Niche Breadth and Overlap Calculator

Calculate Levins niche breadth, Pianka niche overlap, and resource partitioning between species.

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Levins' B and Its Standardised Form

Levins' measure is the reciprocal of Simpson's concentration index applied to resource use. It counts the effective number of resources a species uses, weighted by how evenly it uses them.

B = 1 / Σpi²     Bstd = (B − 1)/(n − 1)
Resource useBBstdInterpretation
[0.25, 0.25, 0.25, 0.25]4.01.0Perfect generalist
[0.4, 0.3, 0.2, 0.1]3.330.78Moderate generalist
[0.7, 0.2, 0.05, 0.05]1.870.29Fairly specialised
[1.0, 0, 0, 0]1.00Complete specialist

Standardising by the number of categories is essential, because raw B is bounded by n. A species using all four of four resources equally scores B = 4; the same behaviour across ten resources scores 10. Raw B values from studies with different resource classifications cannot be compared.

Pianka Overlap and What It Cannot Show

Ojk = Σ(pijpik) / √(Σpij² × Σpik²)

Pianka's index runs from 0 to 1 and is symmetric. That symmetry is a limitation: a specialist entirely contained within a generalist's diet experiences far more competitive pressure than the generalist does, yet the index reports one number for both.

High overlap does not demonstrate competition. Two species can share resources completely where those resources are superabundant. Competition requires that the resource be limiting, which overlap measures cannot establish.

The Ghost of Competition Past

The deeper interpretive problem is that observed overlap reflects current coexistence, which may itself be the product of past competition. Species that competed historically may have diverged in resource use, so the species now showing least overlap may be those that competed most intensely.

This is why niche studies pair overlap measures with removal experiments or natural comparisons between sites where a competitor is present and absent — character displacement is far stronger evidence than overlap alone.

Worked Examples

Example 1: Generalist: p=[0.25,0.25,0.25,0.25]
B=1/Σ(0.0625×4)=1/0.25=4
Result: B_std=1.0 — perfect generalist
Equal use of all resources
Example 2: Species overlap: p=[0.4,0.3,0.2,0.1], q=[0.1,0.2,0.4,0.3]
Pianka overlap=Σ(pi×qi)/√(Σpi²×Σqi²)
Result: Overlap0.70 — high overlap
Partial resource partitioning
Example 3: Why standardisation matters
Equal use of 4 resources versus equal use of 10
Result: B = 4 versus B = 10, both Bstd = 1.0
Both are perfect generalists within their resource sets. Only the standardised form makes them comparable.
Example 4: Asymmetric competitive impact
Specialist using only resources the generalist also uses
Result: Same overlap value, unequal effect
The specialist has nowhere else to go; the generalist has alternatives. Pianka's symmetric index cannot capture this.

Common Mistakes

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Comparing raw B across studies

B is bounded by the number of resource categories. Different classification schemes make raw values incomparable; use the standardised form.

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Inferring competition from high overlap

Overlap only matters when the resource is limiting. Species can share superabundant resources entirely without competing.

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Treating Pianka overlap as symmetric in effect

The index is mathematically symmetric but competitive impact is not. A specialist nested within a generalist's diet suffers far more.

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Ignoring the ghost of competition past

Species that competed historically may have diverged. Low current overlap can be the product of past competition rather than evidence against it.

Frequently Asked Questions

Competitive exclusion?
Complete overlap (Pianka=1) in same environment → competitive exclusion (Gause's law). Coexistence requires niche differentiation. Hubbell's neutral theory: equivalent competitors can coexist via drift. Real communities: both niche and neutral processes.
Dietary breadth in conservation?
Specialists (narrow niche, low B): more vulnerable to habitat change. Generalists (wide niche, high B): more resilient. Endangered species often specialists (giant panda: bamboo only). Conservation: protect key resources for specialists.
What does Levins' B measure?
The effective number of resources used, weighted by evenness. B = 1 indicates a complete specialist and B = n a perfect generalist across n resources.
Why standardise niche breadth?
Because raw B is bounded by the number of resource categories, so studies using different classifications cannot be compared directly.
Does high overlap prove competition?
No. Competition requires the shared resource to be limiting. Species can overlap completely on superabundant resources without competing at all.
What is the ghost of competition past?
The possibility that low observed overlap results from historical competition driving divergence, meaning current data understates past competitive interaction.