Population attributes and age pyramids
A village has 20 lotus plants one year and 8 new plants the next. Counting births, deaths and the proportion of young and old gives a picture of how the group will change.
A population is a group of individuals of the same species living in a defined area and sharing or competing for resources. It has attributes that individuals do not have: birth rate, death rate, sex ratio, age distribution and population density (size). The proportions of the pre-reproductive, reproductive and post-reproductive groups are shown as an age pyramid.
In the figure : A bell-shaped or stable pyramid: the three age groups are in balance.
In the figure : The shape of the pyramid shows whether the population is growing, stable or declining.
Rule 1: Birth rate, death rate, sex ratio — Birth and death rates are measured per capita (per individual). If 8 new lotus plants are born in a year from 20, the birth rate is 8/20 = 0.4 per plant per year. If 4 of 40 flies die in a week, the death rate is 4/40 = 0.1 per fly per week. Sex ratio is the ratio of males to females, for example 60 per cent females and 40 per cent males.
- Easy : Birth rate = births ÷ initial number.
- Medium : If 5 of 50 mice die, the death rate is 0.1.
- Exam-type : Q: What is the birth rate if 6 new plants appear in a population of 30? A: 0.2 per plant.
Rule 2: Population density and size — Density may be measured by numbers, biomass or per cent cover. Density is affected by four factors: natality and immigration (increase), and mortality and emigration (decrease). New habitats may gain more from immigration than from births.
- Easy : Immigration increases density.
- Medium : Emigration reduces density.
- Exam-type : Q: Name the factors that increase population density. A: Natality and immigration.
Population density at time t+1 = N + [(B + I) – (D + E)], where B = births, D = deaths, I = immigrants, E = emigrants.
Writing density as the number of births. Density is the number (or biomass) of individuals per unit area.
Memory clue: B-I up, D-E down — Birth and Immigration increase; Death and Emigration decrease.
Spot the difference
| Point | Natality | Mortality |
|---|---|---|
| Meaning | Number of births | Number of deaths |
| Effect on density | Increases it | Decreases it |
| Partner factor | Immigration | Emigration |
Practice questions
- 1Define a population.
- 2Which two factors increase the density of a population?
- 3What does an age pyramid show?
- 4Name two attributes of a population that an individual lacks.
- 5What is emigration?
- 6What does a broad base in an age pyramid mean?
- 7In a pond of 80 fish, 8 are born in a month. What is the birth rate?
- 8Why is immigration important in a newly colonised habitat?
Show answers (try them yourself first)
- 1A group of individuals of the same species living in a defined area.
- 2Natality and immigration.
- 3The proportion of pre-reproductive, reproductive and post-reproductive age groups.
- 4Any two of birth rate, death rate, sex ratio, age distribution.
- 5Number of individuals leaving the habitat.
- 6Many young individuals; the population is growing.
- 78/80 = 0.1 per fish per month.
- 8Few individuals are present, so immigrants contribute more than births.
Population growth: exponential and logistic
A few bacteria in a flask double again and again, but not forever; when the food runs out, the growth slows and stops.
When resources are unlimited, growth is exponential: dN/dt = rN, where N is the population size, r the intrinsic rate of natural increase (r = b – d), and the curve is J-shaped. In nature resources are limited, so growth is logistic (Verhulst–Pearl): dN/dt = rN (K – N) / K, where K is the carrying capacity. The curve is S-shaped.
In the figure : The logistic curve has a lag phase, an exponential phase and then a stationary phase at K.
In the figure : When N reaches K, births equal deaths and the population stops growing.
Rule 1: Exponential growth — If the population starts with N₀ individuals, then N at time t is N₀ e^(rt). A larger r means faster growth. This is the growth pattern when food and space are unlimited, as in Paramecium in the early phase of a culture.
- Easy : r = b – d.
- Medium : If r is zero, there is no growth.
- Exam-type : Q: Why is the exponential curve J-shaped? A: The number increases faster and faster as the population gets bigger.
Rule 2: Logistic growth and life history — The environment can support only a limited number of individuals, its carrying capacity (K). As N approaches K, the factor (K – N)/K becomes smaller and growth slows. Life history traits evolve to maximise fitness: some breed once (Pacific salmon, bamboo), some many times (birds, mammals); some make many small offspring (oysters), others few large ones (mammals).
- Easy : Pacific salmon breeds once in its life.
- Medium : Mammals produce few, large offspring.
- Exam-type : Q: What is carrying capacity? A: The maximum number of individuals a habitat can support.
Exponential: dN/dt = rN. Logistic: dN/dt = rN (K – N)/K. At N = K, dN/dt = 0.
Thinking that the logistic curve keeps rising. It levels off at K.
Memory clue: J → Jump, S → Settle — J curve jumps up forever; S curve settles at K.
Spot the difference
| Point | Exponential growth | Logistic growth |
|---|---|---|
| Curve shape | J | S |
| Resources | Unlimited | Limited |
| Final size | No limit | Limited to K |
Practice questions
- 1What does r stand for?
- 2What is K?
- 3What is the shape of the logistic growth curve?
- 4Write the equation for exponential growth.
- 5Which curve is typical when resources are unlimited?
- 6Name one organism that breeds only once in its life.
- 7If K = 1000 and N = 1000, what is dN/dt in logistic growth?
- 8If b = 0.3 and d = 0.1, find r and say whether the population grows.
Show answers (try them yourself first)
- 1The intrinsic rate of natural increase.
- 2The carrying capacity of the environment.
- 3S-shaped (sigmoid).
- 4dN/dt = rN.
- 5The J-shaped exponential curve.
- 6Pacific salmon (or bamboo).
- 7Zero, since (K – N) = 0.
- 8r = 0.2; positive, so the population grows.
Population interactions: predation and competition
A lion hunting a deer, two cattle species sharing a pasture, a prickly pear cactus spreading over farmland: all are species affecting each other.
Interactions between two species are classified by the effect on each: predation and parasitism (+ –), competition (– –), commensalism (+ 0), amensalism (– 0) and mutualism (+ +). In predation, predators transfer energy, control prey numbers and keep diversity. Competition lowers the fitness of one species in the presence of another.
In the figure : + means benefit, – means harm, 0 means no effect.
In the figure : Competition can occur even when resources are not limiting (interference).
Rule 1: Predation — Predators keep the prey population in check; without predators, exotic invaders like the prickly pear cactus in Australia in the 1920s spread over millions of hectares until the cactus-feeding moth (Cactoblastis) was introduced. Prey have defences: camouflage, poison (monarch butterfly), thorns, chemicals such as cardiac glycosides in Calotropis.
- Easy : Predators control prey numbers.
- Medium : Cactoblastis moth controlled prickly pear.
- Exam-type : Q: How do plants defend themselves from herbivores? A: Thorns, spines, toxic chemicals (cardiac glycosides, nicotine, caffeine, quinine, strychnine).
Rule 2: Competition — Gause's competitive exclusion principle: two closely related species competing for the same limited resources cannot coexist indefinitely; the inferior is eliminated (Paramecium experiments). Connell's barnacle Balanus excluded Chthamalus on rocky intertidal. Species avoid this by resource partitioning: MacArthur's five warbler species feeding on different parts of the same tree. Competitive release occurs when a superior competitor is removed.
- Easy : Competitive exclusion: one species wins.
- Medium : Resource partitioning allows coexistence.
- Exam-type : Q: What is resource partitioning? A: Different species use the same resource at different times or places to avoid competition.
Competition can also happen between unrelated species (flamingos and fish both feed on zooplankton in lakes).
Thinking competition always needs limiting resources. Interference competition occurs even if resources are abundant.
Memory clue: PPC-MA — Predation, Parasitism, Competition, Mutualism, Amensalism — plus Commensalism.
Spot the difference
| Point | Predation | Competition |
|---|---|---|
| Effect | + for predator, – for prey | – for both |
| Example | Tiger and deer | Flamingo and fish for zooplankton |
| Result | Energy transfer | Exclusion or partitioning |
Practice questions
- 1Name the principle of Gause.
- 2What is predation?
- 3Give one chemical defence of a plant.
- 4What is resource partitioning?
- 5Who studied warblers?
- 6What is competitive release?
- 7How was the prickly pear controlled in Australia?
- 8Why are predators important for biodiversity?
Show answers (try them yourself first)
- 1The competitive exclusion principle.
- 2An interaction in which one animal kills and feeds on another.
- 3Cardiac glycosides in Calotropis (or nicotine, caffeine, quinine).
- 4Use of resources by competing species in different ways or at different times.
- 5MacArthur.
- 6Expansion of the range of a species when its competitor is removed.
- 7By introducing the cactus-feeding moth Cactoblastis.
- 8They reduce competition among prey species so that more species coexist.
Parasitism, commensalism, amensalism and mutualism
A tick on a dog, an orchid on a mango branch, a lichen on a rock: very different lifestyles, each with a different pattern of give and take.
In parasitism the parasite benefits and the host is harmed. Ectoparasites live on the host (lice, ticks, Cuscuta); endoparasites live inside (liver fluke, tapeworm, Plasmodium). In brood parasitism a bird lays eggs in another bird's nest. Commensalism: one benefits, the other is unaffected. Mutualism: both benefit.
In the figure : In commensalism the second partner is neither helped nor harmed.
Rule 1: Parasitism — Parasites show host specificity and co-evolve with the host. Adaptations: loss of unnecessary sense organs, suckers or hooks, loss of the digestive system, and high reproductive capacity. The human liver fluke needs two intermediate hosts (a snail and a fish); Plasmodium needs the mosquito as a vector. Brood parasitism: the koel lays eggs in a crow's nest and the eggs resemble the host's eggs.
- Easy : Lice and ticks are ectoparasites.
- Medium : The cuckoo (koel) is a brood parasite.
- Exam-type : Q: Give two adaptations of a parasite. A: Loss of sense organs and high reproductive capacity.
Rule 2: Commensalism, amensalism and mutualism — Cattle egrets feed on insects stirred up by grazing cattle (commensalism). Amensalism: one species is harmed, the other is unaffected. In mutualism, the fig tree and a particular wasp species depend on each other: the wasp pollinates the fig and lays eggs in the developing fruit, and the larvae feed on some seeds. In the Mediterranean orchid Ophrys the flower resembles a female bee so the male bee pollinates it (sexual deceit).
- Easy : Fig and wasp are mutualists.
- Medium : Lichen = fungus + alga.
- Exam-type : Q: Which interaction is shown by an orchid growing on a mango tree? A: Commensalism.
Ectoparasite lives on the body; endoparasite lives inside. Mycorrhiza: the fungus gets carbohydrates from the plant; the plant gets nutrients (especially phosphorus).
Mistaking commensalism for mutualism. In commensalism one partner gets no benefit.
Memory clue: +0 → Comm., ++ → Mut. — Commensalism: one gains, one neutral (+ 0); mutualism: both gain (+ +).
Spot the difference
| Point | Ectoparasite | Endoparasite |
|---|---|---|
| Lives | On the surface of host | Inside host |
| Example | Lice, ticks, Cuscuta | Liver fluke, tapeworm |
| Life cycle | Simple | Complex, often with intermediate hosts |
Practice questions
- 1Define parasitism.
- 2Give one example of an ectoparasite.
- 3What is an endoparasite?
- 4Name an example of commensalism.
- 5What is a lichen?
- 6What is mycorrhiza?
- 7Why do the eggs of the koel resemble the eggs of the crow?
- 8Why is the fig tree–wasp relationship called an example of co-evolution?
Show answers (try them yourself first)
- 1An interaction where one species (parasite) benefits and the other (host) is harmed.
- 2Lice (or ticks).
- 3A parasite that lives inside the host body.
- 4Cattle egret and cattle (or orchid on mango).
- 5A mutualistic association of a fungus and an alga or cyanobacterium.
- 6A mutualistic association between a fungus and plant roots.
- 7Natural selection favours eggs that the host does not recognise and remove.
- 8Each species evolved to depend on the other; the flower and its pollinator are tightly linked.