Biodiversity & population indices

Why we need an index: Saying a habitat is “biodiverse” is too vague for science.

Two communities can have the same number of species yet feel very different: one where every species is common, and one where a single species dominates and the rest are rare.

A diversity index combines two things into one number:

Richness — how MANY species there are.

Evenness — how EQUALLY the individuals are spread between those species.

We also often need to estimate how many individuals of one species there are when we cannot count them all. Both jobs are done with a simple formula and some counting.

Biodiversity

The variety of living organisms in an area — it depends on both the number of species (richness) and how evenly individuals are spread among them (evenness).

Species richness

Simply the NUMBER of different species present in a community.

Evenness

How equally the individuals are distributed across the species. High evenness = no single species dominates.

Simpson's reciprocal diversity index ()

A single number combining richness and evenness. A LARGER D means GREATER diversity. The smallest possible value is 1 (only one species present).

Lincoln index (capture–mark–recapture)

A method to ESTIMATE the size of a mobile animal population that is too large to count directly, by marking some individuals and seeing what fraction turn up in a second sample.

“Reciprocal” — bigger means more diverse: We use the reciprocal form, , on purpose.

With this version a higher number = more diverse — which is the intuitive direction.

The lowest value can take is 1 (a community with only one species). There are no units.

Simpson's reciprocal diversity index: $$D = \dfrac{N(N-1)}{\sum n(n-1)}$$

where $N$ = the total number of individuals (all species added together), and $n$ = the number of individuals of each species.

Method: for every species work out , add those up to get , then divide by that total.

Pond A was sampled with a net and the catch sorted into four species. Build the column first, then add it up:

What the number means — compare two ponds: Pond B has the same richness (4 species) and the same $N = 20$, but one species dominates:

Same species count, very different diversity: For Pond B: .

Pond A scored 3.80; Pond B scored only 1.40 — even though both have 4 species and 20 animals.

The difference is evenness: Pond A's individuals are spread fairly evenly, while Pond B is dominated by snails. Higher $D$ = greater diversity, which is usually linked to a more stable ecosystem.

The Lincoln index (capture–mark–recapture): $$N = \dfrac{n₁ \times n₂}{n₃}$$

$n_1$ = number caught, marked and released first; $n_2$ = number caught in the second sample; $n_3$ = number in that second sample that were already marked; $N$ = the estimated total population.

The idea: the fraction of the second catch that is marked equals the fraction of the whole population that was marked — so if few of the marked ones turn up again, the population must be large.

How this is tested: On Paper 1B (and in the IA) you may be given raw counts and asked to calculate Simpson's reciprocal or use the Lincoln index, then interpret the result.

The formulas are provided in the question — you are marked on the method (building the column, substituting correctly) and on a sensible interpretation, not on memorising the equation. Always show your working and keep units/decimal places as asked.

✓ Why this scores full marks: It shows the substitution for both years, gets both values, and ties the rise in to richness AND evenness before concluding.

A common slip is to compare only the species count (3 → 4) — but also captures evenness, which is why it jumps so much more than the species count alone does.