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Measuring biodiversity: richness, evenness and the index that catches both

Counting species is easy and tells you less than you think. Two fields with four plant species each can be completely different places, and the arithmetic that notices the difference takes about a minute — provided you know which of the two Simpson formulae you are using, because they run in opposite directions.

Before this Random sampling with quadrats and transects · Alleles, heterozygosity and gene pools · Mean and standard deviation

Before you start

The habitat with the most individuals in it is the most diverse. It is an easy thing to believe when you are standing in a field of tall grass with insects everywhere, and it is the exact mistake every diversity index is built to prevent. A hectare of ryegrass ley can hold extraordinary numbers of organisms belonging to very few species. What makes a place diverse is not how much life there is but how it is distributed: how many different species, and how evenly the individuals are shared between them. A field where 88 plants in every 100 are one grass is not diverse, however dense the sward, and the number you calculate should say so.

What you should be able to do

Distinguish species richness from species diversity, and say what evenness adds.
Calculate an index of diversity using the form your board specifies, and state which form you have used.
Explain why one Simpson form rises with diversity and the other falls, and interpret a value correctly either way.
Describe how genetic diversity within a species is measured, and why observable characteristics are a poor measure of it.
Explain how agriculture and monoculture reduce diversity at the habitat, species and genetic levels, and describe measures that offset this.

Three levels, and only one of them is a species count

Biodiversity is used at three scales and a question will usually tell you which one it wants. Habitat diversity is the number of different habitats in an area: a farm with a wood, a pond, hedges and a stream has more than a farm with one enormous field. Species diversity is the number of species in a community and the abundance of each. Genetic diversity is the variety of alleles within a single species, and it is the level students most often forget exists.

The three are not independent. Remove hedges and you lose habitat diversity, which takes species diversity with it, and a species reduced to a few isolated populations loses genetic diversity as well.

Species richness: The number of different species in a community.
Species evenness: How equally the individuals are shared out between those species.
Species diversity: Richness and evenness together, usually expressed as an index.
Genetic diversity: The number of different alleles present in the gene pool of a population or species.

Richness on its own is a count. It treats a species represented by one individual exactly like a species represented by a thousand, so it cannot tell a functioning community from one that is a monoculture with three survivors clinging on at the edges. Any index of diversity is an attempt to make that distinction with a single number.

Same richness, four species each. The dots make the difference obvious before any arithmetic happens, and the table underneath shows three different measures agreeing about which community is which — while moving in different directions.

Simpson's index, in the two forms boards actually set

This is the part of the topic that costs marks, and it is worth being slow about. Simpson's original quantity is the probability that two individuals picked at random from a community belong to the same species. Call it D:

D = Σ (n ÷ N)²n is the number of individuals of one species, N the total number of individuals of all species, and Σ means 'add this up across every species'.

Read that quantity carefully. It is a measure of dominance. If one species has almost everything, two random individuals are very likely to be the same species, so D is close to 1. If the community is evenly shared between many species, D is close to 0. D on its own falls as diversity rises. That is the trap, and it is why nobody quotes D by itself.

Boards fix it in two different ways, and you must know which one your specification uses.

Simpson's index of diversity: D = 1 − Σ (n ÷ N)²Used by OCR A and by CAIE 9700. Runs between 0 and 1, and rises with diversity. Notice that these boards attach the letter D to the subtracted version, not to the raw sum.

Index of diversity: d = N(N − 1) ÷ Σ n(n − 1)Used by AQA, and given in the AQA formulae booklet. Has no upper limit, has a minimum value of 1 when every individual belongs to the same species, and rises with diversity.

Both of the second pair rise with diversity, so a bigger answer means a more diverse community in either. They are not on the same scale and cannot be compared with each other. The AQA form uses N(N − 1) and n(n − 1) rather than squares because it treats the sample as a finite population being sampled without replacement — you cannot draw the same individual twice — and for a large sample its value is close to 1 ÷ D, the reciprocal of the raw dominance.

Whichever form you use, say so. Writing 'index of diversity = 3.95' with no formula is a number an examiner cannot mark; writing 'd = N(N − 1) ÷ Σn(n − 1) = 3.95' is.

Both forms, one set of counts

Two grassland plots are sampled and every plant in a hundred-plant sample is identified. The grazed pasture gives ryegrass 88, clover 6, daisy 4, plantain 2. The hay meadow gives ryegrass 32, clover 27, daisy 23, plantain 18. Both totals are 100. Calculate the species richness and both indices for each plot, and say what the numbers show. These counts are idealised; a real sample would not come to a round hundred.

Richness. Four species in each plot. The count cannot separate them at all, which is the point of the exercise.

Pasture, AQA form. Work out Σn(n − 1) first: 88 × 87 = 7656, 6 × 5 = 30, 4 × 3 = 12, 2 × 1 = 2. The sum is 7700. N(N − 1) = 100 × 99 = 9900. So d = 9900 ÷ 7700 = 1.29.

Meadow, AQA form. 32 × 31 = 992, 27 × 26 = 702, 23 × 22 = 506, 18 × 17 = 306. The sum is 2506. d = 9900 ÷ 2506 = 3.95.

Pasture, the 1 − D form. The proportions are 0.88, 0.06, 0.04 and 0.02. Squaring: 0.7744, 0.0036, 0.0016, 0.0004, which add to 0.78. So D = 1 − 0.78 = 0.22.

Meadow, the 1 − D form. 0.32² = 0.1024, 0.27² = 0.0729, 0.23² = 0.0529, 0.18² = 0.0324, adding to 0.2606. D = 1 − 0.2606 = 0.74.

What the numbers show. Both indices say the meadow is the more diverse plot, and they say it emphatically: 3.95 against 1.29, or 0.74 against 0.22. Richness said the two plots were identical. The difference is entirely evenness — in the pasture, grazing and fertiliser have let one grass take 88 per cent of the sward.

The trap, shown deliberately. The raw sums you calculated along the way were 0.78 for the pasture and 0.26 for the meadow. If you had learned 'Simpson's index' as that raw sum and stopped there, you would have read 0.78 as the higher score and called the grazed pasture the more diverse plot. It is the least diverse plot in the question.

One caution about interpretation, because indices invite a lazy sentence. A high index is not automatically a good thing and a low one is not automatically bad. A raised bog, a chalk stream and a saltmarsh are all species-poor by design, and the few species they hold live nowhere else; 'improving' their index by adding common generalists would be a loss. Diversity is a description of a community, not a score it is trying to win.

Where the numbers have to come from

An index is only as good as the sample under it, and a mark scheme will happily give you the arithmetic and take the marks back on the sampling. The technique itself belongs to the field-sampling practical; what matters here is how the choices you make out there show up in the number you calculate.

Quadrats must be placed at random coordinates, generated before you walk anywhere. Walking until somewhere looks interesting produces a sample biased towards whatever caught your eye, and an index calculated from it describes your attention rather than the field. A question asking how randomness was achieved wants 'numbered grid, random number generator, quadrat placed at the coordinates', not 'we threw them over our shoulders'.

How many quadrats is a real question with a real answer. Plot the running total of species against the number of quadrats placed and the curve rises steeply and then flattens; you stop when it has flattened, because further quadrats are adding effort and no information.

One quadrat found four species and looked decisive. Six had still missed three of the thirteen. The flattening is the argument for stopping, and it cannot be judged from a single sample.

Two other choices change what the index means. Percentage cover is the sensible measure for plants that grow as mats or clumps where individuals cannot be told apart, and frequency — the proportion of quadrats a species appears in — is used where you want presence rather than abundance; but Simpson's index needs counts of individuals, so a cover estimate cannot simply be dropped into it. And a transect answers a different question altogether: it is for a gradient, from the top of a shore to the bottom or out from the shade of a wood, and using one where there is no gradient produces a tidy graph of nothing.

Mobile animals are counted differently again, by mark, release and recapture, and the estimate that comes out of it carries assumptions of its own. That belongs with the practical rather than here, but a diversity index built from recapture estimates inherits every one of those assumptions.

Diversity inside a species

Two populations of the same species can hold very different amounts of variation, and the difference matters because variation is the raw material selection works on. A population in which every individual is nearly identical has nothing to offer when a new disease arrives or the climate shifts.

The definition is about alleles. A gene locus is a position on a chromosome; a locus is polymorphic if more than one allele of that gene is present in the population. The commonest measure at this level is the proportion of loci that are polymorphic.

proportion of polymorphic gene loci = number of polymorphic loci ÷ total number of loci examinedA proportion between 0 and 1, or a percentage. It depends on which loci were sampled, so two studies are only comparable if they looked at the same ones.

Nothing in this figure is about how many organisms there are. A population of ten thousand can look like the lower row if it passed through a bottleneck, and that is the point.

A proportion, and what it does not tell you

A survey examines 40 gene loci in a population of red squirrels on an island and finds 12 of them carrying more than one allele. On the mainland, the same 40 loci are examined and 26 are polymorphic. Calculate both proportions and comment.

Island: 12 ÷ 40 = 0.30. Mainland: 26 ÷ 40 = 0.65.

The island population has less than half the genetic diversity of the mainland one by this measure. The likely reason is history: an island population was founded by a small number of colonists carrying a fraction of the alleles in the source population, and has been isolated since, so nothing has come in to replace what was lost. Small populations also lose alleles by chance from one generation to the next.

What the number does not tell you is anything about the animals' health today. They may be perfectly viable. The concern is about the future: a smaller stock of alleles means fewer variants available if squirrelpox or a change in the woodland arrives.

Genetic diversity is measured directly, on molecules. Comparing the base sequence of DNA is the most complete method and is now cheap enough to be routine. Comparing the base sequence of mRNA looks at the genes actually being transcribed in a tissue. Comparing the amino acid sequence of a protein detects the differences that changed the product, and misses the ones the degenerate code absorbed.

What genetic diversity should not be measured by is observable characteristics, and a question will often invite you to say why. Most measurable characteristics are polygenic, so a single phenotype is the summed effect of many loci and cannot be read back to them. Many are strongly affected by the environment, so two genetically different plants raised in the same soil may look alike and two identical ones in different soils may not. And a large amount of allelic variation has no visible effect at all.

Two words for the same historical problem come up constantly. A genetic bottleneck is a sharp reduction in population size that leaves the survivors carrying only a fraction of the original alleles; the northern elephant seal, hunted down to a few dozen animals in the 1890s, now numbers well over a hundred thousand and remains strikingly uniform genetically. The founder effect is the same loss produced by a small group establishing a new population. In both cases numbers can recover quickly and diversity does not, because only mutation restores it, and mutation is slow.

What farming does to all three levels

Agriculture is the largest single influence on biodiversity in Britain, and the mechanism is worth stating precisely rather than as a complaint. Farming selects for one species in a field and against everything competing with it, and it does that at scale.

Monoculture is a single crop grown over a large area, often as the same crop year after year. The habitat it creates is uniform in structure, uniform in age and harvested all at once, so species that need anything else — a nesting site, a food plant, a sheltered overwintering place — have nowhere to be. Fewer plant species means fewer herbivores, which means fewer predators and parasites, so the loss propagates up the food web.

Practice	What it removes	Level of diversity affected
Removing hedgerows to enlarge fields	Nesting sites, shelter, corridors between habitats, hundreds of plant and invertebrate species	Habitat and species
Monoculture and continuous cropping	Structural variety and the sequence of flowering and seeding through the year	Species
Herbicides	Arable weeds, and the insects that depend on them	Species
Pesticides	Target pests, and non-target insects including pollinators and natural enemies	Species
Inorganic fertiliser on grassland	The wildflowers of unimproved meadows, outcompeted by a few vigorous grasses	Species, through evenness
Draining wetland and ploughing old grassland	Whole habitats that took centuries to develop	Habitat
Selective breeding of crops and livestock	Alleles not present in the few high-yielding lines that are grown everywhere	Genetic

That last row is the one that gets left out of answers, and it is the one with the sharpest consequences. Modern varieties are bred from a narrow set of parents and then planted over enormous areas, so the genetic diversity of a crop across a whole country can be tiny. A pathogen that defeats the resistance of one variety defeats it everywhere at once. The alleles that solve the problem usually turn out to be in a wild relative or a traditional landrace nobody was growing.

Farming is also where most of the practical response happens, because most of the land is farmed. Hedgerows can be kept and replanted; field margins and beetle banks left uncropped give overwintering cover; sowing a crop in spring rather than autumn leaves winter stubble for seed-eating birds; grassland managed without heavy fertiliser keeps its wildflowers. In England these are paid for through agri-environment schemes such as Countryside Stewardship, which is the honest way to put it: they cost the farmer yield or land, and the payment is what makes them happen.

There is a genuine argument underneath, and it is not resolved by asserting that biodiversity matters. Land taken out of production has to be made up somewhere, and one side of the argument holds that farming intensively on a smaller area and leaving more land wild protects more species overall, while the other holds that a landscape farmed less intensively throughout supports species that need farmland itself. Both positions are held by serious ecologists, and the evidence goes different ways for different groups of species.

TRY IT — Reading an index the wrong way round

A student samples two woodland plots and calculates, for each, the quantity Σ(n ÷ N)². Plot A gives 0.61 and plot B gives 0.19. The student concludes that plot A is the more diverse, and adds that plot A must also contain more species.

Identify both errors and give the correct conclusion, including the value of Simpson's index of diversity for each plot.

Check your answer

The first error is direction. Σ(n ÷ N)² is the probability that two individuals taken at random are the same species, so it measures dominance and falls as diversity rises. A value of 0.61 means that in plot A there is a 61 per cent chance two random individuals are the same species, which is a community dominated by one or two species.

Converting: Simpson's index of diversity is 1 − 0.61 = 0.39 for plot A and 1 − 0.19 = 0.81 for plot B. Plot B is the more diverse.

The second error is about richness. Neither figure says anything directly about the number of species. Plot A could easily contain more species than plot B and still score worse, if most of them are represented by one or two individuals while a single species takes the rest. Richness and evenness are separate things, and an index combines them rather than reporting either.

The lesson for the exam: write the formula down before you write the number, and read off which way it runs.

In the exam

State the formula you are using before the arithmetic. Two different forms of Simpson's index are in circulation, they run in opposite directions, and only the written formula tells the examiner which answer you are giving.
AQA candidates: d = N(N − 1) ÷ Σn(n − 1), and it is in the booklet. OCR A and CAIE candidates: D = 1 − Σ(n ÷ N)². Both rise with diversity.
Keep full precision through the working and round at the end. Rounding each n(n − 1) term or each squared proportion first will lose you the final mark on a close comparison.
'More diverse' needs both parts. A good comparison names the richness and the evenness — 'the same four species, but far more evenly spread' — rather than quoting the index and stopping.
For genetic diversity, the measure examiners want is the proportion of polymorphic gene loci, and the reason observable characteristics will not do is that most are polygenic and affected by the environment.
Questions about agriculture want a mechanism, not a list. 'Hedgerow removal reduces diversity' scores once; 'hedgerow removal takes away nesting sites and food plants, so the insect and bird species that depend on them are lost from the farm' scores properly.

Check yourself

A conservation officer samples two ponds. Pond 1 contains four invertebrate species with 50, 30, 15 and 5 individuals. Pond 2 contains six species with 85, 5, 4, 3, 2 and 1 individuals. Using d = N(N − 1) ÷ Σn(n − 1), calculate the index for each, and explain why the pond with more species scores lower.

Answer

Pond 1. N = 50 + 30 + 15 + 5 = 100, so N(N − 1) = 100 × 99 = 9900. The terms are 50 × 49 = 2450, 30 × 29 = 870, 15 × 14 = 210 and 5 × 4 = 20, which add to 3550. d = 9900 ÷ 3550 = 2.79.

Pond 2. N = 85 + 5 + 4 + 3 + 2 + 1 = 100, so N(N − 1) = 9900 again. The terms are 85 × 84 = 7140, 5 × 4 = 20, 4 × 3 = 12, 3 × 2 = 6, 2 × 1 = 2 and 1 × 0 = 0, which add to 7180. d = 9900 ÷ 7180 = 1.38.

Pond 2 has six species to pond 1's four, and scores less than half as high. The reason is evenness. In pond 2, 85 of the 100 individuals belong to a single species, so two individuals picked at random are very likely to be the same species and the denominator is dominated by the 7140 term. The five other species are present but barely — one of them is a single animal, contributing 1 × 0 = 0 to the sum, which is the arithmetic noticing that a species represented once adds nothing to the chance of drawing two alike.

Pond 1 spreads its hundred individuals across four species with no single one taking more than half, so the sum is far smaller and the index far larger.

The ecological reading is that pond 2 is probably a stressed or recently disturbed pond in which one tolerant species has taken over and the rest are hanging on. Species richness alone would have called it the better pond.

Questions

Written to the command words the boards use. Try them on paper before opening a scheme: the marks go to points made, not to length.

Question 15 marks

A farmer is offered a payment to take a strip six metres wide out of production around every field and to replant the hedgerows removed in the 1970s. Evaluate this scheme as a way of raising biodiversity on the farm.

Mark scheme

B1 for: hedgerows restore habitat diversity, supplying nesting sites, shelter and food plants that a bare field boundary does not, and they link fragments of habitat so that species can move between them
B1 for: an uncropped margin is neither sprayed nor harvested, so arable weeds survive and the insects feeding on them return, and with them the birds and predators above — species diversity rises at more than one level in the food web
B1 against: the strips and hedges take land out of production, so the yield of the farm falls and the same food has to be grown somewhere else, possibly by farming another area more intensively
B1 against: the scheme does nothing about the genetic diversity of the crop itself, which is bred from a narrow set of parents and planted over enormous areas, and margins cannot recreate habitats such as unimproved grassland that took centuries to develop
B1 judgement: the scheme is worth doing where hedgerow removal is what reduced diversity, because it addresses that mechanism directly, but it should be judged by measuring richness and evenness on the farm rather than assumed to work — and the payment is needed precisely because the farmer bears the cost in yield and land

Question 24 marks

A student samples the ground beetles of a woodland floor and records four species, with 40, 25, 20 and 15 individuals. Using D = 1 − Σ(n ÷ N)², calculate Simpson's index of diversity, and state whether a higher value of this form means a more or a less diverse community.

Mark scheme

M1 N = 40 + 25 + 20 + 15 = 100, and each n ÷ N is that species' proportion of the total: 0.40, 0.25, 0.20 and 0.15
M1 the squared proportions are 0.1600, 0.0625, 0.0400 and 0.0225, which sum to 0.285
A1 D = 1 − 0.285 = 0.715, or 0.72 to two decimal places
B1 a higher value of this form means a more diverse community, because the sum that is subtracted is the probability that two individuals taken at random are the same species and so falls as diversity rises

Question 34 marks

A grassland plot is sampled and five plant species are recorded, with 60, 20, 10, 6 and 4 individuals. Using d = N(N − 1) ÷ Σn(n − 1), calculate the index of diversity for the plot. These counts are idealised.

Mark scheme

M1 N = 60 + 20 + 10 + 6 + 4 = 100, so N(N − 1) = 100 × 99 = 9900
M1 the terms n(n − 1) are 60 × 59 = 3540, 20 × 19 = 380, 10 × 9 = 90, 6 × 5 = 30 and 4 × 3 = 12
A1 Σn(n − 1) = 4052
A1 d = 9900 ÷ 4052 = 2.44

Question 44 marks

Explain why two communities containing exactly the same number of species can have very different values of an index of diversity.

Mark scheme

B1 species richness is only a count, and it treats a species represented by one individual exactly like a species represented by a thousand
B1 an index also depends on evenness, which is how equally the individuals are shared out between the species present
B1 where one species holds most of the individuals, two organisms taken at random are very likely to belong to the same species, so the dominance term is large and the index of diversity is low
B1 where the individuals are spread evenly that probability is much lower and the index is high, so two communities of equal richness are separated by evenness alone

Question 53 marks

Describe how the genetic diversity of a population can be measured, giving more than one method.

Mark scheme

B1 measure the proportion of gene loci that are polymorphic: the number of loci at which more than one allele is present, divided by the total number of loci examined
B1 compare the base sequence of DNA between individuals, which is the most complete method, or the base sequence of mRNA, which shows only the genes a tissue is actually transcribing
B1 compare the amino acid sequence of a protein between individuals, which detects differences that changed the product but misses those the degenerate code absorbed

Question 63 marks

A student places six quadrats in a meadow and calculates an index of diversity from her counts. Suggest two reasons her index may not describe the meadow, and suggest what she should do about each.

Mark scheme

B1 if she chose where to put the quadrats, the sample is biased towards whatever caught her eye, so she should number a grid and place the quadrats at coordinates produced by a random number generator
B1 six quadrats may not be enough: plotting the running total of species against the number of quadrats placed shows whether the curve has flattened, and she should carry on sampling until it has
B1 if she recorded percentage cover rather than counts of individuals, those figures cannot be put into Simpson's index at all, because the index requires numbers of individuals

Worth remembering

Richness counts species; evenness describes how the individuals are shared; diversity needs both.
D = Σ(n ÷ N)² measures dominance and falls as diversity rises. Never quote it as a diversity score.
OCR A and CAIE: D = 1 − Σ(n ÷ N)², between 0 and 1. AQA: d = N(N − 1) ÷ Σn(n − 1), minimum 1, no maximum. Both rise with diversity.
Genetic diversity is measured as the proportion of polymorphic gene loci, using DNA, mRNA or amino acid sequences rather than what the organism looks like.
Monoculture and hedgerow removal cut habitat and species diversity; selective breeding cuts genetic diversity within the crop.

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