Organisms and Populations

The chapter is organised around a single level of biological organisation — the population — asking what can be measured about a group of interbreeding, resource-sharing individuals that cannot be measured about any one of them. It opens with population attributes (birth rate, death rate, sex ratio, age distribution) and the ways population density is measured. It turns to population growth, defining the four processes that raise or lower density and deriving the exponential and logistic growth models, including the chessboard-and-wheat anecdote. A short section on life history variation asks how organisms allocate reproduction to maximise fitness. The chapter closes with population interactions — predation, competition, parasitism, commensalism, amensalism and mutualism — each illustrated with NCERT's standard examples, from the prickly pear cactus of Australia to the fig wasp's one-to-one partnership with its host tree.

Population attributes: what a group has that an individual does not

In nature, isolated single individuals of a species are rare; the overwhelming majority live in groups, sharing or competing for similar resources in a well-defined geographical area, and potentially interbreeding. This is a population — all the cormorants in a wetland, the rats in an abandoned dwelling, the teakwood trees in a forest tract, the bacteria in a culture plate, the lotus plants in a pond. "Interbreeding" implies sexual reproduction, but a group produced even by asexual reproduction is still generally treated as a population for ecological purposes. Population ecology matters because it is at the population level, not the individual level, that natural selection actually operates to evolve traits, linking ecology directly to population genetics and evolution. A population has attributes an individual organism cannot have. An individual has births and deaths as one-off events; a population has birth rates and death rates, expressed as per capita changes relative to population size. If a pond held 20 lotus plants and reproduction added 8, taking it to 28, the birth rate is $8/20 = 0.4$ offspring per lotus per year. If 4 of 40 lab fruit flies died over a week, the death rate is $4/40 = 0.1$ individuals per fruit fly per week. An individual is male or female; a population has a sex ratio — say, 60 per cent female and 40 per cent male. A population also contains individuals of different ages; plotting the percentage in each age group produces an age pyramid, drawn separately for males and females in humans, whose shape reveals whether the population is growing, stable, or declining.

Population density: measuring the size of a population

The size of a population tells us a great deal about its status in a habitat, and whatever ecological process we investigate — competition, predation, a pesticide's impact — we ultimately evaluate it as a change in population size, technically population density, designated N. Sizes range from fewer than 10 (Siberian cranes wintering at Bharatpur in a given year) to millions (Chlamydomonas in a pond). Total number is usually the best measure, but not always: if an area holds 200 carrot grass (Parthenium hysterophorus) plants but a single huge banyan tree, calling the banyan's density "low" underestimates its ecological role, so per cent cover or biomass is more meaningful. Total number also becomes impractical for a huge, fast-changing population, such as a dense bacterial culture in a petri dish. Sometimes relative density suffices: fish caught per trap is a good proxy for total density in a lake. Population sizes are often estimated indirectly, without seeing or counting individuals at all — the tiger census in Indian reserves has traditionally relied on pug marks and faecal pellets.

Population growth: the four processes and the growth equation

The size of a population is never static; it keeps changing with food availability, predation pressure, weather and more, and these changes tell us whether a population is flourishing or declining. They arise from four basic processes. Natality is the number of births during a given period, added to the initial density. Mortality is the number of deaths during that period. Immigration is individuals of the same species entering the habitat from elsewhere. Emigration is individuals leaving the habitat for elsewhere. Natality and immigration add to density; mortality and emigration subtract from it. If N is the density at time t, its density at time $t+1$ is

so density increases whenever births plus immigrants (B + I) exceed deaths plus emigrants (D + E). Under normal conditions births and deaths dominate this balance; immigration and emigration matter mainly in special situations — for instance, when a new habitat is being colonised, immigration can contribute more to growth than the birth rate itself.

Growth models: exponential and logistic growth

Does population growth follow any specific, predictable pattern over time? Two models answer this, and the difference between them is really a question about resources.

Exponential growth occurs when resources (food and space) are unlimited, so a species can fully realise its innate potential to grow — the situation Darwin had in mind for natural selection. If per capita birth rate is b and death rate is d, the change in N over unit time t is $dN/dt = (b - d) \times N$. Writing $r = b - d$ gives the compact form $dN/dt = rN$, where r is the intrinsic rate of natural increase, used routinely to gauge the impact of any factor on a population's growth. Its value varies hugely: r is 0.015 for the Norway rat, 0.12 for the flour beetle, and was 0.0205 for the Indian population in 1981. Solving the equation gives $N_t = N_0 e^{rt}$ ($N_0$ = density at time zero, $e = 2.71828$), which plots as a J-shaped curve. Even small r values compound fast — the old anecdote of a minister betting one wheat grain on a chessboard's first square, doubling on each square thereafter, bankrupts his king's entire kingdom's wheat before half the 64 squares are filled; a Paramecium doubling daily by binary fission would show the same explosion over 64 days.

Logistic growth is what actually happens, because no population ever has unlimited resources — individuals compete for what is limited, and the fittest survive and reproduce. A habitat supports only a maximum number of individuals, its carrying capacity (K), beyond which no further growth is possible. Growth shows an initial lag phase, then acceleration and deceleration, and finally an asymptote at K. Plotting N against time produces a sigmoid (S-shaped) curve, the Verhulst-Pearl logistic growth model:

where N is population density at time t, r is the intrinsic rate of natural increase, and K is the carrying capacity. Because resources are finite and eventually limiting for essentially every animal population, the logistic model is considered the more realistic description of population growth.

Life history variation: how organisms allocate reproduction

Populations evolve to maximise their reproductive fitness, also called Darwinian fitness (a high r value), within their habitat. Under a given set of selection pressures, organisms evolve toward the most efficient reproductive strategy available, and different species have converged on strikingly different answers. Some breed only once in a lifetime — semelparity — such as Pacific salmon and bamboo, while others breed many times — iteroparity — as most birds and mammals do. Some produce a large number of small offspring (oysters, pelagic fishes); others produce a small number of large offspring (birds, mammals). Ecologists hold that these life history traits have evolved in relation to the specific constraints imposed by a habitat's abiotic and biotic components, an active area of ongoing research.

Population interactions: the ecology of coexistence

No natural habitat is inhabited by just a single species — every species needs, at minimum, one other species it can feed on, and even an autotrophic plant needs soil microbes to recycle nutrients and animal agents for pollination. Animals, plants and microbes cannot live in isolation; they interact to form a biological community. Interspecific interactions arise from populations of two different species affecting each other, and the effect on either species can be beneficial (+), detrimental (-) or neutral (0). Combining these signs gives every possible outcome.

Both species benefit in mutualism, and both lose in competition. In parasitism and predation, only one species benefits (the parasite or the predator) while the other is harmed (the host or the prey). In commensalism, one species benefits and the other is unaffected; in amensalism, one species is harmed while the other is unaffected. Predation, parasitism and commensalism share a common feature — the interacting species live closely together.

Predation. Predation transfers the energy fixed by autotrophic plants up through higher trophic levels. A sparrow eating a seed is no less a predator than a tiger eating a deer — herbivores are functionally similar to predators. Predators keep prey populations under control; an exotic species introduced without its natural predators can turn invasive, as the prickly pear cactus did across Australian rangeland in the 1920s, controlled only after a cactus-feeding moth was introduced (biological pest control). Predators also maintain diversity by curbing competition among prey: removing the starfish Pisaster from a Pacific-coast intertidal zone caused over 10 invertebrate species to go locally extinct within a year. An overly efficient predator can drive its prey extinct and then starve, so predators in nature tend to be "prudent." Prey defences include camouflage and poisons — the Monarch butterfly is distasteful to birds from a chemical acquired as a caterpillar. For plants, herbivores are the predators; nearly 25 per cent of insects are phytophagous, and plants have evolved thorns (Acacia, cactus) and chemicals such as the cardiac glycosides in Calotropis, plus nicotine, caffeine, quinine, strychnine and opium, all originally anti-herbivore defences.

Competition. Interspecific competition is not confined to related species: flamingoes and fish in South American lakes compete for the same zooplankton despite being unrelated. Nor does it need scarce resources — in interference competition, one species' feeding efficiency is reduced merely by another's presence. Competition is best defined as one species' fitness (its r) being significantly lowered by another's presence. Gause's lab work showed that when resources are limiting, the superior competitor eventually eliminates the other — the Competitive Exclusion Principle — though field evidence is not always conclusive. Strong cases exist: the Abingdon tortoise of the Galapagos went extinct after goats were introduced, and Connell's larger barnacle Balanus excludes the smaller Chthamalus from Scottish intertidal rocks. But many species instead evolve resource partitioning — different feeding times or patterns — as MacArthur showed for five warbler species coexisting on the same tree.

Parasitism. Parasitism has evolved across taxonomic groups from plants to vertebrates. Many parasites are host-specific, driving host and parasite to co-evolve. Adaptations include loss of unnecessary sense organs, adhesive suckers, loss of the digestive system, and high reproductive capacity; life cycles often involve intermediate hosts or vectors — the human liver fluke needs a snail and a fish, the malarial parasite a mosquito. Most parasites harm the host. Ectoparasites live on the host's surface (lice, ticks, copepods on marine fish, Cuscuta on hedges); endoparasites live inside (liver, kidney, lungs, red blood cells), with more complex life cycles and simplified anatomy. Brood parasitism, as in the cuckoo (koel) laying eggs in a crow's nest, has evolved eggs resembling the host's to avoid detection.

Commensalism, amensalism and mutualism. In commensalism one species benefits and the other is unaffected — an orchid epiphytic on a mango branch, barnacles on a whale, the cattle egret foraging beside grazing cattle, the clownfish sheltering among a sea anemone's tentacles. Amensalism is the mirror case: one harmed, the other unaffected. Mutualism benefits both: lichens pair a fungus with an alga or cyanobacterium; mycorrhizae pair fungi with plant roots, trading nutrient absorption for carbohydrates. The most spectacular mutualisms are plant-animal, paying pollinators and dispersers with pollen, nectar and fruit while guarding against "cheaters." Many fig species share a one-to-one relationship with a partner wasp that pollinates the fig while laying eggs in its fruit, in exchange for some seeds as larval food. Orchids attract specific pollinators; the Mediterranean orchid Ophrys practises "sexual deceit," its petal resembling a female bee closely enough that a male bee's "pseudocopulation" dusts it with pollen.

Board level - Calculating birth rate and death rate in two populations

A pond had 20 lotus plants at the start of a year. Through reproduction, 8 new plants were added over the year, taking the population to 28. Separately, a laboratory population of 40 fruit flies was observed for one week, during which 4 individuals died. Calculate (a) the birth rate of the lotus population and (b) the death rate of the fruit fly population, each expressed as a per capita rate over the stated period.

Step 1. A birth rate or death rate is always expressed relative to the population size that produced the births or suffered the deaths — this is what distinguishes a population attribute (a rate) from an individual event.

Step 2. Lotus birth rate: eight new plants added to an initial population of 20 gives $8/20 = 0.4$ offspring per lotus per year.

Step 3. Fruit fly death rate: four individuals died out of an initial population of 40 over one week, giving $4/40 = 0.1$ individuals per fruit fly per week. Answer: birth rate 0.4 offspring per lotus per year; death rate 0.1 individuals per fruit fly per week.

Board level - Finding the intrinsic rate of natural increase from a doubling population

A population growing exponentially is observed to double in size in 3 years. Using the integral form of the exponential growth equation, find the intrinsic rate of natural increase, r, for this population.

Step 1. Set up the doubling condition. Exponential growth follows $N_t = N_0 e^{rt}$. "Doubles in 3 years" means at $t=3$, $N_t = 2N_0$, so $2N_0 = N_0 e^{3r}$.

Step 2. Cancel $N_0$ and take the natural log: $2 = e^{3r}$, so $\ln 2 = 3r$, using $\ln(e^{x}) = x$.

Step 3. Solve for r: since $\ln 2 = 0.693$, $r = 0.693/3 = 0.231$ per year. Answer: $r \approx 0.231$ per year.

Competitive level (NEET) - Comparing logistic and exponential growth rates at the same population size

A population of density $N = 200$ is growing in a habitat with carrying capacity $K = 1000$ and intrinsic rate of natural increase $r = 0.5$ per year. Calculate (a) the population's growth rate, $dN/dt$, under the logistic model, and (b) what its growth rate would be at this same N under the exponential model. (c) State which model predicts the faster growth rate at this N, and why.

Step 1. Logistic rate: $rN = 0.5 \times 200 = 100$; braking factor $(K-N)/K = (1000-200)/1000 = 0.8$; so $dN/dt = 100 \times 0.8 = 80$ individuals per year.

Step 2. Exponential rate at the same N: $dN/dt = rN = 0.5 \times 200 = 100$ individuals per year — no braking factor, since resources are assumed never limiting.

Step 3. The logistic rate (80) is lower than the exponential rate (100) at this N, because logistic growth already "feels" the approaching carrying capacity through $(K-N)/K$. Answer: logistic rate 80 individuals per year; exponential rate 100 individuals per year; exponential growth is always faster than or equal to logistic growth at any N less than K. Timing note: about 90 seconds. The trap is forgetting the braking factor and computing plain $rN$ when K is explicitly given — always check whether K is supplied before choosing the equation. Cross-check: since $N = K/5$ is well below $K/2 = 500$, the logistic rate should stay close to but always below the exponential rate.

The single most frequent scoring error is treating population attributes as if they belonged to individuals. An individual has births and deaths — one-off events — while only a population has birth rates and death rates, per capita; an individual is male or female, but only a population has a sex ratio. Questions asking you to "list the attributes that populations possess but not individuals" want birth rate, death rate, sex ratio and age distribution, not "birth" and "death" as raw events. A second confusion is treating exponential growth as the default pattern for real populations, when logistic growth, bounded by K, is realistic for almost every natural population; its maximum absolute growth rate occurs at $N = K/2$, not at the very start or near K. A related trap: r is a per capita rate, not a raw birth or death count. Finally, the six interactions are easily mixed up when only the sign pattern is remembered without the mechanism. Predation and parasitism share (+,-) but differ in duration — predation is a single lethal encounter, parasitism a sustained association. Commensalism (+,0) is often confused with mutualism (+,+): in commensalism only one partner benefits, as with the orchid on the mango branch. And the Competitive Exclusion Principle is over-applied as an absolute law; it holds only when resources are genuinely limiting, and many species instead evolve resource partitioning to coexist.

• State the definition of a population and list the attributes it has but an individual does not (birth rate, death rate, sex ratio, age distribution), with a worked birth/death-rate calculation.
• Explain population density (N) and name at least three ways it is measured — total count, biomass/per cent cover, relative density, indirect signs such as pug marks.
• Write and interpret $N_{t+1} = N_t + [(B+I) - (D+E)]$, naming natality, mortality, immigration and emigration.
• Derive and use $dN/dt = rN$ and $N_t = N_0e^{rt}$, including calculating r from a given doubling time.
• Derive and use $dN/dt = rN(K-N)/K$, explain carrying capacity K, and identify the lag, acceleration, deceleration and asymptote phases, including where growth rate is maximised.
• Explain why logistic, not exponential, growth is the realistic model for populations in nature.
• Distinguish semelparity from iteroparity and relate life history traits to Darwinian fitness, with named examples.
• Classify any interaction using the +/-/0 convention for the six categories, with at least one NCERT example each.
• Explain, with named examples, how predation regulates prey, transfers trophic energy, and can maintain diversity (the Pisaster experiment).
• State the Competitive Exclusion Principle, its limits, and resource partitioning (MacArthur's warblers) as the mechanism allowing coexistence.

Ask the tutor: Want to work through a full numerical problem that starts from a real r and K, walks through the logistic curve phase by phase, and asks you to predict when the population will be growing fastest?