areas are in hectares or km²

This ensures results are reproducible and comparable across studies.

Key references

  • Saura, S. & Pascual-Hortal, L. (2007). A new habitat availability index to integrate connectivity in landscape conservation planning. Landscape and Urban Planning, 83(2–3), 91–103.
  • Saura, S., Estreguil, C., Mouton, C. & Rodríguez-Freire, M. (2011). Network analysis to assess landscape connectivity trends: application to European forests (1990–2000). Ecological Indicators, 11(2), 407–416.