A population is a group of organisms of the same species living in the same area at the same time, interacting with one another. The “same area” part matters. A population is not just a species name on a page; it is a real set of individuals sharing a habitat, using resources, avoiding predators, finding mates and, in most cases, breeding.

A species is a group of organisms that can interbreed to produce fertile offspring under natural conditions. Within one population, individuals normally breed with each other more often than with individuals from other populations of the same species. Reproductive isolation means separation in breeding between groups, caused by barriers such as distance, geography, behaviour or timing. Ecologists use it to distinguish one population of a species from another.

For example, limpets on one rocky shore may form a population if they can breed with one another. Limpets of the same species on a distant shore may count as a separate population if the larvae do not normally disperse between the two shores. The boundary is not always tidy, so ecologists define the study area carefully.

Population-level properties come from the way individuals interact. A flock, herd or shoal can lower an individual’s risk of predation; crowded seedlings compete strongly for light; breeding adults may defend territories. Because of interactions like these, population size is regulated, rather than being just a simple count of isolated individuals.

A complete count sounds neat in theory. In the field, it’s often impossible. Many organisms are hidden, tiny, numerous, mobile or spread across a large habitat. Counting every individual may also damage the habitat, or take so long that the population has changed by the time the count ends. So, in practice, we usually estimate population size from samples.

An estimate is a value inferred from evidence when the exact value is unknown or impractical to measure.

A sample is a smaller part of a larger whole that is measured to make an inference about the whole. In population ecology, the sample might be several quadrats on a lawn, traps set in woodland, or repeated observations along a transect.

A random sample is a sample selected by a method in which every possible sampling location or individual has an equal chance of being chosen. This does not mean “places that look typical”. Humans introduce bias easily, even without meaning to: we avoid muddy patches, pick places that are easy to reach, or sample where organisms are most obvious. Random numbers, coordinates and pre-planned sampling rules help remove that bias.

Sampling error is the difference between an estimate from a sample and the true value for the whole population. Random sampling does not remove sampling error; it makes the error less biased and easier to handle mathematically. That is a useful nature of science point: sampling gives us defensible estimates, not certainty. More well-chosen random samples usually improve reliability.

A quadrat is a frame, or a marked area of known size, used to sample organisms in a habitat. Quadrat sampling works well for sessile organisms: organisms fixed in place, or moving so little that you can count individuals within a sampling area. Plants, lichens, barnacles, mussels and many seaweeds fit this method. A running beetle does not.

To sample randomly, lay a baseline along one edge of the habitat. Use random numbers to pick a distance along the baseline, then a second distance at right angles into the habitat. Put the quadrat at that coordinate and count the individuals inside. Repeat the process many times. If the population is patchy, you’ll need more replicates.

, where $\bar{x}$ is the mean number of individuals per quadrat (individuals, count). This formula assumes the quadrats are representative of the whole habitat.

Standard deviation is a statistic that describes the spread of values around a mean. You don’t need to memorize its formula here; use a calculator or software. In quadrat work, a low standard deviation for number per quadrat suggests the population is spread fairly evenly, so the mean gives a more dependable estimate. A high standard deviation suggests clumping or uneven distribution, making the estimate less precise unless more quadrats are used.

Uniform, random and clumped distributions affect sampling. A clumped population often produces several empty quadrats and a few crowded ones, so the standard deviation is high. A uniform population gives similar counts in different quadrats, so the standard deviation is low.

Comparison of dispersion patterns and how they affect variation in quadrat counts.

A motile organism is an organism that can move from place to place during the study period. Quadrats usually don’t work well for motile animals, since individuals can simply leave the sampling area. Capture–mark–release–recapture gets around this by asking a simple question: what fraction of the second catch is already marked?

The method is straightforward. Capture a sample of individuals first. Mark them in a harmless, durable way, then release them and give them time to mix back into the population. After that, capture a second sample and count how many of those individuals are marked.

This is the Lincoln index, a calculation used to estimate the size of a motile population from marked and recaptured individuals.

The reasoning is proportional. If marked individuals make up 10% of the second catch, the first marked group is treated as 10% of the whole population. The estimate becomes poor when $R$ is very small, because a tiny recapture number makes the proportion unstable.

The assumptions are the heart of the method:

• no immigration or emigration between capture and recapture;
• no births or deaths during the study period;
• marks are not lost or overlooked;
• marking does not affect survival, movement or chance of being recaptured;
• marked individuals mix fully back into the population;
• the second capture is random with respect to marked and unmarked individuals.

If painted snails hide more because marking disturbed them, or if birds learn to avoid traps after the first capture, the estimate will be biased. Always think biologically before trusting the number.

Carrying capacity is the maximum population size that an environment can support sustainably under a particular set of conditions. It is usually shown as $K$, where $K$ is carrying capacity (individuals, count). Don’t treat $K$ as a magic fixed number. Rainfall, nutrient supply, disease, habitat area, season and human disturbance can all change it.

Populations need resources. A resource is an environmental substance or condition used by organisms that can become limiting when demand exceeds supply. For plants, limiting resources often include light, water, mineral ions such as nitrate, and space for roots. For animals, they can include food, water, dissolved oxygen, nesting sites, breeding territories and shelter.

Competition is an interaction in which organisms use the same limited resource so that each reduces the availability of that resource to others. As population size rises, competition gets stronger because more individuals draw from the same supply. If the population exceeds the carrying capacity, some individuals fail to obtain enough resources, so birth rate may fall and death rate may rise.

Comparison of common limiting resources in plant and animal populations.

This links to one of the big questions in this topic: capacity in biological systems is limited by whichever requirement becomes scarce first. In a pond it might be surface area for floating plants; in a desert, soil water; in a stream, dissolved oxygen; in a seabird colony, safe nesting ledges.

Negative feedback is a regulatory process where a change triggers effects that reduce or reverse the original change. In populations, it tends to pull numbers back towards carrying capacity. When population size gets too high, limiting factors become stronger; when it falls, those pressures ease.

A density-dependent factor is a factor whose effect on population growth changes with population density. Competition is the clearest example: crowded plants shade each other, while crowded animals compete for food or territory. Predation can be density-dependent too, since predators find dense prey populations more easily. Pathogens, parasites and pests also spread more readily when hosts are close together.

A density-independent factor is a factor that affects population size regardless of population density. A severe frost, volcanic eruption, wildfire or flood may kill many individuals whether the population was sparse or crowded. These factors can cause fluctuations, but they do not automatically push the population back towards $K$.

Pay attention to the direction of the feedback. Above carrying capacity, density-dependent factors tend to increase deaths or reduce breeding. Below carrying capacity, competition and disease transmission are often less intense, so survival or reproduction may improve. Real populations are messy: they may overshoot, crash or fluctuate. Even so, density-dependent factors are the main reason many populations do not grow forever.

Exponential growth

Exponential growth means a population increases at a rate that gets faster as the population gets larger. Each generation adds more breeding individuals, and limiting factors are weak. On a normal graph, exponential growth produces a J-shaped curve.

You’re most likely to see early exponential growth when a species moves into a new area with abundant resources, little competition, few predators and few pathogens. The Eurasian collared dove is a useful case study: it spread across parts of Europe during the twentieth century. Food in farmland and gardens was plentiful, so the population rose quickly during the early spread.

To check whether growth is exponential, plot population size on a logarithmic vertical axis against time on a non-logarithmic horizontal axis. If the points sit close to a straight line, the population is close to exponential growth. Practise this skill: the log scale does not “make growth exponential”; it helps show whether proportional growth is constant.

Sigmoid growth curve

A sigmoid growth curve is an S-shaped graph of population size over time. Growth starts rapidly, then slows, and finally levels near carrying capacity. The expected phases are exponential, transitional and plateau. A lag phase is not required in this syllabus version, so do not force one into every answer.

Model

A model is a simplified representation of a system used to describe, explain or predict patterns. The sigmoid curve is an idealized graphical model. Its strength is clarity: it shows how limited resources and density-dependent factors can slow growth. That clarity is also its weakness. Real populations may fluctuate, crash, migrate, be harvested, or be hit by unusual weather. Models help biologists test ideas against data, but they are not the ecosystem itself.

Sigmoid growth is easy to model in the lab with organisms that reproduce quickly and can be kept under controlled conditions. Duckweed is a small floating aquatic plant that produces new fronds as it grows. Yeast is a unicellular fungus that can reproduce asexually by budding. Both work well in a school investigation because the population size can change enough to measure over a short time.

A good duckweed investigation begins with a small number of fronds in containers of nutrient solution. Keep variables such as light intensity, temperature, container surface area and nutrient concentration controlled, unless one of these is the independent variable. Count the fronds at regular intervals, or use image analysis if it’s available. With yeast, population growth can be tracked using cell counts, turbidity or another calibrated measure of cell density.

The experimental conditions are kept deliberately simple: plenty of resources at the start, no predators, no competing species and a closed container. That’s what makes it a model. We strip the system back to show the underlying pattern, then compare it with natural populations, which are usually much messier.

As data are collected, plot population size against time and watch for the curve becoming less steep as resources start to limit growth. In duckweed, carrying capacity may depend on surface area, light or nutrients. In yeast, it may depend on sugar availability, waste products, oxygen availability or space. The practical link is clear: biological capacity is limited by the factor that prevents further increase.

An intraspecific relationship is an interaction between individuals of the same species. Since members of a species usually need the same resources, intraspecific competition is common. They may compete for food, water, light, mates, nesting sites, territories or pollinators.

Intraspecific competition can be intense because the organisms often have almost identical niches. Seedlings of the same tree species compete for light and mineral ions. Male deer may compete for access to females. Barnacles of the same species compete for attachment space on rock. Individuals that get more of the limiting resource are more likely to survive and reproduce, so competition can contribute to natural selection.

Cooperation is an interaction in which individuals act in ways that increase the success or survival of others as well as, directly or indirectly, themselves. When it occurs within a species, cooperation is also intraspecific. Wolves hunting in packs can capture prey that one wolf could not. Penguins huddle to reduce heat loss. Meerkats give alarm calls. Some birds share parental care in crèches.

Competition and cooperation can happen in the same population at the same time. A shoal of fish cooperates in predator avoidance, but the same fish may compete for food. That’s the useful ecological habit of mind: don’t label a species as “cooperative” or “competitive” as if it can only be one. Ask which resource, which behaviour and which conditions.

A community is all the populations of different species living and interacting in an ecosystem. A population is one species in an area; put those living populations together, and you have a community. It includes plants, animals, fungi, bacteria and other microorganisms.

An ecosystem is a biological system made of a community of organisms interacting with the non-living environment. The community is the living part. The ecosystem includes that living community plus abiotic factors such as light, temperature, water, mineral ions, pH, salinity and substrate.

Communities depend on interdependence. A flowering plant may rely on pollinators, herbivores, decomposers, mycorrhizal fungi and seed dispersers. A predator depends on prey, while the prey population may also be shaped by predation pressure. Bacteria and fungi recycle nutrients from dead organisms, allowing producers to keep growing.

That is why population sizes in a community regulate one another. A population does not simply grow according to its own reproductive rate; food supply, competitors, predators, parasites, pathogens and mutualists all push and pull on it. The guiding idea for the topic is that populations are embedded in networks of interaction.

An interspecific relationship is an interaction between organisms of different species. Ecologists sort these interactions by how they affect the species involved.

These categories make interdependence easier to describe precisely. The same pair of species may be involved in more than one relationship, depending on life stage or context, so name the category and describe the evidence too.

Mutualism needs to be kept separate from casual “helping”. A mutualism is an interspecific relationship where both species gain a benefit that improves survival, growth or reproduction. Usually, the two partners bring different abilities to the association.

Root nodules in Fabaceae

Fabaceae, the legume family, includes peas, beans, clover and many related plants. Many of these plants have root nodules containing nitrogen-fixing bacteria, bacteria that convert nitrogen gas into ammonium compounds usable by plants. The plant gives the bacteria sugars from photosynthesis and a protected low-oxygen nodule environment. In return, the bacteria provide fixed nitrogen, which helps the plant make amino acids, nucleotides and other nitrogen-containing compounds. In nitrogen-poor soils, this can give legumes a competitive advantage.

Mycorrhizae in Orchidaceae

A mycorrhiza is a mutualistic association between a fungus and plant roots, with materials exchanged between them. Orchids depend on this strongly because orchid seeds have tiny food reserves. Fungal hyphae can enter young orchid tissues and provide mineral nutrients, water and carbon compounds during early growth. Once the orchid photosynthesizes, it can supply sugars to the fungus. Here, the fungus improves nutrient and water acquisition; the orchid supplies photosynthetic carbon once established.

Zooxanthellae in hard corals

Zooxanthellae are photosynthetic unicellular algae living inside the cells of many reef-building hard corals. The coral provides shelter, carbon dioxide from respiration and a position in shallow, well-lit water. The algae provide oxygen and organic compounds such as sugars and amino acids made by photosynthesis. This mutualism helps explain why coral reefs can be highly productive in nutrient-poor tropical seas.

In examinations, common names or scientific names are acceptable when referring to organisms, but the relationship and benefits to both partners must be clear.

An endemic species is a species native to, and naturally restricted to, a particular geographical area. An invasive species is an introduced species that spreads in a new area and causes ecological, economic or health harm. Many introduced species never become invasive. Trouble starts when the newcomer has a competitive advantage.

Resource competition is often the mechanism behind the decline. An introduced species may grow faster, reproduce earlier, tolerate wider conditions, avoid local predators, or use a resource more efficiently than endemic species. When it takes light, food, nesting space, water or mineral nutrients, endemic populations can fall.

A clear New Zealand example is the introduced common wasp and German wasp in beech forests. These wasps feed heavily on honeydew produced by scale insects on beech trees. Honeydew is also an important food for endemic birds and insects. In years with high wasp densities, wasps can remove a large share of available honeydew. That gives them a resource-acquisition advantage and leaves less food for endemic species. Their success is not mysterious: abundant food, rapid colony growth and few effective natural controls allow them to dominate a shared resource.

For your own local study, follow the same structure: name the invasive species, name the endemic or native species affected, identify the shared resource, then explain the competitive advantage in acquiring that resource.

A pattern may point to interspecific competition, but it doesn’t prove it. If species A is more common where species B is absent, competition could explain the pattern. So could different abiotic preferences, predation, disease, dispersal limits or historical chance.

Hypothesis

A hypothesis is a testable proposed explanation for an observed pattern. “Species B reduces the abundance of species A by competing for space” is a hypothesis, and it can be tested in several ways.

Observation

An observation is a study in which researchers record patterns without deliberately changing the system. Field observations using random sampling can show whether two species tend not to occur together. They often reflect real conditions well, but confounding variables are harder to control.

Experiment

An experiment is a study in which researchers deliberately change one variable to test its effect while controlling other variables as far as possible. In the laboratory, researchers can place two species together or apart under controlled conditions. In the field, they can remove one species from some plots and compare the response with control plots where it remains.

The strongest evidence usually comes from agreement between approaches: random field data show a negative association, removing one species increases the other, and laboratory work confirms that both species use the same limiting resource. Even then, phrase the conclusion carefully. “Supports competition” is safer than “proves competition” unless alternative explanations have genuinely been ruled out.

You can use the chi-squared test for association when you record whether two species are present or absent across many sampling sites. Sort the results into four categories: both species present, species A only, species B only, and neither species present.

The null hypothesis is a testable statement that there is no association between the two species’ distributions. Here, it says the presence of species A is independent of the presence of species B.

Worked 2 × 2 presence/absence table for testing association between two species across 50 sites.

For each category, work out the expected frequency using the row and column totals.

Next calculate

For a $2 \times 2$ presence/absence table,

Compare $\chi^2$ with the critical value for the chosen significance level and degrees of freedom. If $\chi^2$ is larger than the critical value, reject the null hypothesis and conclude that there is evidence of an association.

A negative association means the two species occur together less often than expected, which may provide evidence for interspecific competition. A positive association means they occur together more often than expected, which may suggest shared habitat preferences or mutualistic effects. The test shows association, not cause; ecological interpretation still matters.

A predator–prey relationship can regulate population size because predation pressure often changes with prey density. When prey are abundant, predators find food more easily. They survive better and reproduce more. As predator numbers increase, more prey are killed, so the prey population falls. Once prey become scarce, predators have less food, and predator survival or reproduction drops. The prey population can then recover.

The classic real case study is the Canada lynx and snowshoe hare in the northern forests of North America. Historical fur-trapping records show repeated cycles in their numbers. Hare numbers usually rise first. Lynx numbers rise after a delay, because reproduction takes time. Increased lynx predation helps cause the later fall in hare numbers, and food shortage then helps cause the fall in lynx numbers.

This is density-dependent control: predators have a stronger effect on the prey when prey are dense and easier to encounter. It is not the only factor in the hare cycle. Food quality, vegetation, disease and weather may also contribute. Good ecological explanations usually combine factors, rather than pretending that one interaction explains everything.

Predator–prey cycles also show how populations in communities depend on each other. Hare availability partly controls the lynx population from below, while lynx predation partly controls the hare population from above.

Top-down control

Top-down control is regulation of population size by consumers at higher trophic levels, such as predators, herbivores or parasites. If sea otters reduce sea urchin numbers, kelp can increase because grazing pressure falls. Here, the controlling influence moves down the food chain.

Bottom-up control

Bottom-up control is regulation of population size by resource availability at lower trophic levels, such as light, mineral nutrients, primary productivity or prey abundance. If drought reduces plant growth, herbivore numbers may fall. Predators may then decline later because prey are scarce. Here, the controlling influence moves up the food chain.

Both types of control can act in the same community. The key question is which one dominates under the conditions being studied. In a nutrient-poor lake, phytoplankton may be mainly limited from below by phosphate availability. In another lake, zooplankton grazing may strongly reduce phytoplankton. In a grassland, rainfall may set plant biomass in dry years, while herbivore grazing may dominate in wetter years.

This connects back to models. A simple food-chain diagram is a model: it removes some complexity so we can ask whether control mainly comes from resources or from consumers. Its benefit is focus; its limitation is that real communities contain many species and feedback loops.

Allelopathy is a biological interaction where a plant, alga, fungus or microorganism releases a chemical into its surroundings, affecting the growth, survival or reproduction of nearby organisms. In this topic, treat allelopathy mainly as a way to deter competitors.

Black walnut is a common example. It releases juglone from its roots, leaves and fruit husks. Juglone can inhibit the growth of some neighbouring plant species, which reduces competition for water, mineral ions and light around the walnut tree. The effect is not the same for every species; some plants tolerate juglone better than others.

An antibiotic is a chemical produced by a microorganism that inhibits or kills other microorganisms. In soil, a microorganism can secrete antibiotics to reduce nearby bacterial competitors. For example, Penicillium fungi release penicillin-like compounds that inhibit susceptible bacteria, giving the fungus better access to organic matter and space.

Allelopathy and antibiotic secretion work in a similar way: both release chemicals into the external environment to reduce potential competitors. The main difference is in the organisms and targets usually discussed. Allelopathy is often used for plants affecting neighbouring plants, while antibiotics are classically used for microorganisms affecting other microorganisms.

Where possible, add a local example to your own notes. Use the same structure: name the producer, name the chemical if known, identify the affected competitor, and state which resource competition is reduced.