Biology · Communities, Species Interactions & Food Webs
Community composition, species richness and diversity
Imagine three community records with the same four species labels. In the first, each species has five individuals. In the second, one has seventeen and each of the others has one. In the third, each has ten. Saying that all three contain four species is correct, but it leaves much of their composition unexplained.
Start with Population Ecology & Life-History Patterns, especially population change and per-capita rates. Organisms, Environments & Ecological Niches provides useful background on environmental conditions, dispersal and incomplete detection. Keep the distinction between a supplied model and evidence from a real community in view throughout.
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Describe a bounded community using species identities, counts and explicitly defined diversity measures, while separating complete assigned records from incomplete observations.
Define what belongs to the record
A community includes populations of different species within a chosen place and time. Its boundary is part of the question: a patch, a lake or organisms associated with another organism can each support a community study. A record may include only a defined group, such as plants, rather than every organism present. The inclusion rule must accompany the result.
Composition describes which species are included and how much of each is recorded. Individual counts, biomass and occupied area can give different abundance summaries. Here we use counts of distinct individuals and keep the inclusion rule fixed. A count of twenty cannot be compared directly with twenty units of biomass as though both were the same quantity.
Same richness, different abundance distributions
Read the diagram in words
Counts are 5, 5, 5, 5; 17, 1, 1, 1; and 10, 10, 10, 10. Totals are 20, 20 and 40; all have richness four. Concentrations are 0.25, 0.73 and 0.25; reciprocal concentrations are 4, about 1.37 and 4.
| Species | Individual count | Fraction of included individuals |
|---|---|---|
| Species A | 5 | 5/20 = 0.25 |
| Species B | 5 | 5/20 = 0.25 |
| Species C | 5 | 5/20 = 0.25 |
| Species D | 5 | 5/20 = 0.25 |
| Included total | 20 |
|---|---|
| Represented species | 4 |
| Same-species probability | 0.25 |
| Effective equally common species | 4 |
| Species | Individual count | Fraction of included individuals |
|---|---|---|
| Species A | 17 | 17/20 = 0.85 |
| Species B | 1 | 1/20 = 0.05 |
| Species C | 1 | 1/20 = 0.05 |
| Species D | 1 | 1/20 = 0.05 |
| Included total | 20 |
|---|---|
| Represented species | 4 |
| Same-species probability | 0.73 |
| Effective equally common species | 1.36986301369863 |
| Species | Individual count | Fraction of included individuals |
|---|---|---|
| Species A | 10 | 10/40 = 0.25 |
| Species B | 10 | 10/40 = 0.25 |
| Species C | 10 | 10/40 = 0.25 |
| Species D | 10 | 10/40 = 0.25 |
| Included total | 40 |
|---|---|
| Represented species | 4 |
| Same-species probability | 0.25 |
| Effective equally common species | 4 |
| Two independent draws with replacement | 2 |
|---|
p_i = n_i/N; C = sum(p_i^2); D2 = 1/C
Individuals
Complete constructed counts under the same inclusion rule. Species labels identify hypothetical species. No observation uncertainty, real community data or sampling estimator is supplied.
Richness and evenness answer different questions
Species richness is the number of species represented. All three complete teaching records have richness four. Evenness concerns how abundance is distributed among those species. The first and third records distribute their counts equally; the second is dominated numerically by one species. Greater total abundance does not necessarily mean greater richness or greater evenness.
A relative abundance divides a species count by the total included count. In the first record, each fraction is 5/20 = 0.25. In the third it is 10/40 = 0.25. Doubling every count preserves the fractions. This makes it possible to compare composition without confusing a larger community record with a more evenly distributed one. It does not remove differences in observation coverage.
A diversity measure needs its formula
For the supplied proportions, define concentration as the sum of squared species fractions. It is the probability that two independent draws with replacement have the same species label. Its reciprocal is the inverse Simpson diversity, also called the Hill number of order two. It expresses the effective number of equally common species for that concentration. This measure gives common species substantial weight.
An equally distributed four-species record has concentration 4 × 0.25² = 0.25, so its effective number is four. A dominant species increases the same-species probability and lowers the reciprocal. This definition uses supplied proportions; it is not a claim about unbiased estimation from a small sample. Other diversity measures give rare species different weight. A comparison should name the measure rather than assume every index has the same meaning.
Observation does not expose the whole community
In a second example, an assigned underlying community has counts 40, 10, 5 and 5. Two incomplete records of ten individuals report 8, 2, 0, 0 and 6, 2, 1, 1. The first sees two species; the second sees four. Their different recorded richness does not establish that they came from communities with different underlying richness.
The zeros are missing observations in this example, not proof that the species are absent from the underlying community. In real comparisons, detection, effort, identification and the sampled place or season can matter. Matching sample size alone does not establish equal completeness. The teaching records provide no random sampling rule, so we do not calculate a confidence interval or extrapolate an unseen species total from them.
Two incomplete records from one assigned community
Read the diagram in words
The assigned community has 40, 10, 5 and 5 individuals, richness four. The ten-individual records have counts 8, 2, 0, 0 and 6, 2, 1, 1, with observed richness two and four. Their inverse concentrations are about 1.47 and 2.38; the underlying record's is about 2.06.
| Species | Assigned underlying count | First incomplete count | Second incomplete count |
|---|---|---|---|
| Species A | 40 | 8 | 6 |
| Species B | 10 | 2 | 2 |
| Species C | 5 | 0 | 1 |
| Species D | 5 | 0 | 1 |
| Two incomplete records from one assigned community | Record total | Species | Concentration within this record | Effective species within this record |
|---|---|---|---|---|
| Assigned underlying community | 60 | 4 | 0.4861111111111111 | 2.057142857142857 |
| Incomplete record one | 10 | 2 | 0.68 | 1.4705882352941178 |
| Incomplete record two | 10 | 4 | 0.42 | 2.380952380952381 |
Not recorded in this incomplete observation
Recorded individuals
Original underlying counts and two feasible incomplete count records. No probability sampling design, coverage estimate, detection model or inference is assigned.
A rising share can accompany a falling count
A third count ledger starts with species A at 30 of 100 included individuals and ends with A at 20 of 50. Its count falls by ten, but its share rises from 30% to 40%. Other included species decline enough that the total denominator shrinks faster than A's count.
Both statements are useful: A becomes a larger part of the recorded community while becoming less numerous. Neither identifies the cause. Counts from the same defined boundaries and dates can describe a change; proving that a particular interaction caused it requires evidence beyond the before-and-after ledger.
A larger share with fewer individuals
Read the diagram in words
Earlier counts are 30, 50 and 20, totaling 100; later counts are 20, 20 and 10, totaling 50. Species A falls by ten but rises from 30% to 40% of included individuals. B falls from 50% to 40%; C remains at 20% while its count halves.
| Species | Earlier count | Later count | Earlier fraction | Later fraction | Count change | Share change, percentage points |
|---|---|---|---|---|---|---|
| Species A | 30 | 20 | 0.3 | 0.4 | -10 | 10 |
| Species B | 50 | 20 | 0.5 | 0.4 | -30 | -10 |
| Species C | 20 | 10 | 0.2 | 0.2 | -10 | 0 |
| Earlier record / Later record | Included total |
|---|---|
| Earlier record | 100 |
| Later record | 50 |
Individuals
Two original complete counts for the same defined boundaries; no causal comparison or density/biomass conversion.
Worked example
Compare equally rich records without losing evenness
For counts 17, 1, 1, 1, the fractions are 0.85, 0.05, 0.05 and 0.05. Their squared sum is 0.7225 + 3 × 0.0025 = 0.73. The effective number is 1/0.73 = 100/73, approximately 1.37.
The record still has four represented species. The value 1.37 describes the concentration of its abundance distribution; it is not a claim that only 1.37 biological species exist. The equal record's value of four makes the difference in evenness visible.
Doubling every count leaves all the fractions and this diversity measure unchanged. That mathematical property applies to the complete assigned records. A larger real sample can reveal species missed by a smaller one, so increasing observed counts need not preserve observed richness or estimated diversity.
Check your understanding
Why do counts 5, 5, 5, 5 and 10, 10, 10, 10 have the same inverse Simpson diversity?
Show reasoning
Each record has four fractions of 0.25. Their concentration is 0.25 and its reciprocal is four. Total count differs, but the supplied relative abundance distribution does not.
The first incomplete record contains no individuals of species C or D. What can be concluded?
Show reasoning
They were not recorded in that observation. The assigned underlying record includes both, and no detection model was supplied. An observed zero alone does not establish biological absence.
Species A falls from 30 to 20 individuals while its share rises from 30% to 40%. Is either calculation inconsistent?
Show reasoning
No. Its absolute count decreases while the included total falls from 100 to 50. The smaller denominator raises A's share. This does not show that A benefited in absolute abundance or identify why any species changed.
What to carry forward
A community comparison needs a boundary, an abundance measure, a diversity definition and an account of what was observed.
References
Resources supporting this lesson’s explanations and examples.
- Biology 2e (2018; sections 45.6 and 46.3)Mary Ann Clark, Matthew Douglas and Jung ChoiTextbook sections
- Unifying Species Diversity, Phylogenetic Diversity, Functional Diversity, and Related Similarity and Differentiation Measures Through Hill Numbers (Annual Review of Ecology, Evolution, and Systematics 45:297–324 (2014), doi 10.1146/annurev-ecolsys-120213-091540)Anne Chao, Chun-Huo Chiu and Lou JostScientific synthesis
- Rarefaction and extrapolation with Hill numbers: a framework for sampling and estimation in species diversity studies (Ecological Monographs 84(1):45–67 (2014), doi 10.1890/13-0133.1)Anne Chao, Nicholas J. Gotelli, T. C. Hsieh, Elizabeth L. Sander, K. H. Ma, Robert K. Colwell and Aaron M. EllisonOriginal research article