Ecological Sampling Virtual Lab

Ecologists want to know how many organisms of each kind live in a place, how those numbers change from one part of the habitat to another, and why. Counting every individual is almost never possible, so they sample: they measure small, carefully chosen parts of the habitat and use the results to estimate the whole. This laboratory lets you do that in a procedurally generated meadow where the true answer is known, so you can see how good your estimates are and what makes them go wrong.

The notes work in three layers. Material marked Foundation needs only counting, means and percentages. Core material matches the sampling and statistics content of A level and Cambridge AS/A Level Biology, IB Diploma Biology, AP Biology and AP Environmental Science, and WASSCE Biology fieldwork, and uses standard error, confidence intervals and simple diversity and correlation statistics. Extension material goes towards first-year university ecology and uses derivations, the Student t distribution and the properties of estimators.

The simulated field is 40 m wide and 24 m deep, an area of 960 m². It holds five plant species whose abundance depends on soil moisture, which rises steadily from the dry left edge to the wet right edge. You place quadrats and transects, record counts and percentage cover, and then analyse the data: a population estimate with its standard error, a Simpson index of diversity, and a Spearman rank correlation between soil moisture and abundance with a line of best fit. A short section covers mark, release, recapture for animals.

Learning outcomes

Foundation

• Explain why ecologists sample instead of counting everything, and name the equipment used to sample plants.
• Describe how to use a quadrat and a transect, and why quadrats should be placed at random.
• Calculate a mean count, a density (number per square metre) and a percentage cover.
• Estimate a population by multiplying mean density by the area, and state that the answer is an estimate.
• Name two ways that a sample can be unrepresentative.

Core

• Choose between random, systematic, stratified and convenience sampling, and explain the bias that each can cause.
• Calculate the standard deviation, standard error and 95% confidence interval of a mean, and carry them through to a population estimate.
• Calculate and interpret Simpson index of diversity, D.
• Rank data, calculate Spearman’s rank correlation coefficient and decide whether it is significant.
• Draw a line of best fit, read its gradient with an uncertainty, and say what it does and does not show.
• Use the Lincoln index for mark, release, recapture and state its assumptions.
• Plan a fieldwork investigation that includes a risk assessment and ethical safeguards.

Extension

• Derive the standard error of a mean, the sample size formula, Simpson index and the Lincoln index from first principles.
• Explain why a systematic sample with a random start is unbiased and often more precise than a random sample when there is a gradient.
• Relate percentage cover to density through a random (Poisson) pattern of plants.
• Describe the Chapman correction and the effect of trap-happy or trap-shy animals on a mark-recapture estimate.

Population, community and habitat

Foundation

A population is all the individuals of one species in an area. A community is all the populations living together. A habitat is the place where they live. Ecologists describe abundance in several ways. Count is the number of individuals. Density is the count divided by the area, for example 4 plants per square metre. Frequency is the proportion of sample units in which the species occurs. Percentage cover is the proportion of the ground covered when the plants are viewed from above. Counting works well for separate, easily recognised plants. Cover works better for grasses and mosses where individuals merge.

Why sample

A census counts every individual. It is exact, but in a 960 m² meadow with about 9,000 plants it would take days and would trample the habitat. A sample is a small fraction chosen to represent the whole. The price is uncertainty, and the skill is to measure that uncertainty and keep it small. A good sample is representative, which usually means that every part of the habitat had a known chance of being chosen, and large enough that chance alone does not dominate the result.

Sampling designs

Core

• Random sampling. Every position has the same chance of being chosen, for example by drawing two random numbers as coordinates. It removes the recorder’s preferences and makes statistical tests valid.
• Systematic sampling. Positions are evenly spaced, usually on a grid, with a random starting point. It covers the whole area, which helps when there is a gradient, but it can be biased if the spacing happens to match a regular pattern in the habitat.
• Stratified sampling. The habitat is divided into zones (strata) that differ, such as wet and dry ground, and each zone is sampled separately and in proportion to its size. It is useful when zones differ a lot.
• Convenience sampling. The recorder picks spots that look typical or are easy to reach. It is the commonest source of bias in student fieldwork, because people choose lush, accessible patches. In the simulator the convenient method chooses the lushest of six random spots for each quadrat.
• Transects. A line is laid across a gradient. A line transect records what touches the line at set intervals. A belt transect records a strip of fixed width, usually as a row of contiguous quadrats. An interrupted belt samples quadrats at intervals, which saves time on a long line. Transects reveal zonation, the orderly change of species along an environmental gradient.

Distribution patterns

Within a small area plants may be random (each position equally likely), regular (more even than random, often because of competition), or clumped (in patches, often because seeds fall near the parent). In the simulator the rush grows in clumps and the other four species are scattered at random within their preferred moisture zone. The variance-to-mean ratio of quadrat counts is close to 1 for random patterns, below 1 for regular patterns and above 1 for clumped patterns.

Error and bias

Core

Random error makes estimates scatter around the true value and shrinks as the sample grows. Bias (systematic error) pushes every estimate the same way, and collecting more data with the same flawed method does not remove it. Precision describes the scatter of repeated estimates, and accuracy describes how close they are to the truth. Random sampling aims for accuracy on average, and a large sample gives precision. The bias experiment in the Analyse step shows both effects.

Density, mean and population estimate

Foundation

For one quadrat of area a containing n plants, the density is n / a. For k quadrats with counts x₁ to x_k, the mean count is the sum of the counts divided by k. If all quadrats have the same area a, then

mean density = mean count / a    estimated population N̂ = mean density × A

where A is the area of the whole habitat. In the simulator A = 960 m². Always convert counts to a density before comparing quadrats of different sizes.

Standard deviation, standard error and confidence interval

Core

The sample standard deviation of the counts is

s = √[ Σ(x − x̄)² / (k − 1) ]

The mean of a sample varies from sample to sample, and its spread is the standard error, SE = s / √k. The population estimate has standard error SE(N̂) = SE of the mean density × A. A 95% confidence interval for the mean is x̄ ± t × SE, where t is the critical value of the Student t distribution with k − 1 degrees of freedom (2.201 for k = 12; it approaches 1.96 as k grows). The interval is a statement about the method: about 95% of intervals made this way, from random samples, contain the true value.

Why the standard error is s / √k Extension

If the counts are independent with variance σ², the variance of their sum is kσ². The mean is the sum divided by k, so its variance is kσ² / k² = σ² / k, and its standard deviation is σ / √k. Dividing by k − 1 rather than k in s² makes the estimate of σ² unbiased. This also shows the cost of precision: to halve the standard error you need four times as many quadrats. Strictly, when the sample is a large fraction f of the habitat the variance should be multiplied by (1 − f), the finite population correction. For 30 quadrats of 1 m² in 960 m², f = 0.031, so the correction factor on the standard error is √(1 − 0.031) = 0.984, and it is usually ignored.

How many quadrats

Suppose you want the half-width of the confidence interval to be E, a chosen fraction p of the mean. Setting t × s / √n = E gives

n = (t × s / E)²    with E = p × mean

The value of t depends on n, so start with 1.96, find n, update t, and repeat until n stops changing. The pilot sample supplies s and the mean.

Simpson index of diversity

Pick two individuals at random without putting the first back. For species i with n_i individuals out of N, the probability that both are species i is (n_i / N) × ((n_i − 1) / (N − 1)). Adding over species gives the chance that the two are the same, and the index of diversity is the chance that they differ:

D = 1 − Σ n(n − 1) / [N(N − 1)]

D runs from 0 (one species) towards 1 − 1/S for S equally common species. The reciprocal form, 1 / Σ[n(n − 1) / (N(N − 1))], is the effective number of equally common species. Some courses use the with-replacement form 1 − Σp² where p = n / N. The two agree closely when N is large. Follow the formula in your own course.

Spearman rank correlation

Core

Rank each variable from smallest (rank 1) upwards, giving tied values the mean of the ranks they would share. The Spearman coefficient ρ is the Pearson correlation of the two sets of ranks. With no ties it simplifies to

ρ = 1 − 6Σd² / [n(n² − 1)]

where d is the difference between the two ranks of each pair. The value runs from −1 (perfectly decreasing) through 0 (no monotonic trend) to +1 (perfectly increasing). With ties, use the Pearson-on-ranks definition, because the shortcut formula is then slightly off. To judge significance the simulator uses t = ρ √[(n − 2) / (1 − ρ²)] with n − 2 degrees of freedom. This is an approximation, adequate for about 10 pairs or more. Your course may give a table of critical values of ρ instead.

Line of best fit Core

The least-squares line y = a + bx minimises the sum of squared vertical distances from the points. With S_xx = Σ(x − x̄)² and S_xy = Σ(x − x̄)(y − ȳ), the gradient is b = S_xy / S_xx and the intercept is a = ȳ − bx̄. The residual standard deviation is s = √[Σ(residual)² / (n − 2)] and the standard error of the gradient is s / √S_xx. A 95% interval for the gradient is b ± t × SE with n − 2 degrees of freedom.

Percentage cover and density Extension

Suppose crowns of radius r are scattered at random with density D. A point on the ground is uncovered only if no plant centre lies within a distance r, a circle of area πr². The number of centres in that circle is Poisson with mean Dπr², so the chance of none is e^−Dπr² and

expected cover = 1 − e^−Dπr²  ≈  Dπr² when this is small

The simulator’s self-test checks its point-frame cover against this formula.

Lincoln index Core

Mark and release M animals. After they have mixed with the rest, catch C animals, of which R are marked. If catching is random, the marked fraction in the catch estimates the marked fraction in the whole population: R / C = M / N. Rearranging gives

N = M × C / R

When R is small this estimate is biased high. The Chapman estimator N = (M + 1)(C + 1) / (R + 1) − 1 reduces the bias and is defined even when R = 0. Its variance is estimated by (M + 1)(C + 1)(M − R)(C − R) / [(R + 1)²(R + 2)], and an approximate 95% interval is the estimate plus or minus 1.96 standard errors.

Every number below was checked by computation. Use the examples to check your own working in the Analyse step.

Core

The Experiment step draws four graphs from your data, and the Analyse step adds three more. Learn what each is for and how to read it.

Abundance along the gradient

Quadrats are sorted into bins of soil moisture and the mean density in each bin is plotted for each species. A species with a rising line prefers wet soil, a falling line prefers dry soil, and a hump shows a preferred middle value. The sketch below shows the underlying response curves used to build the simulated field. Your plotted points will scatter around them, and the scatter is larger where a bin holds few quadrats.

Running mean and uncertainty

This plots the mean after the first 2, 3, 4 and more quadrats, with a band of one standard error. Early values swing widely. As the number of quadrats grows the line settles and the band narrows, roughly as 1 / √n. It is a direct picture of why sample size matters, and it shows when adding more quadrats stops paying off.

Transect profile

A belt transect plots density, and a line transect plots percentage cover, against distance along the line. Run along the gradient, the profile shows zonation: one species fading out as the next rises. Run across the gradient, the profile is mostly flat.

Counts per quadrat

This histogram compares your counts with those expected from a random pattern having the same mean (the grey curve, a Poisson distribution). A tall column at zero and a long right-hand tail mean clumping.

Scatter plot with line of best fit

Put the environmental variable (moisture) on the horizontal axis because you chose or measured it, and the abundance on the vertical axis. Draw the line of best fit and, if you can, the 95% band around it, which is narrowest in the middle of the data. Check that the points scatter evenly above and below the line along its length. A curved cloud means the straight line is the wrong summary, even if ρ is large. The ranks plot in the simulator shows what Spearman’s method actually uses.

Good graph habits

• Label both axes with the quantity and unit.
• Use a scale that spreads the data over most of the grid.
• Plot points first and add the line of best fit afterwards. Do not join the dots unless the order matters, as it does along a transect.
• Show uncertainty, as error bars or a band, whenever you present an estimate.

Core

The simulator is tidy by design. Real fieldwork meets all of the following difficulties, and a good report names the ones that matter for its data.

• Counting rules. Plants that straddle a quadrat edge must be counted by a rule decided in advance, such as counting a plant if its stem base is inside, or counting those on two sides only. Clonal plants such as grasses have no clear individuals, so cover or shoot counts are used. In the simulator a plant is counted when its centre lies inside the quadrat.
• Edge effects. Quadrats near a boundary may sample a different habitat. Random positions that must lie fully inside a field give the margins a slightly lower chance of being chosen. The effect is small here but should be considered.
• Patchiness and scale. Counts depend on quadrat size. A quadrat that is too small is dominated by zeros and chance, and one that is too large is slow and tiring. A common rule is to use a quadrat that usually contains several individuals of the species of interest.
• Observer error and detectability. People miss small plants, mis-identify look-alikes and tire after long sessions. Animals hide or flee. Calibrate observers against each other, and for mobile animals use methods that account for detection.
• Season and weather. Plants flower, die back or are eaten at different times, so counts depend on the date. Soil moisture varies with the weather in the days before measurement, so record when you measured.
• Non-independence. Quadrats close together tend to resemble each other (spatial autocorrelation). Tests such as the t interval and the Spearman test assume independent samples. Counting several adjacent quadrats of one transect as independent overstates the evidence. Replicate in separate places.
• Measurement error in the environmental variable. The moisture probe in the simulator has an error of about 1.5 percentage points. Real probes depend on soil type, depth and contact.
• Statistical limits. Counts are not normally distributed, especially with many zeros, so a small-sample confidence interval from the t distribution is approximate. Spearman’s method detects only steady (monotonic) trends, so it can miss a hump-shaped response, as the fescue shows. A significant correlation does not prove that moisture causes the pattern: temperature, shade and nutrients may change along the same gradient.
• Mark-recapture assumptions. The population must be closed, marks must last and not harm the animal, every animal must be equally easy to catch, and marked animals must mix completely. Trap-happy animals (easier to catch again) make the Lincoln index too low. Trap-shy animals make it too high. Births, deaths and migration between the two catches break the closed-population assumption.

Start with a question and a prediction

Foundation

A good ecological investigation asks a question that sampling can answer and predicts the result before any data are collected. Examples: How many white clover plants are there in this field? Does the density of creeping buttercup change with soil moisture? Is the community more diverse on the dry side than the wet side? Write a hypothesis you can test, such as buttercup density increases as soil moisture increases, and the matching null hypothesis, there is no monotonic relationship between buttercup density and soil moisture.

Variables

Core

• Independent (environmental) variable: soil moisture, measured at every quadrat.
• Dependent variable: abundance, as a count, a density or a percentage cover.
• Controlled variables: quadrat size, counting rule, date and time window, observer, and the depth and method of the moisture measurement.
• Uncontrolled variables: shade, grazing, soil type, nutrients and trampling. Name them and say how they might affect the results.

Choosing the method

Choosing quadrat size and number

Do a short pilot study: place 8 to 10 random quadrats of two or three sizes and see which gives counts that are neither nearly all zero nor so large that counting is slow. Then use the pilot mean and standard deviation in the sample size formula, n = (ts / E)², to find how many quadrats will give the precision you want. The calculator in the Analyse step does this and shows its working. In the simulated field, 73 quadrats of 1 m² are needed for a mean with a 10% half-width when the standard deviation is 43% of the mean, but only 21 are needed for a 20% half-width. Always say what precision you aimed for and why.

Placing quadrats at random

1. Lay two long tape measures along adjacent edges of the area to make x and y axes.
2. Generate two random numbers for each quadrat, using a calculator, a random number table or a phone, scaled to the lengths of the two edges.
3. Walk to the coordinates and place the corner of the quadrat exactly there. Do not nudge it towards a better-looking spot.
4. If the position falls on a path, a wall or another habitat, reject it and draw a new pair of numbers, and note how many were rejected.

Planning a transect

A belt of contiguous 1 m quadrats along a 20 m line needs 20 quadrats. An interrupted belt with 1 m quadrats and 1 m gaps needs n = ⌊(20 + 1) / (1 + 1)⌋ = 10 quadrats and samples 10 m². Choose a start at random if you want an unbiased view of the field, and run the line along the gradient so that the environmental variable changes steadily. Record the distance to the centre of each quadrat. Measure the environmental variable at the centre of each quadrat at the same time of day.

Procedure checklist

1. Write the risk assessment and obtain permission to work on the site (see section J).
2. Mark out the area and measure its size, so that densities can be scaled up to the whole area.
3. Do the pilot study, then decide quadrat size and number.
4. Place each quadrat, count each species by the agreed rule, estimate percentage cover, and measure soil moisture. Record all of these in a table before moving on.
5. Have a second person check a sample of counts.
6. Leave the site as you found it. Replace any soil you disturbed.
7. Enter the data in a spreadsheet the same day, while you can still correct mistakes.

Planning a mark-recapture study

Core

Decide a marking method that does not harm the animal or change its behaviour, such as a small spot of non-toxic paint on a part of the body that does not affect movement. Catch and mark as many animals as practical (M), release them where they were caught, allow enough time for mixing but not so long that births, deaths or migration occur, then take a second sample of similar size (C) in the same way. Aim for enough recaptures (R of at least 10) that the estimate is not dominated by chance.

Using the simulator

Step 3 (Experiment) holds the sampling tools. Create or choose a field, tick Shade by soil moisture if you want to see the gradient, and place quadrats by the three automatic methods or by clicking. Run belt and line transects from a random start or from the chosen position. Everything you record appears in the table and can be downloaded as a CSV file for a spreadsheet.

Tidy the data first

Foundation

Check every row for impossible values (a negative count, a moisture over 100%), missing entries and mixed units. Keep unusual values unless you can show a recording error: a quadrat that happens to land on a patch is part of the real variation. Convert counts to densities before comparing quadrats of different sizes.

Report an estimate and its uncertainty together

Core

A population estimate without an uncertainty is almost meaningless. Report the estimate, its standard error and the confidence interval, for example: the estimated population is 4,000 daisies (SE 455; 95% confidence interval about 3,000 to 5,000). The relative uncertainty is the standard error divided by the mean, 0.474 / 4.167 = 11.4% in worked example 2, or the half-width of the interval divided by the mean, 25%. State uncertainties to one or two significant figures and give the estimate to a matching number of places. Writing 4,000.0 plants would suggest a precision the data do not have.

Interpreting a confidence interval

A 95% confidence interval comes from a method that captures the true value in about 95% of repeat samples. It does not say that the true value has a 95% chance of lying in this particular interval, and it does not say that 95% of plants lie inside it. If two intervals for two sites do not overlap, the sites almost certainly differ. If they overlap a little, a proper test is needed.

Choosing and carrying out a significance test

1. State the null hypothesis (no monotonic relationship between moisture and abundance).
2. Calculate ρ from the ranks, using average ranks for ties.
3. Compare with the critical value for your n from your course tables, or use the t approximation and find p.
4. If p is below the significance level (commonly 0.05), reject the null hypothesis: the trend is unlikely to be chance. If not, say that the data do not show a trend, and do not say that there is none.
5. Describe the strength and direction of the relationship using the sign and size of ρ, and discuss other factors that could explain it.

Remember that p depends on sample size. A large sample can make a tiny trend significant, and a small sample can miss a large one. Always look at the graph.

Evaluating a line of best fit

• Look at the points before trusting the line. Is the cloud straight, or curved? Are there outliers that pull the line?
• Report the gradient with its standard error or confidence interval. A gradient whose interval includes zero is not distinguishable from no trend.
• Report R², the fraction of the variation in the vertical variable that the line accounts for (0.83 in worked example 6).
• Use the line only inside the range of the data.

Random and systematic errors in fieldwork

Comparing communities

To compare diversity, calculate Simpson index D for each site from pooled counts. Compare sites only when sampling effort is similar, because small samples miss rare species. If you have repeat samples at each site, you can calculate D for each and compare the means.

A model results sentence

Buttercup density showed a strong positive monotonic relationship with soil moisture (Spearman ρ = 0.82, n = 40, p < 0.001), with a gradient of 0.08 plants per m² per percentage point (95% interval 0.06 to 0.10). This supports the hypothesis, although shade was not measured and may also vary along the gradient. Numbers in this sentence are only an example of the layout. Replace them with your own.

Quadrats and frames

Foundation

A quadrat is a square frame laid on the ground to define the sampled area. Common sizes are 0.25 m by 0.25 m for dense short vegetation, 0.5 m by 0.5 m, and 1 m by 1 m for sparse or tall plants. A gridded quadrat is divided into smaller squares (often 100) so that each square counts as 1% when you estimate cover. A point frame (point quadrat) has a row of pins or a grid of points. Lower each pin and record the species it touches first or all species it touches. The simulator’s cover is a 10 by 10 point frame, with 100 points per quadrat.

Estimating cover

Core

• Direct estimate of squares or points: count the grid squares at least half filled, or the points that touch the species. It is repeatable and gives a direct percentage.
• Abundance scales such as DAFOR (dominant, abundant, frequent, occasional, rare) and cover-abundance classes in the Braun-Blanquet style are quick but coarse and depend on the observer. They suit surveys that compare many sites, and the results are ranks, not measurements.

Transect equipment

A long tape measure or marked rope, pegs or ranging poles at each end, and a compass or the sun to hold direction. For a line transect, record the species touching the line at every metre or at every 0.5 m, as the simulator does. For a belt, lay quadrats against the line, contiguous or at fixed intervals.

Measuring the environment

• Soil moisture (probe): a handheld meter pushed to a fixed depth gives a quick reading. Calibrate it for the soil type.
• Soil moisture (gravimetric): weigh a fresh soil sample, dry it in an oven until its mass stops changing, and weigh it again. Percentage moisture on a dry-mass basis is (wet mass − dry mass) / dry mass × 100. For 48.2 g of wet soil drying to 38.6 g, the water mass is 9.6 g and the moisture is 9.6 / 38.6 × 100 = 24.9%. Quote which basis you use. Follow your laboratory safety rules for hot ovens.
• Light, temperature, pH, wind: light meters, thermometers, pH probes and anemometers. Take the measurement at the same height and time for every quadrat.
• Position: tape measures give distances to the nearest centimetre. A hand-held GPS usually gives a few metres, which is too coarse for quadrat work but fine for locating a site.

Equipment for animals

For mark-recapture, the mark must be visible, non-toxic, safe for the animal, and long-lasting over the study period. Handle the animal for the shortest time possible and release it where it was caught.

Recording

Use a prepared table with a column for each variable, and units in the headings. Record the observer, date, time, weather and any odd events. Take photographs of quadrats if allowed, to check counts later. Copy the data to a second place before leaving the site.

Limits of the simulation

Foundation

• The field is a model. Plants are points with a fixed crown radius, scattered by a mathematical process. Real vegetation has layers, seedlings, dead material and many more species.
• The environmental gradient is a single smooth soil-moisture surface with small patchy variations. Real gradients combine many factors that change together.
• Each species responds to moisture with a bell-shaped curve and nothing else, and no species affects another. In real communities, competition, grazing and disease shape abundance.
• Counts are exact. Real counts have observer error, missed plants and boundary doubts.
• The mark-recapture animals are a statistical model with no behaviour. They are always mixed fully between samples.
• The numerical results are for learning. They are not data about any real habitat, and the marks in the examination are for learning, not an official grade.

Field safety

Core

Before real fieldwork, a teacher or supervisor completes a written risk assessment for the site, following the rules of your school, college or university and any local or national guidance. The points below are common to most sites. They do not replace your own organisation’s procedure.

• Know the site. Walk it first. Identify slopes, water, roads, livestock, cliffs, broken ground, overhead hazards and rubbish. Choose another site if the hazards cannot be managed.
• Weather and clothing. Check the forecast. Wear footwear with grip, long trousers, a waterproof layer and sun protection. Carry water. Stop work in thunderstorms, high winds or extreme heat or cold.
• Working in groups. Never work alone. Agree a meeting point and a time to return, and carry a charged phone and a first-aid kit. Make sure a responsible person knows where the group is.
• Health. Know who has allergies, asthma, hay fever or insect sting reactions, and who carries emergency medicine. Cover cuts. Wash hands before eating. In areas with ticks, wear long clothes, check skin afterwards and follow local advice on removal.
• Plants and animals. Do not touch or taste unknown plants. Some plants cause skin burns or irritation. Avoid contact with animal droppings. Do not handle dead animals.
• Water. Stay away from deep or fast water. Do not enter streams or ponds without a specific supervised plan.
• Equipment. Pegs, tapes and poles can trip people or poke eyes. Keep them tidy and low. Hot ovens and balances used for soil moisture need the usual laboratory precautions.

Ethics and conservation

• Permission and law. Get the landowner’s permission. Some sites, plants and animals are legally protected, and collecting or disturbing them may be illegal. Do not sample in protected areas without approval.
• Minimise harm. Quadrats and transects trample vegetation, so walk on set paths where you can, spread out, avoid nesting areas and keep numbers small. Do not pick or remove plants. Take photographs or notes instead of specimens.
• Treat animals humanely. Capture only as many as you need, hold them briefly and gently, never leave traps unchecked, keep captives out of direct sun, and release them where they were found. Use the least harmful marking method. For vertebrates, the work needs expert supervision and, in many places, a licence.
• Take nothing but data. Remove all litter and equipment and leave gates as you found them.
• Honest data. Record what you see, including inconvenient results. Do not drop points because they spoil a trend. Report your methods and limits fully, and credit other people’s data and ideas.
• Respect for others. Keep noise down, and be considerate of walkers, residents and other site users.

Foundation and Core

• Throwing a quadrat over the shoulder. That is not random: people throw towards open ground, and the quadrat lands where it lands. Use coordinates from random numbers.
• Choosing quadrats that look typical. This is convenience sampling and it biases estimates upward in the simulator by about 50% for total plant numbers.
• Using too few quadrats. Ten small quadrats give a very wide interval. Pilot first and calculate the number needed.
• Forgetting the quadrat area. A mean count of 1.2 in 0.25 m² quadrats is a density of 4.8 per m², not 1.2.
• Giving an estimate with no uncertainty. Always give a standard error or confidence interval.
• Confusing standard deviation and standard error. The standard deviation describes the spread of the counts. The standard error describes the uncertainty in the mean, and is smaller by a factor of √n.
• Dividing by n instead of n − 1 when finding a sample standard deviation.
• Counting the same plant twice or skipping the boundary rule. Agree and write down the rule.
• Mixing up Simpson formulas. Use n(n − 1) and N(N − 1) with the form D = 1 − Σn(n − 1) / [N(N − 1)] and not n², unless your course uses the other form. Note that a high D means high diversity, whereas the sum alone is high when diversity is low.
• Ranking the wrong way or forgetting ties. Rank both variables in the same direction, and share ranks for ties. Check that the ranks of each variable add up to n(n + 1) / 2.
• Treating ρ as proof of cause. A strong correlation shows association, not mechanism.
• Concluding that ρ near 0 means no relationship. A hump-shaped response (the fescue) can give ρ near 0 even with a strong pattern.
• Extrapolating the line of best fit beyond the data.
• Applying the Lincoln index to an open population, or ignoring that marks can be lost.
• Calling an estimate a count. Say ‘estimated’.

Command words

Foundation

A model answer structure for a sampling question

Core

Question: Describe how you would estimate the number of daisy plants in a school field. (5 marks)

• Measure the area of the field.
• Use a tape measure along two sides and random numbers to choose coordinates for each quadrat.
• Place the quadrat at each coordinate and count the daisies inside it, using a rule for plants on the edge.
• Use a large enough number of quadrats, for example 30 or more, or justify the number with a pilot study.
• Calculate the mean count per quadrat, divide by the quadrat area to find the density, and multiply by the area of the field.

Each bullet is a likely mark point. The words random, mean, area and estimate are usually looked for. Marks are earned for the idea, so write each idea clearly in its own sentence.

Calculation questions

1. Write the formula. If the formula is on a data sheet, still show it.
2. Substitute the numbers with their units.
3. Give the answer to a sensible number of significant figures, often 2 or 3, with units.
4. For a population estimate, check that you used the same area units throughout.
5. For Simpson index, show the sum n(n − 1) for each species, the total, and N(N − 1).
6. For Spearman, show a table of ranks, d and d², then Σd², then ρ.

Interpretation questions

• Use the data. Quote values from the table or graph.
• Link the numerical result to the biology: why would clover prefer drier soil?
• When a test is significant, say what it shows in words. When it is not, say the data do not show a relationship, and do not say that none exists.
• Suggest improvements that deal with a stated weakness: more quadrats, random placement, a second observer, measuring a second variable.

Planning and evaluation questions

Be specific. Instead of ‘make it fair’, say ‘use the same size quadrat and the same counting rule each time’. Instead of ‘repeat’, say how many times and what you would do with the repeats. Link every safety point to a named hazard.

Practice with this page

Do the Examination step, then open the notes sections that it flags. In the Practise step, cover each answer and write your own before checking it. Marks on this page are for learning and not an official grade. Check the mark scheme conventions in your own specification.

Ecological sampling appears in almost every secondary and first-year university biology course. The table gives typical topic names only. Courses change, so check your own current specification or course guide for the exact requirements, the formulas you are given and the statistical tests you must know. This page supports your course. It does not replace it and has no connection with any exam board.

If your course uses a different diversity index, such as Shannon or Simpson’s in the with-replacement form, or a different correlation test, the sampling and planning ideas still apply. The calculations can be repeated in a spreadsheet using the downloaded CSV file.

Foundation and Core

• Biodiversity monitoring. Repeated surveys with fixed methods show whether species are increasing or declining, and indices such as Simpson’s turn a species list into a number that can be tracked and compared across sites and years.
• Environmental impact assessment. Before a road or building is built, surveys record which species are present and how abundant they are, so that harm can be avoided or reduced. Transects across a development site and a similar control site show what changes.
• Invasive species. Managers need to know how many individuals there are and how fast they are spreading. Quadrats and transects give densities, and mark-recapture is used for mobile invaders. The confidence interval tells managers whether a control programme has made a real difference.
• Conservation of rare plants and animals. Population estimates with honest error bars support decisions about protection. Mark-recapture is a standard tool for animals that can be caught and released without harm.
• Agriculture and grazing. Quadrat cover estimates give the proportion of weeds or sown species in a pasture, and show the effect of grazing, cutting or fertiliser.
• Fisheries and wildlife management. Catch and tagging data, analysed by capture-recapture models, inform harvest limits and the health of stocks.
• Climate and land-use research. Transects up a mountain or away from a coast record how plant communities change with temperature, moisture or salinity, and repeat surveys detect shifts over decades.
• Citizen science. Volunteers following a fixed method supply large datasets. Random or systematic placement rules and good training keep such data useful.
• Other fields. The same capture-recapture logic is used to estimate hidden populations in public health and in counting documents or errors in software. The ideas of random sampling, bias and uncertainty apply wherever a whole cannot be counted.

Extension

Why a systematic sample with a random start is unbiased

Let the grid have spacing d and a random start u uniform within one spacing. Every point of the field then has the same chance of being the position of a sample unit, in proportion to d, so the expected value of the sample mean equals the field mean. The variance depends on how the quantity varies along the grid. With a smooth gradient, neighbouring grid points differ in a predictable way and the sample mean has a smaller variance than the mean of the same number of random points, because a random sample may by chance bunch in the wet or the dry end. If the habitat has a periodic pattern with a period equal to the spacing, every grid point may land in the same phase of the pattern, and the estimate is badly biased. In the simulator’s bias experiment the systematic standard deviation is usually a little below the random one, and the convenient method is biased high.

Stratification and ratio estimators

If the field is divided into strata with area A_h, mean x̄_h and variance s_h², the stratified estimate of the total is ΣA_hx̄_h and its variance is ΣA_h²s_h²/n_h. Strata chosen to be internally uniform make this smaller than simple random sampling. A ratio estimator uses a cheap variable that is known everywhere, such as soil moisture, to improve the estimate of an expensive one, such as a plant count.

Counts that are not Poisson

For random patterns, counts follow a Poisson distribution, with variance equal to the mean. Clumped patterns have variance greater than the mean and are often modelled with a negative binomial distribution, whose clumping parameter k can be estimated from the mean and variance. Regression of counts on an environmental variable then uses a generalised linear model with a log link instead of a straight line.

Diversity measures and Hill numbers

Species richness counts species. Shannon’s index weights species by −p ln p. Simpson’s index emphasises common species. All three can be expressed as effective numbers of species (Hill numbers of order 0, 1 and 2), and the reciprocal Simpson index used here is the order 2 value. Rarefaction compares samples of different size by asking how many species would be seen in a sample of a standard size.

Spatial structure

Nearby quadrats are more alike than distant ones. Measures such as Moran’s I and the variogram quantify this, and ignoring it overstates the number of independent observations. Pseudoreplication, treating non-independent samples as independent, is a classic error in field studies. Replicate at the scale of the question.

Detection and capture-recapture models

Real surveys miss some individuals. Distance sampling estimates the probability of detection from how detection falls with distance. Multiple-recapture models (such as Schnabel’s method for several sampling occasions and the Jolly-Seber model for open populations) allow births, deaths and migration. Occupancy models separate the chance that a site is occupied from the chance that the species is seen when it is there.

Bootstrap intervals

A bootstrap draws many resamples with replacement from the observed counts, recalculates the estimate each time, and uses the spread of those estimates as the uncertainty. It avoids the normality assumption behind the t interval and works for awkward statistics such as the Simpson index, although it cannot fix a biased sample.

Tasks to try

• Use a gentle gradient and no gradient. How do the Spearman values and the bias experiment change?
• With a steep gradient, compare the spread of systematic and random estimates for 5, 15 and 40 quadrats.
• Estimate the clumping of the rush with the variance-to-mean ratio, then compare the 95% interval for its population with the interval for a randomly scattered species at the same sample size.
• Download your data and fit a curve to the fescue density against moisture. Does a hump fit better than a line?

• A sample is used to estimate a whole. The estimate has uncertainty, which must be stated.
• Random placement gives every position an equal chance of being chosen and avoids the recorder’s bias. Systematic sampling with a random start is also unbiased and covers gradients well. Convenience sampling is biased.
• Transects reveal change along a gradient (zonation). A belt records quadrats, and a line records what touches the line.
• Density = count / area. Population estimate = mean density × total area.
• Standard deviation describes the spread of counts. Standard error = s / √n describes the uncertainty in the mean.
• A 95% confidence interval is the mean ± t × SE.
• To halve the standard error, use four times as many quadrats.
• The number of quadrats needed is n = (ts / E)², found from a pilot study.
• Percentage cover suits plants that cannot be counted as individuals, and it can add to more than 100% when plants overlap.
• Simpson’s D = 1 − Σn(n − 1) / [N(N − 1)] measures diversity. High D means a diverse and even community.
• Spearman’s ρ tests for a monotonic relationship using ranks. Ties share the average rank. It does not prove cause and can miss hump-shaped responses.
• A line of best fit summarises a trend. Report its gradient with an uncertainty and use it only inside the range of the data.
• Lincoln index N = M × C / R assumes a closed population, lasting harmless marks, equal catchability and complete mixing. The Chapman form is less biased when R is small.
• Work safely, get permission, avoid harm to habitats and animals, and report data honestly.

Abundance

How many individuals of a species there are, measured as a count, a density or a cover.

Accuracy

How close an estimate is to the true value.

Bias

A systematic error that pushes estimates in one direction.

Belt transect

A strip of fixed width along a line, usually sampled as a row of quadrats.

Census

A count of every individual.

Chapman estimator

A version of the Lincoln index that is less biased when few marked animals are recaptured.

Clumped distribution

A pattern in which individuals occur in groups, with variance greater than the mean.

Confidence interval

A range calculated from a sample by a method that captures the true value in a stated percentage (often 95%) of repeat samples.

Convenience sampling

Choosing sample sites because they are easy or look typical, which tends to cause bias.

Cover (percentage cover)

The percentage of the ground covered by a species when seen from above.

Degrees of freedom

The number of independent pieces of information used to estimate a quantity, such as n − 1 for a sample standard deviation.

Density

Number of individuals per unit area.

Diversity

A measure of how many species there are and how evenly their numbers are spread.

Frequency

The proportion of sample units in which a species is found.

Gradient

A steady change of an environmental factor over distance.

Habitat

The place where an organism lives.

Lincoln index

An estimate of population size, N = MC/R, from mark, release, recapture.

Monotonic

Always moving in one direction (increasing or decreasing), not necessarily in a straight line.

Null hypothesis

The statement of no effect or no relationship that a test tries to reject.

p-value

The chance of a result at least as extreme as the one found if the null hypothesis were true.

Point frame

A frame with a grid or row of points used to estimate cover.

Population

All the individuals of one species in an area.

Precision

How tightly repeated estimates cluster together.

Quadrat

A frame of known area laid on the ground to define a sample.

Random sampling

Selecting sites so that each has the same chance of being chosen.

Rank

The position of a value when data are sorted from smallest to largest.

Representative

Having the same features as the whole from which it was drawn.

Sampling fraction

The share of the whole area that is sampled.

Simpson index of diversity

1 − Σn(n − 1) / [N(N − 1)].

Spearman’s rank correlation

A coefficient from −1 to +1 measuring how well the ranks of two variables agree.

Standard deviation

A measure of the spread of values about their mean.

Standard error

The standard deviation of a sample mean, s/√n.

Stratified sampling

Dividing the habitat into similar zones and sampling each one.

Systematic sampling

Sampling at regular intervals, usually after a random start.

Transect

A line across a habitat along which samples are taken.

Variance-to-mean ratio

The variance of counts divided by their mean: about 1 for random patterns.

Zonation

An orderly sequence of different communities along a gradient.

Titles are given with the publisher’s home page only. Check current editions, and use the reading list in your own course. Listing a work here does not mean that any examination board or organisation endorses this page.

• Krebs, C. J. Ecological Methodology. Pearson / Benjamin Cummings. pearson.com
• Southwood, T. R. E. and Henderson, P. A. Ecological Methods. Blackwell Science, now Wiley. wiley.com
• Magurran, A. E. Measuring Biological Diversity. Blackwell, now Wiley. wiley.com
• Gotelli, N. J. and Ellison, A. M. A Primer of Ecological Statistics. Sinauer Associates, now Oxford University Press. global.oup.com
• Buckland, S. T. and others. Introduction to Distance Sampling. Oxford University Press. global.oup.com
• Seber, G. A. F. The Estimation of Animal Abundance and Related Parameters. Griffin; reprinted by Blackburn Press.
• Simpson, E. H. (1949). Measurement of diversity. Nature. nature.com
• Spearman, C. (1904). The proof and measurement of association between two things. American Journal of Psychology. University of Illinois Press. press.uillinois.edu
• Student [W. S. Gosset] (1908). The probable error of a mean. Biometrika. Oxford University Press. global.oup.com
• Lincoln, F. C. (1930). Calculating waterfowl abundance on the basis of banding returns. Circular 118, United States Department of Agriculture. usda.gov
• Chapman, D. G. (1951). Some properties of the hypergeometric distribution with applications to zoological sample censuses. University of California Publications in Statistics. ucpress.edu
• Hurlbert, S. H. (1984). Pseudoreplication and the design of ecological field experiments. Ecological Monographs. Ecological Society of America. esa.org
• Field Studies Council, for identification guides and fieldwork resources. field-studies-council.org
• British Ecological Society, for guides to ecological methods and teaching resources. britishecologicalsociety.org
• CLEAPSS, for school science safety guidance in the United Kingdom. cleapss.org.uk