In the logistic growth equation dN/dt = rN[(K−N)/K], the symbol K represents the:

Carrying capacity of the environment

People who move to high altitudes gradually acclimatise by:

Producing more red blood cells and increasing their breathing rate

Producing fewer red blood cells

Lowering their body temperature permanently

Organisms and Populations — Adaptations, Population Growth and Interactions

Ecology begins here at two levels — the individual organism and the population — and each has one idea worth mastering. For the organism, it is adaptation: how living things cope with temperature, water and other stresses, learnt best through named examples. For the population, it is the two growth curves: the J-shaped (exponential) curve of unlimited growth versus the S-shaped (logistic) curve that levels off at the carrying capacity (K) when resources run short. The most examined block is population interactions — mutualism, competition, predation, parasitism, commensalism, amensalism — which are simply classified by who benefits and who is harmed. Build a +/− table for the interactions and learn the growth equations, and this chapter is very scoring.

Adaptations of Organisms

Responses to a stressful environment: regulate (keep the internal state constant, e.g. mammals maintaining body temperature — costly but stable), conform (let the internal state track the surroundings, e.g. most animals and plants), migrate, or suspend (spores, hibernation, aestivation).
Allen's rule: mammals in cold climates have shorter ears and limbs, to reduce heat loss. Kangaroo rats meet their water need by internal fat oxidation. Desert plants have thick cuticles, sunken stomata, and CAM photosynthesis.
Altitude sickness in the thin air of high mountains is met by adaptation — the body makes more red blood cells and increases breathing, raising oxygen capture. This is acclimatisation, a physiological adjustment.

🎯 Regulator versus conformer — the cost of holding steady

Faced with a changing environment, organisms take one of two broad strategies, and the trade-off between them is a favourite conceptual question. A regulator keeps its internal conditions — temperature, water balance, osmotic concentration — constant regardless of the outside. Birds and mammals are the classic thermoregulators, holding a steady body temperature whether it is freezing or scorching outside. This constancy is valuable because the body's biochemistry runs best at a fixed temperature, but it is energetically expensive: keeping warm in the cold or cool in the heat costs a great deal of energy, which is why regulators need to eat a lot. A conformer, by contrast, lets its internal state simply follow the environment — its body temperature rises and falls with the surroundings. The great majority of animals and nearly all plants are conformers, because for a small organism the cost of regulating would be prohibitive: the surface area is large relative to volume, so heat is lost or gained too fast to fight economically. So the deeper point is a cost–benefit balance: regulation buys stable internal conditions at a high energy price, and conformity saves that energy at the price of a fluctuating internal state. Small organisms usually cannot afford to regulate, which is why thermoregulation is largely a large-animal strategy.

Population Growth

Two models of population growth
Model	Curve	When
Exponential	J-shaped; dN/dt = rN	Unlimited resources — growth accelerates without bound
Logistic	S-shaped (sigmoid); dN/dt = rN[(K−N)/K]	Limited resources — levels off at the carrying capacity K

🧠 J or S? It comes down to whether resources run out

The two growth curves look intimidating with their equations, but the choice between them turns on a single physical question: are resources unlimited or limited? With unlimited food and space, a population grows exponentially — each generation multiplies the last with nothing to stop it — giving the ever-steepening J-shaped curve described by dN/dt = rN, where r is the intrinsic rate of natural increase (births minus deaths per individual). No real population can sustain this for long, because resources are always finite. So in the real world growth follows the logistic (S-shaped) curve: it starts slowly (a lag), then speeds up, but as the population approaches the carrying capacity K — the maximum the environment can support — resource shortage slows it, and it levels off at K. The extra term [(K−N)/K] in the logistic equation is exactly this brake: when N is small it is near 1 (growth is nearly exponential), and as N approaches K it shrinks toward 0 (growth stops). So the exam shortcut is: unlimited resources → J-curve → dN/dt = rN; limited resources → S-curve → levels at K. Any real, long-term population is logistic, because carrying capacity always eventually bites.

Population Interactions

Who benefits (+), who is harmed (−), who is unaffected (0)
Interaction	Species A / B	Example
Mutualism	+ / +	Lichen (fungus + alga); mycorrhiza; pollinator + flower
Competition	− / −	Two species contesting the same limited resource
Predation / Parasitism	+ / −	Predator kills prey; parasite lives on/in a host
Commensalism	+ / 0	Orchid on a tree; barnacle on a whale
Amensalism	− / 0	Penicillium releasing penicillin, killing bacteria

ℹ️ Read every interaction as a pair of signs

The six population interactions become effortless once you stop learning them as names and start reading them as a pair of signs — a plus, minus or zero for each of the two species. Mutualism (+/+): both benefit, as in a lichen where the fungus gets food from the alga and the alga gets shelter and water; the pollinator–flower and the mycorrhiza are the same story. Competition (−/−): both are harmed because they contest the same limited resource. Predation and parasitism (+/−): one gains at the other's expense — a predator eating prey, or a parasite feeding on a host. Commensalism (+/0): one benefits and the other is neither helped nor harmed, like an orchid growing on a tree branch just for support, or a barnacle riding a whale. Amensalism (−/0): one is harmed and the other is unaffected, the classic case being a mould releasing an antibiotic that kills nearby bacteria without the mould gaining anything measurable. Draw the two-column sign table and every matching question — "name the interaction where one benefits and the other is unharmed" — is answered by reading off the signs, with commensalism (+/0) and amensalism (−/0) being the pair students most often swap.

Key takeaways

Regulators keep internal conditions constant (costly, e.g. mammals); conformers track the environment (cheap, most life).
Allen's rule: cold-climate mammals have shorter ears/limbs to cut heat loss; altitude → more RBCs.
Exponential growth = J-curve, dN/dt = rN, unlimited resources; r = intrinsic rate of natural increase.
Logistic growth = S-curve, dN/dt = rN[(K−N)/K], limited resources, levels off at carrying capacity K.
Mutualism +/+; competition −/−; predation & parasitism +/−; commensalism +/0; amensalism −/0.
Lichen (fungus+alga) and mycorrhiza are mutualism; an orchid on a tree is commensalism.
Commensalism (+/0) versus amensalism (−/0) is the pair most often confused — check who is HARMED.
In the logistic equation the term (K−N)/K is the brake: near 1 when N is small, near 0 as N→K.

Practice questions (8)

Attempt each one before opening the answer. Every explanation names the tempting wrong option as well as the right one, because that is where marks are lost.

A population growing in a habitat with unlimited resources shows which type of growth curve?
1. A J-shaped (exponential) curve
2. An S-shaped (logistic) curve
3. A straight horizontal line
4. A steadily falling curve
Show answer
Answer: A — A J-shaped (exponential) curve
With no resource limit, growth accelerates without bound, tracing the J-shaped exponential curve dN/dt = rN. The S-shaped curve appears only when limited resources impose a carrying capacity, so it describes the realistic, resource-limited case instead.
In the logistic growth equation dN/dt = rN[(K−N)/K], the symbol K represents the:
1. Carrying capacity of the environment
2. Intrinsic rate of natural increase
3. Initial population size
4. Number of predators
Show answer
Answer: A — Carrying capacity of the environment
K is the carrying capacity — the maximum population the environment can sustain — and growth slows as N approaches it. The intrinsic rate of increase is r, a different symbol in the same equation, so confusing K with r mixes up the two constants.
An orchid growing as an epiphyte on the branch of a tree, gaining support but neither helping nor harming the tree, is an example of:
1. Commensalism (+/0)
2. Mutualism (+/+)
3. Parasitism (+/−)
4. Amensalism (−/0)
Show answer
Answer: A — Commensalism (+/0)
The orchid benefits from support while the tree is unaffected, which is commensalism (+/0). Mutualism would need the tree to benefit too, and parasitism would need it to be harmed, so those change the sign for the tree.
A lichen, in which a fungus and an alga live together to each other's benefit, is an example of:
1. Mutualism
2. Competition
3. Commensalism
4. Predation
Show answer
Answer: A — Mutualism
Both partners benefit — the alga supplies food by photosynthesis and the fungus supplies shelter and minerals — which is mutualism (+/+). Commensalism would leave one partner unaffected, so it cannot describe a relationship where both clearly gain.
A mammal that keeps its body temperature constant regardless of the external temperature is called a:
1. Regulator
2. Conformer
3. Migrator
4. Suspender
Show answer
Answer: A — Regulator
Maintaining a constant internal temperature despite the environment defines a regulator, at the cost of high energy expenditure. A conformer does the opposite — its temperature tracks the surroundings — so it is the contrasting strategy, not the one described.
The release of penicillin by the mould Penicillium, which kills nearby bacteria while the mould itself is unaffected, is an example of:
1. Amensalism (−/0)
2. Commensalism (+/0)
3. Mutualism (+/+)
4. Competition (−/−)
Show answer
Answer: A — Amensalism (−/0)
The bacteria are harmed while Penicillium gains nothing measurable, giving the −/0 pattern of amensalism. Commensalism is +/0 — one benefits — so it has the wrong sign for the mould, which is the pair students most often swap.
People who move to high altitudes gradually acclimatise by:
1. Producing more red blood cells and increasing their breathing rate
2. Producing fewer red blood cells
3. Lowering their body temperature permanently
4. Stopping all physical activity
Show answer
Answer: A — Producing more red blood cells and increasing their breathing rate
The thin, oxygen-poor air prompts the body to make more red blood cells and breathe faster, raising oxygen capture — a physiological adaptation called acclimatisation. Making fewer red cells would worsen oxygen delivery, the opposite of what acclimatisation achieves.
In the exponential growth equation dN/dt = rN, the symbol r stands for the:
1. Intrinsic rate of natural increase (births minus deaths per individual)
2. Carrying capacity
3. Total number of species
4. Rainfall in the habitat
Show answer
Answer: A — Intrinsic rate of natural increase (births minus deaths per individual)
r is the intrinsic rate of natural increase, the per-capita difference between birth and death rates that drives exponential growth. Carrying capacity is K, a separate term that appears only in the logistic equation, so equating r with K confuses the two.