What is a population?
A population is all the members of one species living in one place at one time and able to breed with each other. Example: all the lotus plants in one lake, or all the chital deer in one forest.
A single animal is born and dies, but it has no birth rate. Only a group has rates. So a population has special features, called population attributes:
- Density (N): number per unit area or volume. When counting is hard we use other measures: percent cover for grass, biomass for big trees, or indirect signs like pugmarks and droppings for tigers.
- Birth rate (natality): number born per member per unit time.
- Death rate (mortality): number dying per member per unit time.
- Sex ratio: share of females and males, e.g. 60% female.
- Age structure: how many are young, adult and old.
Birth rate and death rate
Rates are always per member. If a pond has 20 frogs and 8 new frogs hatch in a year, the birth rate is 8 ÷ 20 = 0.4 per frog per year. If 4 out of 40 fruit flies die in a week, the death rate is 4 ÷ 40 = 0.1 per fly per week.
The growth equation
Four things change N between time t and t + 1:
N(t+1) = N(t) + [(B + I) − (D + E)]
B = births, I = immigration (coming in), D = deaths, E = emigration (going out). Births and deaths matter most in normal times. Immigration becomes big when a new place is being colonised.
Age structure and age pyramids
Put the population into three groups: pre-reproductive (too young to breed), reproductive and post-reproductive (too old). Draw each group as a bar, youngest at the bottom. The shape tells the future:
- Triangle with a wide base: many young → the population will grow (expanding).
- Bell shape: young ≈ breeding adults → numbers stay about the same (stable).
- Urn shape (narrow base): fewer young than adults → the population will shrink (declining).
For people this is called an age pyramid. It helps a government plan schools, jobs and old-age care.
Population growth: exponential (J-curve)
If food and space are unlimited, every member keeps breeding at full speed. Let b = birth rate and d = death rate per member. The intrinsic rate of natural increase is r = b − d.
dN/dt = rN. Growth speed is proportional to N itself, so a bigger population grows even faster. The graph of N against time is a J-shaped curve.
Solving it gives N(t) = N₀ e^(rt), where N₀ is the starting number and e ≈ 2.718. Some values of r: Norway rat about 0.015, flour beetle about 0.12 per day (real studies). Such fast growth cannot last in nature.
Population growth: logistic (S-curve) and carrying capacity
Real habitats have limited food and space. The largest number a habitat can support for a long time is its carrying capacity (K).
dN/dt = rN (1 − N/K) (Verhulst–Pearl logistic growth).
- When N is small, (1 − N/K) ≈ 1, so growth looks exponential (lag and fast phase).
- When N = K/2, growth is fastest.
- When N reaches K, (1 − N/K) = 0, so growth stops (plateau).
The graph is S-shaped (sigmoid). Most real populations follow this model, so it is called more realistic.
Life history in one line
Species evolve the best way to breed for their habitat: some breed once in life (Pacific salmon, bamboo), others many times (most birds, mammals); some make many tiny young (oysters), others a few large ones (birds, mammals).
Population interactions: the sign table
Two species living together can help, harm or ignore each other. Write + for gain, − for loss, 0 for no effect.
| Interaction | Species A | Species B |
|---|---|---|
| Mutualism | + | + |
| Competition | − | − |
| Predation | + | − |
| Parasitism | + | − |
| Commensalism | + | 0 |
| Amensalism | − | 0 |
Predation, parasitism and commensalism need the two species to live close together.
Mutualism
Both partners gain.
- Lichen: a fungus and an alga (or cyanobacterium). The alga makes food; the fungus gives shelter and holds water.
- Mycorrhiza: fungi on plant roots take in phosphorus for the plant; the plant gives them sugar.
- Fig and fig wasp: each fig species is pollinated by one wasp species; the wasp lays eggs inside the fig and its larvae feed on some seeds.
- Orchids and bees: the Ophrys orchid petal looks like a female bee, so male bees try to mate with it and carry pollen (sexual deceit).
Partners often co-evolve: if one changes, the other must change too.
Competition
Both lose, because they want the same limited resource (food, light, space). It happens between species that are related and also between unrelated ones (flamingos and fish in a South American lake both eat zooplankton).
- Interference: one species can reduce the other's feeding even when food is plenty (e.g. goats on the Galapagos Islands made Abingdon tortoises vanish within ten years).
- Gause's competitive exclusion principle: two species competing for exactly the same resource cannot live together forever; the weaker one is removed.
- Resource partitioning: species escape by sharing the resource differently. MacArthur found five warbler species living on the same tree by feeding at different heights and branches.
- Removing a stronger competitor lets the other spread: barnacle Balanus pushes out Chthamalus on rocky shores.
Predation
The predator (+) kills and eats the prey (−). Herbivores eating plants are also predators in ecology.
Why predators matter
- They pass energy from plants to higher trophic levels.
- They keep prey numbers in check. The prickly pear cactus spread over millions of hectares in Australia until a moth that eats cactus was brought in (biological control).
- They keep many species alive by stopping one strong competitor from winning (Pisaster starfish removal caused 10+ species to vanish).
How prey defend themselves
Camouflage (frogs, insects), poison (monarch butterfly tastes bad because its caterpillar eats a poisonous weed), and in plants thorns (cactus, Acacia) and chemicals (Calotropis makes heart-harming glycosides; nicotine, caffeine and quinine also started as plant defences).
Parasitism, commensalism and amensalism
Parasitism (+/−): the parasite lives on or in the host and takes food from it without killing it at once.
- Ectoparasites live outside: lice on humans, ticks on dogs, and the plant Cuscuta (dodder) on hedge plants.
- Endoparasites live inside: tapeworm, liver fluke, Plasmodium. They often lose unneeded organs and make huge numbers of eggs. Many need more than one host (liver fluke needs a snail and a fish).
- Brood parasitism: the koel lays eggs in the crow's nest; its eggs look like crow eggs so the crow raises the chicks.
Commensalism (+/0): an orchid growing on a mango branch; barnacles on a whale; cattle egret eating insects stirred up by grazing cattle; sea anemone and clown fish.
Amensalism (−/0): the mould Penicillium releases penicillin that kills bacteria while the mould is not affected.
What the board exam asks
The unit Ecology carries about 10 marks. Common questions: write and explain the logistic equation, draw J and S curves, calculate a birth/death rate, draw age pyramids, and name the interaction with its signs and an example (especially orchid-bee, fig-wasp, koel-crow, Cuscuta, cattle egret, Gause's principle). Draw the table of signs; it makes a 2-mark answer fast and neat.
Key formulas and definitions
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Worked examples
1. A 5 m² patch of grass has 150 dandelion plants. Find the density.
Density = N ÷ area = 150 ÷ 5 = 30 plants per m².
2. A pond had 50 frogs. In a year 20 tadpoles grew into frogs and 10 frogs died. Find the birth rate and death rate.
Birth rate = 20 ÷ 50 = 0.4 per frog per year. Death rate = 10 ÷ 50 = 0.2 per frog per year.
3. A deer herd had 300 animals. In one year: 60 births, 25 deaths, 10 came in, 15 went out. Find N after one year.
N(t+1) = 300 + (60 + 10) − (25 + 15) = 300 + 70 − 40 = 330 deer.
4. Using the herd above, find r (ignore migration) and say if it grows or shrinks.
b = 60/300 = 0.2, d = 25/300 ≈ 0.083. r = b − d ≈ 0.117 per year. r is positive, so the herd grows.
5. A bacterial culture starts with 1000 cells and r = 0.693 per hour, with unlimited food. How many cells after 3 hours?
N = N₀e^(rt) = 1000 × e^(0.693 × 3) = 1000 × e^(2.079) ≈ 1000 × 8 = 8000 cells. (e^0.693 = 2, so it doubles every hour: 1000 → 2000 → 4000 → 8000.)
6. In a logistic population K = 500 and r = 0.2 per year. Find dN/dt when N = 100 and when N = 250.
N = 100: dN/dt = 0.2 × 100 × (1 − 100/500) = 20 × 0.8 = 16 per year. N = 250: 0.2 × 250 × (1 − 0.5) = 50 × 0.5 = 25 per year (the fastest, because N = K/2).
7. Same population: what is dN/dt when N = 500? What does that mean?
dN/dt = 0.2 × 500 × (1 − 500/500) = 100 × 0 = 0. The population has reached carrying capacity: births balance deaths, and the S-curve is flat.
8. A population has r = 0.035 per year and grows exponentially. Find its doubling time.
t = 0.693 ÷ 0.035 ≈ 19.8 years, about 20 years.
9. Name the interaction and signs: (a) cattle egret with grazing buffalo, (b) Cuscuta on a hedge, (c) Balanus and Chthamalus on rocks.
(a) Commensalism (+/0): egret gains insects, buffalo neither gains nor loses. (b) Parasitism (+/−): Cuscuta takes food from the host. (c) Competition (−/−): both want the same rock space; Balanus wins.
Common mistakes
- Saying a single organism has a birth rate. Rates belong only to populations.
- Mixing up r and K: r is how fast a population grows per member; K is the maximum the habitat can support.
- Thinking logistic growth is fastest near K. It is fastest at N = K/2 and becomes zero at K.
- Calling the orchid on a mango tree a parasite. It only uses the branch for support and makes its own food: commensalism (+/0).