Biology · Biodiversity, Global Change & Conservation
Genetic, species and ecosystem diversity and their measurement
Two complete communities each contain twenty individuals belonging to four species. In one, every species contributes five; in the other, one contributes seventeen. Calling both “four-species communities” is correct, but it leaves out a large difference in relative abundance. Biodiversity has several levels, and a measure becomes informative when its question and denominator are clear.
Begin with the biological levels, species identity and ordinary fractions introduced in the earlier biology lessons. Population Ecology & Life-History Patterns helps with demographic accounts, expected counts and conditional probabilities. Ecosystems, Energy Flow & Biogeochemical Cycles supplies the distinction between a process, a stock and an ecosystem boundary, while Species, Speciation & Macroevolution helps with the meaning and limits of species identities. The copy-pool probability examples can be read as complete sets of alternatives before learning binomial notation; return to the genetics lessons for inheritance, drift and relatedness.
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Describe what a diversity measure counts, distinguish richness from composition and weighted abundance, and retain its biological and spatial limits.
Start with variation inside a species
Genetic diversity concerns inherited variation within a species: for example, different alleles at a locus and different combinations across genomes. An allele is one variant at a specified genetic locus. Counting species does not reveal this variation. Four individuals of the same species can share all the measured variants or contain several, depending on the loci and the organisms examined.
For a diploid autosomal locus, each individual contributes two copies. The constructed population P has four individuals with genotypes AA, Aa, Aa and aa. Its eight copies contain four A and four a. Population Q has AA, AA, AA and aa, so it retains the same two alleles but in frequencies six eighths and two eighths. Allele richness alone therefore does not describe their frequency balance.
Observed heterozygosity asks which individuals actually carry two different alleles: two of four in P, none in Q. A different-copy probability calculated from two independent draws from the copy pool is another quantity. It would match a random-pairing expectation under the appropriate conditions, but it need not equal the observed heterozygote fraction. Nor does variation at one neutral locus reveal the whole genome, adaptation or a preferred conservation action.
Copies and pairings describe different genetic variation
Read the diagram in words
Population P has genotypes AA, Aa, Aa and aa: four A copies and four a copies, with two heterozygotes out of four. Q has AA, AA, AA and aa: six A and two a copies, with no heterozygotes. Both have allele richness two. Independent replacement draws give different-copy probabilities 0.5 for P and 0.375 for Q; Q’s observed heterozygote fraction is zero.
| Diploid individual | Observed genotype | Allele copies at this locus |
|---|---|---|
| Individual 1 in P | AA | A · A |
| Individual 2 in P | Aa | A · a |
| Individual 3 in P | Aa | A · a |
| Individual 4 in P | aa | a · a |
| Assigned population P | = |
|---|---|
| Diploid individual | 4 |
| Allele copies at this locus | 8 |
| Copies of A | 4 |
| Copies of a | 4 |
| Share of the eight allele copies | A = 0.5; a = 0.5 |
| Distinct alleles present | 2 |
| Individuals with two different alleles | 2 |
| Heterozygotes divided by four individuals | 0.5 |
| Probability that two independent copy draws differ | 0.5 |
| Diploid individual | Observed genotype | Allele copies at this locus |
|---|---|---|
| Individual 1 in Q | AA | A · A |
| Individual 2 in Q | AA | A · A |
| Individual 3 in Q | AA | A · A |
| Individual 4 in Q | aa | a · a |
| Assigned population Q | = |
|---|---|
| Diploid individual | 4 |
| Allele copies at this locus | 8 |
| Copies of A | 6 |
| Copies of a | 2 |
| Share of the eight allele copies | A = 0.75; a = 0.25 |
| Distinct alleles present | 2 |
| Individuals with two different alleles | 0 |
| Heterozygotes divided by four individuals | 0 |
| Probability that two independent copy draws differ | 0.375 |
H = 1 − p(A)² − p(a)²
Observed individual pairings remain separate from random copy draws
One locus does not describe the whole genome or predict fitness
Original complete genotypes at one autosomal diploid locus, four individuals and eight allele copies per population. A/a are neutral identity symbols with no phenotype, dominance, relatedness or fitness assignment. Random-pair diversity concerns two independent replacement draws from the copy pool, not the observed pairing of alleles within individuals.
Species identity and relative abundance answer different questions
Species richness counts the distinct species recognised within a stated place, time and observation account. Composition says which species they are. Evenness concerns how evenly individuals are distributed among those species. A community can retain richness while a once-common species becomes scarce, or while one species replaces another. Keeping the identities and counts prevents these changes from disappearing behind a single total.
In the two twenty-member communities, richness is four in both. For one useful abundance weighting, let p(i) be the fraction belonging to species i. The sum of the squared fractions, C, is the probability that two independent draws with replacement have the same species. Replacement means the first drawn member is available again; a draw of two distinct individuals without replacement would be a different calculation.
The reciprocal, D = 1/C, asks how many equally common species would give that concentration. Four equally common species give C = 0.25 and D = 4. Strong dominance raises C and lowers D. This effective number is allowed to be noninteger. It is an interpretation under this weighting, rather than a claim that only that many species actually exist or that rare species have no conservation value.
Four species can have very different relative abundances
Read the diagram in words
Both communities have twenty individuals and richness four. Counts 5, 5, 5, 5 give concentration 4 × 0.25² = 0.25 and equivalent number four. Counts 17, 1, 1, 1 give concentration 0.85² + 3 × 0.05² = 292/400 = 0.73 and equivalent number 400/292, approximately 1.37.
| Shared species identity | Individuals of this species | Share of the twenty individuals |
|---|---|---|
| Assigned species S1 | 5 | 0.25 |
| Assigned species S2 | 5 | 0.25 |
| Assigned species S3 | 5 | 0.25 |
| Assigned species S4 | 5 | 0.25 |
| Even assigned community | = |
|---|---|
| Σ Individuals of this species | 20 |
| Number of species present | 4 |
| Probability of two replacement draws having the same species | 0.25 |
| Equivalent number of equally common species | 4 |
| Shared species identity | Individuals of this species | Share of the twenty individuals |
|---|---|---|
| Assigned species S1 | 17 | 0.85 |
| Assigned species S2 | 1 | 0.05 |
| Assigned species S3 | 1 | 0.05 |
| Assigned species S4 | 1 | 0.05 |
| Dominance-weighted assigned community | = |
|---|---|
| Σ Individuals of this species | 20 |
| Number of species present | 4 |
| Probability of two replacement draws having the same species | 0.73 |
| Equivalent number of equally common species | 1.36986301369863 |
C = Σ p(i)²; D = 1/C
Common species contribute more under this particular weighting
Different observation coverage would require an additional comparison argument
Original complete same-area community accounts at one time with twenty individuals each and fixed species identification. Concentration is the probability of the same species on two independent replacement draws. Its reciprocal is the equivalent number of equally common species under this weighting; it is not observed richness, a corrected sampling estimate or a measure of all biodiversity.
Keep local variation, regional variation and ecosystem context visible
Local richness refers to a selected site; regional richness refers to distinct species across a wider boundary. If both sites contain the same two species, the regional union has two, even though adding the two local counts gives four. If their species sets do not overlap, the union has four. Both regions can have the same mean local richness while differing in turnover between sites.
Ecosystem diversity adds the variety of ecological systems and their relationships with nonliving conditions. A forest, grassland and wetland comparison depends on how those ecosystem types are defined and mapped; their boundary areas and ecological condition also matter. Counting three labels alone does not show whether their processes or characteristic communities persist. No one species-abundance index measures all these levels.
Measured richness also depends on observation coverage, identification and detection. A longer or differently placed record can reveal additional species without a biological increase. The complete constructed accounts here avoid that uncertainty so the measures can be compared. In actual evidence, keep sampling effort and coverage comparable or use a justified method to account for their differences; an undetected species is not automatically absent.
Shared local richness can hide regional turnover
Read the diagram in words
All four sites have local richness two. The first region repeats S1 and S2, giving regional richness two. The alternative region has S1/S2 at X and S3/S4 at Y, giving regional richness four. Adding local counts to four would double-count shared identities in the first region.
| Site inside the stated region | Species present in the complete account | Species present at this site |
|---|---|---|
| Site X in the repeated region | Assigned species S1 / Assigned species S2 | 2 |
| Site Y in the repeated region | Assigned species S1 / Assigned species S2 | 2 |
| Region with repeated species identities | = |
|---|---|
| Mean local richness across the two sites | 2 |
| Distinct species in the regional union | Assigned species S1 / Assigned species S2; 2 |
| Site inside the stated region | Species present in the complete account | Species present at this site |
|---|---|---|
| Site X in the differing region | Assigned species S1 / Assigned species S2 | 2 |
| Site Y in the differing region | Assigned species S3 / Assigned species S4 | 2 |
| Region with differing species identities | = |
|---|---|
| Mean local richness across the two sites | 2 |
| Distinct species in the regional union | Assigned species S1 / Assigned species S2 / Assigned species S3 / Assigned species S4; 4 |
A species shared by sites is counted once in the regional union
The same local richness does not establish the same regional composition
Original complete species-presence accounts at a single time. Sites have no abundance counts, temporal transitions, detection uncertainty or assigned habitat quality. Regions are alternatives, not before/after observations. Species S1–S4 retain the same definitions across all sites.
Worked example
Compare the three questions without swapping denominators
P’s A frequency is 4/8 = 0.5 and Q’s is 6/8 = 0.75. The different-copy probabilities are 1 − 0.5² − 0.5² = 0.5 and 1 − 0.75² − 0.25² = 0.375. Q’s observed heterozygote fraction remains 0/4 = 0, because its supplied individual pairings are all identical-allele pairs.
For the even species account, each fraction is 5/20 = 0.25; four squares sum to 0.25 and the reciprocal is 4. For the dominated account, 17/20 = 0.85 and each of the other three fractions is 0.05. Thus C = 0.85² + 3 × 0.05² = 0.73, and D = 400/292, approximately 1.37. Richness stays four.
At the regional scale, take the union of species identities rather than adding site richness. Repeated S1/S2 gives two regional species; S1/S2 at one site and S3/S4 at the other gives four. None of these calculations determines ecosystem condition, observed genetic fitness or future persistence.
Check your understanding
Why can population Q retain both A and a but have no observed heterozygotes?
Show reasoning
Its copies are paired as AA, AA, AA and aa. Both variants occur in the population, but none of its four individuals has one of each. The random-copy diversity 0.375 is a different probability account and does not replace the observed pairing data.
Does an effective species number of about 1.37 mean that the dominated community has fewer than four species?
Show reasoning
No. All four supplied species remain present. The value 1.37 expresses the concentration as an equivalent number of equally common species under this particular weighting. Richness, identities and individual counts still describe other important aspects of the same community.
Two sites each have richness two. What information is needed before stating the regional richness?
Show reasoning
The species identities and their overlap are needed. If both contain S1/S2, the regional union is two; if one contains S1/S2 and the other S3/S4, it is four. Adding local richness without comparing identities can double-count shared species.
What to carry forward
Name the biological level, identities, spatial boundary and observation account before interpreting a diversity number.
References
Resources supporting this lesson’s explanations and examples.
- Convention on Biological Diversity, Article 2: Use of Terms (1992 Convention; official Article 2 text)Convention on Biological DiversityOfficial biological definitions
- Entropy and diversity (Oikos 113(2):363–375, 2006; doi:10.1111/j.2006.0030-1299.14714.x)Lou JostResearch abstract
- An introduction to the mathematical structure of the Wright–Fisher model of population genetics (Theory in Biosciences 132:73–82, 2013; doi:10.1007/s12064-012-0170-3)Tat Dat Tran, Julian Hofrichter and Jürgen JostOriginal population-genetic theory