1The idea in one paragraph

A population is all the members of one species living and breeding in one area. You almost never count it; you estimate it, with quadrats for things that stay still and mark–recapture for things that move. A population grows exponentially while resources are plentiful, then slows and levels off at the carrying capacity, because crowding strengthens competition, predation and disease, and those push numbers back down: negative feedback. All the populations of an area together make a community, bound by relationships between species, herbivory, predation, competition, mutualism, parasitism and pathogenicity, which make the populations depend on each other: predators and prey cycle together, and a predator at the top or a nutrient at the bottom can set the numbers of a whole food chain.

2Populations

A population is a group of organisms of the same species living in the same area at the same time, and interacting with each other. Its members normally breed with each other.

A species can be made up of many populations. What separates them is reproductive isolation: if two groups of the same species do not, in practice, interbreed, they are two populations. Brown trout in two lakes with no stream between them are one species but two populations: each group breeds only among itself, and its numbers rise and fall on its own.

3Why we sample, and why the sample must be random

Counting every individual is usually impossible: there are too many, they hide, and a full count would disturb the habitat. So ecologists estimate population size from a sample and scale it up.

A sample only represents the whole if it is taken at random: every individual, or every point in the habitat, must have the same chance of being included. If you choose where to look, you choose the interesting places and bias the estimate.

Even a perfectly random sample gives an estimate, not the truth. The difference between the estimate and the true size of the whole population is the sampling error. It is unavoidable when you measure part instead of the whole, and is reduced, not removed, by taking more samples.

4Random quadrat sampling, for organisms that stay still

Sessile organisms do not move about: plants, and animals fixed to one place such as barnacles or mussels. Their population is estimated with a quadrat, a square frame of known area, usually 1 m × 1 m or 0.5 m × 0.5 m. Figure 1 shows the method in a school field.

Two tapes are laid at right angles along two edges of the area to make a grid. A random number generator gives a pair of coordinates, the quadrat goes at that point, and the individuals inside it are counted. Repeat for at least ten quadrats. Then:

Population estimate = mean number per quadrat × (total area ÷ area of one quadrat)

Here is the field in Figure 1, 60 m × 40 m, sampled with ten 1 m² quadrats.

With a 0.5 m × 0.5 m quadrat (0.25 m²), divide the mean by 0.25 first to get a density per m². Forgetting that is the commonest wrong answer here.

What the standard deviation tells you. Your calculator will give the standard deviation of the counts: a measure of how spread out they are about the mean. You do not need the formula. For the counts above it is 1.83. Now suppose a second field gave these counts: 0, 0, 12, 1, 0, 9, 0, 8, 0, 0. The mean is also 3.0, but the standard deviation is 4.71. A small standard deviation means most quadrats hold about the same number: the population is spread evenly. A large one means a few quadrats are crowded and most are empty: the population is clumped, perhaps because seeds fall near the parent, and more quadrats are needed for a reliable mean.

5Capture–mark–release–recapture, for organisms that move

Animals that move, motile organisms, cannot be counted in a quadrat: they walk in and out of it. Their population is estimated by capture–mark–release–recapture, and the estimate is calculated with the Lincoln index. Figure 2 follows the method with garden snails.

1. Catch as many individuals as possible in a set time, mark each one harmlessly, and count them. That is M.
2. Release them where they were caught, and leave time for them to mix back into the population.
3. Catch a second sample with the same effort. Count the total caught, N, and how many of them carry a mark, R.

Population size estimate = (M × N) ÷ R

The logic is a proportion: one in five of the second sample was marked, so one in five of the whole population is taken to be marked, and 5 × 48 = 240.

The estimate is only as good as its assumptions, and exam questions ask for them.

• Marked individuals mix completely and randomly back into the population before the recapture.
• The mark does not wear off, and does not harm the animal or make it easier or harder to catch (a bright mark might attract a thrush).
• Marked and unmarked animals are equally likely to be caught the second time; being caught once does not make an animal trap-shy or trap-happy.
• No births, deaths, immigration or emigration between the two samples, so the population is closed and unchanged.

6Carrying capacity, and how density-dependent factors hold a population there

The carrying capacity (K) is the maximum population size that an environment can support indefinitely. What sets it is whichever resource runs short first: food, water, light for plants, nesting sites for birds, space for barnacles on a rock, oxygen in a stream.

Two kinds of factor change population size.

Density-independent factors act regardless of how crowded the population is. A frost, flood, drought or fire kills a similar proportion of a sparse population and a dense one. They make numbers fluctuate but push them towards no particular value.

Density-dependent factors grow stronger as the population becomes denser. There are three the guide names.

• Competition for limited resources. More individuals share the same food and space, so each gets less; fewer survive and fewer breed.
• Predation. A dense prey population is easy to find, so predators take more, and predator numbers may rise too.
• Pathogens and pests. Diseases and parasites pass from host to host far faster when hosts are crowded together.

Because these factors strengthen above the carrying capacity and weaken below it, they act as negative feedback: any change in population size sets off an effect that reverses it. Figure 3 draws the loop.

Above K, deaths rise and births fall until numbers drop; below K, births exceed deaths and numbers rise. The population fluctuates about K rather than sitting exactly on it.

7Population growth curves

Put a few individuals into an environment with plenty of resources and they grow in a characteristic way. Figure 4 shows the two shapes.

Exponential growth. At first nothing is in short supply, so individuals breed at their maximum rate and almost none die of crowding. Each generation is bigger than the last and so produces even more offspring: the population multiplies by the same factor in every interval, and the curve steepens. That is the J-shape in panel (a), and no population keeps it up for long.

Sigmoid growth. In reality the growth slows, because the density-dependent factors of section 6 start to bite. Panel (b) is the resulting S-shaped or sigmoid curve, in three phases.

1. Exponential phase. Resources plentiful, births far exceed deaths, numbers multiply.
2. Transitional phase. Resources start to run short, competition, predation and disease increase, and the growth rate falls, although numbers are still rising.
3. Plateau phase. Births and deaths balance and the population fluctuates around the carrying capacity.

The guide's model starts with the exponential phase; a lag phase is not expected.

A case study from a real ecosystem. In 1944, 29 reindeer were released onto St Matthew Island in the Bering Sea, which had rich lichen pastures and no wolves. The herd grew roughly exponentially, to about 6,000 by 1963. By then it had grazed the slow-growing lichen faster than it could regrow, destroying its own carrying capacity, and after a hard winter only 42 animals were left by 1966. A population that overshoots and damages its resource can crash instead of levelling off.

Nature of science: models are simplifications. The sigmoid curve is an idealised model: one fixed carrying capacity, a closed population, smooth responses to crowding. Real curves are bumpier, and some, like St Matthew Island, do not fit at all. The model is still useful because it shows the main forces at work and gives real data something to be compared against.

Testing data against the exponential model. The guide asks you to do this on a graph with a logarithmic scale for population size and an ordinary scale for time. On a log scale, equal distances mean equal multiplications (10 to 100 is the same height as 100 to 1,000), so growth by a constant factor plots as a straight line. Figure 5 shows duckweed growing in a beaker.

On the ordinary scale, panel (a), the curve is sigmoid. On the log scale, panel (b), the first four intervals are a straight line: from 20 to 165 fronds the count rises by a factor of about 1.7 every two days, so growth is exponential. From about day 10 the points fall below the dashed line, because the fronds are covering the water and competing for light and nutrients. You can collect such data yourself: duckweed (Lemna) in a beaker of pond water, or yeast in sugar solution counted on a haemocytometer, gives a full sigmoid curve in two or three weeks.

8Competition and cooperation within a species

Members of one species need exactly the same resources, so they are each other's closest competitors. Intraspecific competition is competition between members of the same species for a limited resource: food, water, light, space, territory, nest sites or mates. Some real examples:

• Beech seedlings on a woodland floor compete for light; the fastest-growing shade the rest out.
• Red deer stags fight in the autumn rut for groups of hinds; the strongest father most of the calves.

But members of a species also cooperate, when working together gives each individual a better chance than acting alone.

• Meerkats take turns as sentinels, watching for eagles while the group forages.
• Wolves hunt in packs and bring down prey, such as elk, that one wolf could not kill.
• Emperor penguins huddle through the Antarctic winter, rotating from the cold edge into the warm centre.

The two are not exclusive: a wolf pack cooperates to hunt, then its members compete over who eats first.

9Communities, and the six relationships between species

A community is all the populations of all the different species living and interacting in one area: plants, animals, fungi and bacteria together. An ecosystem is a community plus its physical environment.

The populations in a community affect each other through interspecific relationships, relationships between different species. The guide names six categories, set out in Figure 6.

• Herbivory: a primary consumer feeds on a plant or other producer. A rabbit grazing grass.
• Predation: a predator kills and eats another animal, its prey. A barn owl catching a field vole.
• Interspecific competition: two species use the same limited resource, so each has less. Both lose.
• Mutualism: two species live in close association and both benefit (section 10).
• Parasitism: a parasite lives on or in a host and feeds from it, usually without killing it quickly. A pork tapeworm in a pig's gut, or a tick on a deer.
• Pathogenicity: a pathogen, a microorganism or virus, causes disease in its host. Plasmodium causing malaria in humans, or the fungus that causes ash dieback in ash trees.

In the exam, either the common name or the scientific name of an organism is accepted.

10Mutualism, and the three examples you must know

Mutualism is an interspecific relationship in which both species benefit. The guide names three examples, and for each you must give the benefit to both partners. Figure 7 sets them side by side.

Root nodules in the legume family (Fabaceae). Peas, beans and clover have root swellings called nodules, packed with Rhizobium bacteria. The bacteria fix nitrogen: they convert nitrogen gas (N₂) from the soil air into ammonia, which the plant uses to make amino acids. Plants cannot use N₂ themselves, and nitrogen is often the scarcest soil nutrient. In return the plant gives the bacteria sugars from photosynthesis and a protected home in the nodule.

Mycorrhizae in the orchid family (Orchidaceae). A mycorrhiza is an association between a fungus and a plant root. Fungal threads, hyphae, grow into the orchid's root cells and far out into the soil, absorbing mineral ions and water from a much larger volume than the roots could reach and passing them to the orchid. Orchid seeds are dust-like, with almost no food store, so they cannot germinate without the fungus, which supplies the seedling with sugars too. Once the orchid is green and photosynthesising, carbon compounds pass from plant to fungus: the fungus's benefit.

Zooxanthellae in hard corals. Reef-building corals are animals, colonies of small polyps. Inside the cells of each polyp live photosynthetic algae called zooxanthellae. The algae pass most of the sugars they make to the coral, which is how corals thrive in clear tropical water that holds little food, and their oxygen helps the coral respire. The coral gives the algae a protected place in shallow, well-lit water, plus carbon dioxide and nitrogen-containing wastes. In water that is too warm, corals expel their algae and turn white, coral bleaching, and may starve.

11Invasive species and competition with endemic species

An endemic species is one that is native to an area. An introduced species is one that humans have brought in from elsewhere. An introduced species becomes invasive when it spreads and harms the native community, and very often the reason is that it is better at getting a resource than the endemic species it competes with.

Grey squirrels in Britain. Grey squirrels were brought from North America in the late nineteenth century. Both they and the endemic red squirrel eat tree seeds, and in broadleaved woods much of the autumn food is acorns, rich in tannins. Greys digest acorns efficiently and reds gain far less from them, so where oaks are common greys take more of the shared food, survive winter better and breed more. Reds have disappeared from most of England and Wales and survive mainly in Scotland and in conifer forests. (Greys also carry squirrelpox, which kills reds: a pathogen effect on top of the competition.)

Choose a local example if you can. The answer always has the same shape: the two species, the resource, and the invader's specific advantage in getting it.

12Testing for interspecific competition

If two species compete, each should do better when the other is absent. That is the prediction every test checks. The guide describes three approaches.

Laboratory experiments. Grow each species alone and then together under controlled conditions. In the 1930s Georgy Gause grew two species of Paramecium on bacteria in culture tubes: each thrived alone, but together one always died out.

Field observations by random sampling. Sample many sites at random and record where each species is found. If the two are found together less often than chance predicts, competition is one possible explanation. Section 13 is the statistical test for this.

Field manipulation by removing one species. Remove one species from marked plots, leave control plots untouched, and see whether the other spreads. On a Scottish rocky shore, Joseph Connell removed the barnacle Balanus from rocks low on the shore, and a second barnacle, Chthamalus, normally found only higher up, then survived there too: Balanus had been excluding it by competing for space.

A positive result indicates competition but does not prove it. One species may do better without the other for a different reason: the other might carry a disease, or attract a predator, or the two may simply prefer different conditions.

Nature of science: experiments and observations. In an experiment the investigator changes one variable and controls the others, as Gause and Connell did. In an observation the investigator records what is already happening without changing it, as in random sampling. Experiments give stronger evidence of cause; observations show what happens in real, complex habitats and are the only option when an experiment is impossible. Both can test the same hypothesis.

13The chi-squared test for association between two species

The chi-squared (χ²) test asks whether the pattern in your counts differs from what chance alone would produce. Here it asks whether two species occur together more often, or less often, than they would if they were distributed independently of each other.

A student recorded the presence or absence of bluebells (species A) and bramble (species B) in 80 random quadrats in a wood. The data are invented.

Step 1: the hypotheses. The null hypothesis (H₀): there is no association between the two species; they are distributed independently. The alternative hypothesis (H₁): there is an association between them.

Step 2: expected frequencies. If the species were independent, each cell would be expected to hold (row total × column total) ÷ grand total.

Step 3: calculate χ². For each cell, (O − E)² ÷ E, then add the four together.

Step 4: degrees of freedom. (rows − 1) × (columns − 1) = (2 − 1) × (2 − 1) = 1.

Step 5: compare with the critical value. From a table of critical values, at 1 degree of freedom and the 0.05 (5%) significance level, the critical value is 3.84. The calculated χ² of 13.6 is greater than 3.84, so the null hypothesis is rejected: there is a significant association between the two species.

Step 6: say what kind of association. The species were together in 8 quadrats where 16.15 were expected, so they occur together less often than chance predicts: a negative association. That is consistent with competition, but not proof: they might simply prefer different soils or shade. A positive association, more often together than expected, suggests shared habitat needs.

If the calculated χ² is greater than the critical value, reject the null hypothesis: the association is significant. Then compare observed with expected to say whether it is positive or negative.

14Predator–prey relationships as density-dependent control

A predator is a density-dependent factor for its prey, and its prey is a density-dependent factor for the predator. The two populations therefore regulate each other and often rise and fall in linked cycles, as Figure 8 shows.

Plentiful prey feed predators, which breed and increase. More predators eat more prey, so prey fall. Short of food, predators starve or fail to breed and fall too, and with fewer predators the prey recover. Predator peaks come after prey peaks, because extra food takes time to become extra predators.

A real case study: the snowshoe hare and the Canada lynx. The Hudson's Bay Company bought furs from trappers across northern Canada for well over a century, and its records show the numbers of lynx and snowshoe hare pelts rising and falling in cycles of about ten years, with lynx peaks following hare peaks. Later field studies found the hare cycle is driven partly by predators and partly by the hares' food running short at high density: real populations are usually controlled by more than one factor at once.

15Top-down and bottom-up control

Populations in a food chain can be controlled from either end. Figure 9 shows both, using a kelp forest.

Top-down control: a population is limited by the trophic level above it, its predators or herbivores. Along the Pacific coast of North America, sea otters eat sea urchins, and sea urchins graze kelp. When fur hunters killed most of the otters, urchin numbers rose and the urchins stripped whole kelp forests down to bare rock. Where otters returned, urchins fell and the kelp grew back. The predator at the top set the numbers of the levels below it.

Bottom-up control: a population is limited by the level below it, and ultimately by the resources at the base: nutrients, water, light. In many lakes, the growth of algae is limited by the supply of phosphate. Add phosphate, and algae increase, then the animals that eat algae, then the fish that eat those animals. The resources at the bottom set the numbers above.

Both kinds of control are possible in any community, but usually one is dominant.

16Allelopathy and antibiotics: chemical competition

Some organisms compete by releasing a chemical into the environment that deters their competitors.

Allelopathy is the release by a plant of chemicals that inhibit the germination or growth of other plants nearby. The black walnut tree releases a compound called juglone from its roots, leaves and fallen husks; many plants, such as tomatoes, fail to grow beneath it, which leaves the walnut more water, minerals and light.

Secretion of antibiotics is the same strategy used by microorganisms. The mould Penicillium secretes penicillin, which kills many bacteria that would compete with it for nutrients; Alexander Fleming saw this in 1928 as a clear zone of dead bacteria around a mould colony on a culture plate. Soil bacteria of the genus Streptomyces do the same; one is the source of streptomycin.