Diversity, Disturbance and Succession

Two plots each hold the same four species and 100 individuals. One of them is more diverse, and which one depends on what you decide to count. A community is the set of species living and interacting in one place. Describing it with a single number sounds simple, but every index makes a choice about how much rare species matter. And communities change: a storm, a fire or a plough knocks them back, and they rebuild. This lesson measures diversity, then asks how communities rebuild and whether disturbance raises or lowers diversity.

Counting a community: richness, evenness and effective species

Start with a species-by-count table: rows are species, and each entry is how many individuals of that species were counted. Three ideas come out of it.

Richness, S, is the number of species present. Relative abundance, p_i, is the proportion of individuals that belong to species i. Evenness describes how equally the individuals are spread among species.

Two indices combine richness and evenness. Shannon entropy uses the natural logarithm here, so its unit is the nat. Simpson concentration, lambda, is the probability that two individuals drawn at random (with replacement) belong to the same species.

H = -sum of (p_i x ln p_i) lambda = sum of p_i^2

Because “Simpson index” is used for lambda, for 1 - lambda (the Gini-Simpson index, the probability that two draws are different species) and for 1/lambda, always name the convention. Lambda runs the opposite way from the other two: it rises as one species dominates.

Think of a bag of marbles. If you keep pulling pairs and they usually match in colour, the bag is dominated by a few colours. Lambda is that matching rate.

Indices in nats or probabilities are hard to compare, so convert them to effective numbers of species: the number of equally common species that would give the same value. These are Hill numbers. Order zero is S, order one is exp H, and order two is 1/lambda.

effective species: order 0 = S order 1 = exp H order 2 = 1/lambda evenness E = (1/lambda) / S

Worked problem. Two samples are invented for this exercise and counted completely, 100 individuals each, across four species: sample A has 25, 25, 25 and 25; sample B has 40, 40, 10 and 10.

1. Proportions. In A, every p_i = 0.25. In B, p = 0.4, 0.4, 0.1 and 0.1. Both have S = 4.
2. Shannon entropy. H_A = -4 x (0.25 x ln 0.25) = ln 4 = 1.386 nats. For B, 0.4 x ln 0.4 = -0.3665 and 0.1 x ln 0.1 = -0.2303, so H_B = 2(0.3665) + 2(0.2303) = 0.733 + 0.461 = 1.194 nats.
3. Simpson. lambda_A = 4 x 0.25^2 = 0.25. lambda_B = 2(0.16) + 2(0.01) = 0.34. The complements are 0.75 and 0.66.
4. Effective numbers and evenness. exp H gives 4.00 species for A and 3.30 for B. 1/lambda gives 4.00 for A and 2.94 for B. Evenness E is 4.00/4 = 1.00 for A and 2.94/4 = 0.735 for B.
5. Read it. Richness is tied. By every abundance-weighted measure A is more diverse. B has the larger lambda, which is why you must say which Simpson you mean. Now swap the labels of B’s species: every number is unchanged. No index tells you which species are present.

Sample A: 25, 25, 25, 25 Sample B: 40, 40, 10, 10 Shuffle labels

Richness S

4

Shannon H (nats)

1.386

Simpson λ

0.25

Gini-Simpson 1 − λ

0.75

exp H (species)

4.00

1/λ (species)

4.00

Evenness E = (1/λ)/S

1.000

Individuals counted

100

In this sketch: every individual is counted (complete counts, no sampling error), four labelled species, H uses the natural logarithm, and "Simpson" here means λ = Σ p² with 1 − λ and 1/λ named separately.

Rule to keep: richness ignores abundance, higher orders discount rare species, and no index tells you which species are present, so shuffling the labels changes nothing.

Notice the pattern in B: order one gave 3.30 species and order two gave 2.94. Higher orders give more weight to common species, so B’s two rare species count for less as the order rises. Each measure misses something. Richness ignores abundance. Higher orders discount rare species. None sees identity, so two plots with identical indices can share no species at all.

One more trap: observed richness rises with sampling effort, because more individuals means more chances to find a rare species. Compare samples only after rarefaction, which recalculates each one at a common number of individuals.

Succession: three ways one community replaces another

Succession is the change in species composition at a site over time after a disturbance. Primary succession starts on surfaces with no previous community: new lava, rock bared by a retreating glacier, a new seawall. Secondary succession follows a disturbance that leaves soil, seeds or roots behind, as on an abandoned pasture or a burned forest.

Microbes take part too. In the forefield of the Puca Glacier in southeastern Peru, Knelman and colleagues (2014) randomly assigned 16 plots of soil, exposed by deglaciation about three years earlier, to control, nitrogen, phosphorus or both. After one year, bacterial communities given both nutrients most resembled those of soils exposed about 85 years. They identified bacteria by gene sequencing (see sequencing and genomes). That is a shift in bacterial composition in one forefield, not recovery of a whole ecosystem.

Why does one set of species replace another? In 1977 Joseph Connell and Ralph Slatyer set out three models as alternatives.

• Facilitation: early species change the site (adding soil, shade or nitrogen), and later species can establish only after that change.
• Tolerance: early species neither help nor much hinder later ones; later species persist because they can grow at lower resource levels.
• Inhibition: whoever arrives first holds the space and keeps later colonists out until it is damaged or dies.

The three cannot be told apart by watching the sequence, because all of them produce early species followed by later ones. They differ when you remove the early occupants. Under facilitation, removal delays later species; under inhibition, it speeds them; under tolerance, it changes little. This is the same logic as removal experiments in competition and predation. Nothing in these models has a goal. Early species are not preparing anything; they alter conditions, and later species do better or worse as a result. Nor does succession necessarily run to one fixed endpoint: where it goes depends on which species arrive, in what order, and how often the site is disturbed again.

Disturbance: Sousa’s boulders and the debate over the hump

A disturbance is an event that kills or removes organisms and frees space or resources. The intermediate disturbance hypothesis (IDH) predicts that the diversity of competing species peaks at intermediate disturbance frequency or intensity. Too little, and the best competitors exclude the rest; too much, and only fast colonizers survive. Connell’s 1978 paper in Science on tropical forests and coral reefs is the one usually cited, but versions of the idea appeared earlier, including in work by J. Philip Grime (1973).

In a southern California intertidal boulder field, Wayne Sousa (1979) found the pattern the IDH predicts. Winter storm waves overturned small boulders often, and they carried sparse early assemblages of Ulva and barnacles. Large boulders were rarely overturned and were dominated by the red alga Gigartina canaliculata. Boulders of intermediate size carried the most diverse assemblages; large boulders usually had fewer species, except in spring after winter stripped their canopy. But size and disturbance were confounded, so Sousa compared stabilized boulders with unstable ones, turning a pattern into a test on that shore.

Hall and colleagues (2012) went further in the laboratory. In microcosms of the bacterium Pseudomonas fluorescens, they crossed five frequencies (0 to 16 disturbances in 16 days) with three intensities (10%, 99.9% or 99.999% mortality per event), measuring 1 - lambda among morphotypes of one strain. Diversity rose with frequency, peaked or stayed flat, depending on the combination. In a later bacterial study by Gibbons and colleagues (2016), a diversity peak appeared only transiently, while community states mixed.

Jeremy Fox (2013) argued that the IDH should be abandoned, partly because humped curves are found only rarely. Michael Huston (2014) replied that critics had ignored the linked predictions his model makes for disturbance and productivity together. The IDH is neither confirmed nor refuted: it is debated, and experiments give conditional answers.

Description, mechanism and scale

Keep three questions apart. Description reports a pattern: diversity is highest on intermediate boulders. Mechanism needs a manipulation or a tested alternative: stabilize boulders and see whether communities change. Scale says where the comparison sits: diversity within one boulder or plot, differences among plots, or the pooled species list of a region. A hump among plots can coexist with no hump within them, so state the level, the plot size and the sampling effort.

Many succession studies use a chronosequence, a set of sites of different ages read as one trajectory (a space-for-time substitution). Rozendaal and colleagues (2019) pooled 56 Neotropical secondary-forest sites this way. In the 45 sites with old-growth reference plots, the model’s mean predicted tree richness 20 years after abandonment was 80% of old-growth values, but composition was only 34% of the way to old-growth similarity. Both are model estimates from sites of different ages, not one forest followed for 20 years, and the two numbers measure different things. Richness can recover while the identity of the species lags far behind.

Design problem

On a boulder shore, waves overturn small boulders often, large ones rarely and intermediate ones in between, and intermediate boulders carry the most species. Design a test of whether disturbance frequency, rather than boulder size, causes the pattern.

One way to do it

Choose small boulders of matched size, rock type and tidal height, and randomly assign them to three groups: stabilized (bolted or anchored so waves cannot turn them), handling controls (drilled and handled the same way but left free), and untouched. The handling control tells you whether drilling itself changes the community.

Mark every boulder and record overturning directly, for example by checking a painted face after each storm, so you know the disturbance each one actually received. Census the upper surfaces of all boulders at fixed intervals through the year, using the same quadrat area and effort each time, and record species richness, percent cover and composition.

If stabilized small boulders gain later-successional species and come to resemble intermediate or large boulders, while handling controls resemble untouched ones, overturning rather than size explains the pattern. If stabilized boulders stay sparse, something tied to size, such as surface area or scour, matters. Either result holds for this shore and these years.