Topic 03: Carrying Capacity & Population Growth

Carrying capacity and its determinants, exponential vs logistic population growth curves, density-dependent vs density-independent regulation, r-selected vs K-selected species, the demographic transition model, Malthusian theory, ecological footprint vs biocapacity, and the St. Matthew Island overshoot-crash case study.

GS Paper III — Environment & Ecology UPSC Prelims + Mains High Importance Updated: July 2026

1.Carrying Capacity — Concept, Determinants & Dynamics
2.Conceptual Clarity — Growth Models (Exponential vs Logistic)
3.Density-Dependent vs Density-Independent Factors
4.r-Selected vs K-Selected Species
5.Human Population Growth — Demographic Transition Model
6.Malthusian Theory vs Modern Carrying-Capacity Debates
7.Ecological Footprint vs Biocapacity
8.Case Studies — Overshoot & Carrying-Capacity Debates
9.Current Affairs Link
10.Prelims PYQs
11.Mains PYQs
12.15-Minute Revision Box

Conceptual Clarity — Why this Topic Matters

UPSC tests Carrying Capacity & Population Growth in three distinct ways. Knowing which question-type you face decides how you study each heading below:

Definitional / static — "What does carrying capacity (K) mean?", "Which stage of the DTM shows the fastest growth?", or the exact form of the logistic equation dN/dt = rN(1−N/K). Memorise definitions, equations, DTM stages and dates (Verhulst 1838, MacArthur & Wilson 1967, Malthus 1798).
Statement-elimination — two/three statements distinguishing exponential vs logistic, density-dependent vs density-independent, or r-selected vs K-selected traits, where one wrong word makes a statement false. Trains you to read boundaries precisely.
Applied / current — Mains and analytical Prelims linking K to India's development planning, demographic dividend, ecological footprint vs biocapacity, and Earth Overshoot Day. Needs concept + latest population/footprint data.

Focus especially on the highest-frequency themes: the exponential vs logistic distinction (and N=K/2 → MSY), density-dependent vs density-independent factors, the r/K selection contrast, and the Demographic Transition Model + India's placement. These account for the bulk of every question set on this topic.

1. Carrying Capacity — Concept, Determinants & Dynamics

Carrying capacity (K) is the maximum population size of a species that a given environment/habitat can support indefinitely, given the food, water, space, and other resources available, without long-term degradation of the resource base. Beyond K, the environment can no longer sustain further growth.

Factors Determining Carrying Capacity

Resource Availability

Food, water and nutrients set the primary ceiling — e.g., forage grass availability caps deer/reindeer numbers on an island.

Space & Territory

Nesting sites, breeding territory and shelter limit numbers even when food is adequate — e.g., seabird colonies limited by cliff-ledge space.

Predation Pressure

Predators cap prey numbers below the resource-set ceiling — e.g., wolf predation historically kept elk populations in check in Yellowstone.

Disease & Parasites

Pathogen/parasite load spreads faster in dense populations, pulling numbers back toward K — e.g., mange outbreaks in dense fox populations.

Competition

Intraspecific (same species) and interspecific (different species) competition for the same limited resources reduces effective K for each competitor.

Waste & Self-Pollution

Accumulation of metabolic waste/toxins in a confined habitat can itself become limiting — e.g., algal blooms poisoning their own pond.

Carrying Capacity Is Dynamic, Not Fixed

K rises and falls with seasonal and climatic variation — e.g., a good monsoon raises grassland K for herbivores; drought sharply lowers it.
K can be artificially raised by technology for humans — irrigation, fertilisers and the Green Revolution raised India's food-based human carrying capacity manifold since the 1960s.
K can be degraded (lowered) by habitat loss — forest fragmentation has reduced the effective carrying capacity for tiger populations across many Indian landscapes.
K can be restored/raised by conservation — habitat restoration, corridor creation and anti-poaching enforcement can push K back up (e.g., rising tiger K in well-protected reserves like Corbett and Kanha).

Relevance to Sustainable Development & Human Population Planning: Because K is not fixed, debates on "how many people the Earth can support" hinge on assumptions about technology, consumption patterns and resource substitution — this tension underlies the entire Malthusian-vs-modern debate (Section 6) and frames India's own land, water and food-security planning.

2. Conceptual Clarity — Population Growth Models (Exponential vs Logistic)

How a population actually approaches (or overshoots) carrying capacity is described by two classical growth models. UPSC frequently tests confusion between the two — get the equations, shapes and assumptions exactly right.

Fig 3.1 — J-shaped exponential curve vs S-shaped logistic curve, with the four phases of logistic growth marked (Lag → Exponential → Deceleration → Stationary).

Exponential Growth — J-shaped Curve

Equation (in words): rate of change of population = intrinsic growth rate (r) × current population size (N), i.e. dN/dt = rN.
Assumes unlimited resources and no environmental resistance — every individual reproduces at the same constant per-capita rate regardless of how crowded the population becomes.
Produces a J-shaped curve — growth accelerates continuously and, mathematically, has no ceiling.
Rare in nature and only ever short-lived — seen when a species colonises a new resource-rich habitat (invasive species establishment) or in the very early phase of a bacterial/microbial culture in fresh medium.

Logistic Growth — S-shaped (Sigmoid) Curve

Equation (in words): rate of change of population = intrinsic growth rate × current population × (1 − current population ÷ carrying capacity), i.e. dN/dt = rN(1 − N/K).
The term (1 − N/K) is the "environmental resistance" factor — it is close to 1 (little resistance) when N is small, and approaches 0 (maximum resistance) as N approaches K.
First formulated by Pierre-François Verhulst (1838), later revived by Raymond Pearl — hence also called the Verhulst-Pearl logistic equation.
Produces an S-shaped (sigmoid) curve that levels off at K — the realistic model for most natural populations with finite resources.

Four Phases of the Logistic Curve

Phase	What Happens
Lag phase	Population is small; growth is slow as individuals establish themselves and adjust to the environment
Exponential (log) phase	Resources still abundant relative to population; growth accelerates, closely resembling the J-curve
Deceleration phase	Resources start becoming limiting as N approaches K; growth rate slows sharply
Stationary phase	N fluctuates around K; births ≈ deaths; net growth rate ≈ zero

Where Is Growth Rate Fastest?

In the logistic model, the absolute number of new individuals added per unit time is greatest at N = K/2 (the steepest point of the S-curve) — this is the biological basis of Maximum Sustainable Yield (MSY) in fisheries and wildlife harvest management, where the harvestable surplus is largest at roughly half of carrying capacity, not at K itself.

UPSC Trap: "The logistic growth model assumes unlimited resources" is FALSE — that is the definition of the EXPONENTIAL model. The logistic model explicitly builds in resource limitation via the (1−N/K) term. Also, growth rate is zero AT K, not fastest at K — it is fastest at K/2.

3. Density-Dependent vs Density-Independent Factors

Population regulation operates through two broad classes of limiting factors, distinguished by whether their impact scales with how crowded the population is.

Density-Dependent Factors Negative Feedback

Intensity of impact increases as population density rises.
Food/resource competition — scarcer per capita as numbers rise.
Predation — predators concentrate where prey is dense.
Disease & parasitism — spreads faster through crowded populations.
Intraspecific competition for mates, territory and nesting sites.
Accumulation of metabolic waste/toxins in a confined space.
Acts as a stabilising negative feedback, pulling N back toward K.

Density-Independent Factors No Feedback

Impact is the same proportion of the population regardless of density.
Extreme weather events — storms, frost, heatwaves.
Natural disasters — floods, wildfires, volcanic eruptions, cyclones.
Sudden pollution events or oil spills.
Large-scale human habitat destruction (e.g., clear-felling).
Can crash a population sharply whether it was sparse or dense.

Feature	Density-Dependent	Density-Independent
Effect scales with density?	Yes — stronger at high density	No — same regardless of density
Feedback type	Negative feedback — stabilising, regulates toward K	None — can strike randomly
Typical examples	Food competition, predation, disease, intraspecific competition	Storms, floods, wildfires, drought, sudden pollution
Role in logistic model	Underlies the (1−N/K) resistance term	Not captured by the logistic equation

Liebig's Law of the Minimum: A population's growth is capped not by the total resources available but by the scarcest resource relative to need — even abundant water and sunlight cannot support plant growth if soil nitrogen is critically deficient.

4. r-Selected vs K-Selected Species

r/K selection theory (Robert MacArthur & E.O. Wilson, 1967) classifies species along a spectrum based on whether natural selection favours a high intrinsic growth rate (r) in unstable environments, or competitive efficiency near carrying capacity (K) in stable environments.

Characteristic	r-Selected (r-Strategists)	K-Selected (K-Strategists)
Habitat type	Unstable, unpredictable, opportunistic	Stable, predictable, resource-limited
Reproductive rate	High — many offspring per event	Low — few offspring per event
Offspring size	Small	Large
Parental care	Minimal to none	Extensive, prolonged
Age at maturity	Early/young	Late/older
Body size	Typically small	Typically large
Lifespan	Short	Long
Survivorship curve	Type III (high early mortality)	Type I (survival into old age)
Population stability	Fluctuates widely, often near/above K, boom-bust	Stable, hovers close to K
Examples	Insects, rodents, bacteria, weeds, most fish	Elephants, whales, tigers, great apes, humans, oak/redwood trees

Conservation Relevance: K-strategists (elephants, whales, tigers) recover very slowly from population crashes because of low reproductive rates — this makes them disproportionately vulnerable to extinction from poaching/habitat loss. r-strategist pest and invasive species, by contrast, rebound rapidly, making eradication difficult (e.g., locust swarms, invasive weeds like Lantana camara).

UPSC Trap: r/K selection is a spectrum, not a strict binary — many species show intermediate traits. Do not assume ALL insects are r-strategists or ALL large mammals are K-strategists without checking the specific life-history details given in a question.

5. Human Population Growth — Demographic Transition Model

Applying carrying-capacity thinking to humans is complicated because technology, trade and innovation can raise the effective carrying capacity over time. The Demographic Transition Model (DTM) — first outlined by Warren Thompson (1929) — describes how birth and death rates shift as a society industrialises.

Fig 3.2 — Demographic Transition Model: birth rate (orange) and death rate (blue) across five stages, with the natural-increase gap (green) and the Stage-5 decline zone (red).

Stage	Birth Rate	Death Rate	Population Growth	Typical Example
Stage 1 — High Stationary	High	High	Slow/stable — high births offset by high deaths	Pre-industrial societies
Stage 2 — Early Expanding	Stays high	Falls sharply (sanitation, medicine, food supply)	Rapid growth — widening birth-death gap	19th-century Britain; parts of Sub-Saharan Africa today
Stage 3 — Late Expanding	Begins falling (urbanisation, education, family planning)	Continues falling slowly	Growth slows but population still rising	India (many states, historically)
Stage 4 — Low Stationary	Low	Low	Near-zero growth	Most developed economies; India nationally approaching this
Stage 5 — Declining	Falls below death rate	Rises slightly (ageing population)	Negative — population shrinks	Japan, South Korea, several European nations

India's Population Trajectory

India's Total Fertility Rate (TFR) has fallen from ~5.2 (1971) to 2.0 (NFHS-5, 2019-21) — at/below the replacement level of 2.1, signalling India is now moving from late Stage 3 toward Stage 4.
India overtook China as the world's most populous country in 2023 (UN estimate), with population around 1.45 billion in 2025-26.
Sharp regional heterogeneity — southern states (Kerala, Tamil Nadu, Andhra Pradesh) already show TFR below 1.8, resembling Stage 4/5; northern states (Bihar, Uttar Pradesh) still have TFR above 2.5-3, resembling Stage 2/3.
UN projections suggest India's population may peak around the mid-2060s before gradually declining, opening a limited-duration demographic dividend window (large working-age share) that policy must exploit before the population ages.

6. Malthusian Theory vs Modern Carrying-Capacity Debates

Malthusian Theory (Thomas Malthus, 1798)

Population grows geometrically (1,2,4,8,16...) while food supply grows only arithmetically (1,2,3,4,5...).
This gap inevitably produces "checks" on population — positive checks (famine, disease, war — raising the death rate) or preventive checks (delayed marriage, moral restraint — lowering the birth rate).
Predicted recurring "Malthusian catastrophes" where population overshoots food-carrying capacity.

Why Malthus's Simple Prediction Failed to Materialise Globally

Ester Boserup's counter-view (1965): Population pressure itself drives agricultural innovation — necessity pushes societies to intensify farming and adopt new technology, expanding effective carrying capacity ("necessity is the mother of invention").
Green Revolution (1960s-70s): High-yielding seed varieties, irrigation and fertilisers multiplied global and Indian food output, repeatedly pushing K far beyond Malthus's arithmetic assumption.
Paul Ehrlich's "The Population Bomb" (1968) revived Malthusian alarm, predicting mass famines by the 1970s-80s — largely averted by the Green Revolution, though resource-stress concerns persist in a modified form.

Modern Carrying-Capacity Debate

Modern ecologists agree K is not fixed but argue it is still ultimately bounded — technology can defer, but not permanently eliminate, ecological limits (soil degradation, freshwater depletion, climate change, biodiversity loss).
The Planetary Boundaries framework (Rockström et al., 2009) reframes this as nine Earth-system limits (climate change, biodiversity loss, nitrogen/phosphorus cycles, freshwater use, land-system change, etc.) that humanity should not cross — a scientific update to the carrying-capacity idea at planetary scale.
India's own planning debates (NITI Aayog river-basin and hill-state carrying-capacity studies) increasingly assess regional ecological carrying capacity for tourism, urbanisation and infrastructure, rather than relying on a single national number.

UPSC Trap: Do not treat Malthusian theory as either "fully proven" or "fully disproven" — UPSC expects a balanced answer: Malthus's mechanism (positive/preventive checks) was real historically, but technology repeatedly raised K faster than population grew; the debate has shifted from "food scarcity" to broader ecological/resource limits.

7. Ecological Footprint vs Biocapacity

Ecological Footprint Demand

The biologically productive land and water area (in global hectares, gha) required to produce the resources a population consumes and to absorb the waste (chiefly CO₂) it generates.

Biocapacity Supply

The biologically productive area actually available within a region/the planet to generate renewable resources and absorb waste — the ecological "income."

When Footprint > Biocapacity → ecological overshoot/deficit — the population is drawing down natural capital faster than it regenerates (running an ecological "debt").
When Biocapacity > Footprint → ecological surplus/reserve — the region is a net ecological "creditor" (typically low-consumption, resource-rich regions).
Concept developed by Mathis Wackernagel & William Rees (1990s) and tracked annually by the Global Footprint Network (GFN).

Earth Overshoot Day

The calendar date each year when humanity's cumulative demand on nature for that year exceeds what Earth's ecosystems can regenerate in that year — after this date, humanity operates in ecological deficit for the rest of the year.
Humanity's global ecological footprint has exceeded Earth's total biocapacity since roughly the early 1970s — humanity currently uses resources at a rate equivalent to more than 1.7 Earths per year (GFN estimate).
As per Global Footprint Network's provisional 2025 calendar, Earth Overshoot Day fell around 24 July 2025 — among the earliest dates on record, signalling worsening global overshoot.

India's Position: India's per-capita ecological footprint remains well below the global average and below most developed economies (lower per-capita consumption), so India's own national Overshoot Day (if India were the only country on Earth) falls much later in the calendar year. However, India's sheer population size means its total/absolute footprint is large, and India as a whole still runs a national biocapacity deficit.

8. Case Studies — Overshoot & Carrying-Capacity Debates

St. Matthew Island Reindeer Crash (1944-1966)

In 1944, the US Coast Guard introduced 29 reindeer onto uninhabited St. Matthew Island, Alaska, which had abundant lichen (their primary food) and no predators.
With unlimited food and no predation, the population grew almost exponentially — reaching roughly 1,350 by 1957 and an estimated ~6,000 by 1963, far exceeding the island's true long-term carrying capacity.
By the time researcher David Klein surveyed the island in 1966, the lichen pasture had been devastated by overgrazing — the population had crashed to just 42 reindeer (a ~99% die-off), and the surviving animals showed signs of starvation.
Classic textbook example of ecological overshoot — when a population exceeds K, it does not stabilise gently at K but can crash far below it after degrading the resource base itself.

Key Lesson: The St. Matthew Island reindeer demonstrate that when a population's growth outpaces its resource base (especially when growth is exponential due to absent predators/competitors), the "correction" is not a smooth return to K but often a catastrophic crash — a cautionary parallel invoked in debates on human population and resource overshoot.

India / Global Carrying-Capacity Debates

Malthus vs Boserup vs Ehrlich — recurring historical debate on whether population growth outpaces resources (Section 6); India's own experience (avoiding mass famine post-Green Revolution while population nearly quadrupled since 1951) is cited as evidence for the Boserupian, technology-driven view.
Regional carrying-capacity studies — NITI Aayog and state governments have commissioned carrying-capacity assessments for ecologically fragile regions (e.g., Himalayan hill states post the 2013 Uttarakhand floods, and the Char Dham pilgrimage routes) to cap tourist inflows and construction within sustainable limits.
Global footprint debate — critics of a single "global carrying capacity" number argue it depends heavily on assumed consumption levels (a world at US consumption levels needs ~5 Earths; at average Indian consumption levels, far fewer) — highlighting that carrying capacity is as much about consumption patterns as raw population numbers.

9. Current Affairs Link (2024–2026)

Earth Overshoot Day & Global Populationcheck for latest update or data

UN World Population Prospects 2024 Revision (July 2024): global population ~8.2 billion; projected to peak at ~10.3 billion in the mid-2080s before gradual decline — a downward revision reflecting faster-than-expected fertility decline worldwide.
Earth Overshoot Day 2024 = 1 August; 2025 ≈ 24 July (Global Footprint Network) — humanity exhausts its annual "ecological budget" nearly 5 months before year-end; current global demand ≈ 1.7–1.8 Earths.
India (2024–2026): retained position as world's most populous nation (~1.45 billion, overtaking China since April 2023); growth slowing as TFR fell to ~2.0 (NFHS-5), at/below replacement level.
UN World Population Day (11 July, annual): 2024–25 themes stressed rights-based family planning and harnessing demographic dividend — recurring current-affairs hook.

UPSC Relevance: Carrying capacity, ecological footprint and demographic transition concepts are staple inputs for GS-III essays on sustainable development, alongside recurring Prelims fact-based questions on population statistics, growth-curve equations, and r/K selection traits.

10. Prelims PYQs

UPSC Prelims 2023

Q: With reference to "carrying capacity" of an environment, consider the following statements:

It is the maximum population size that a habitat can sustain indefinitely with the resources available.
Carrying capacity is a fixed, unchanging value for any given species.
Habitat degradation can lower a species' carrying capacity.

Which of the statements given above are correct?

(a)1 and 2 only
(b)2 and 3 only
(c)1 and 3 only
(d)1, 2 and 3

Ans: (c) 1 and 3 only. Statement 2 is incorrect — carrying capacity is dynamic, changing with resource availability, climate, technology and habitat quality, not fixed.

UPSC Prelims 2022

Q: The logistic growth curve of a population differs from the exponential growth curve primarily because the logistic model —

(a)Assumes unlimited resources at all times
(b)Incorporates a resistance term that slows growth as the population approaches carrying capacity
(c)Produces a straight-line growth pattern
(d)Applies only to human populations

Ans: (b). The logistic model incorporates a resistance term, expressed as (1−N/K), that slows growth as N approaches carrying capacity K.

UPSC Prelims 2021

Q: Which one of the following is a "density-independent" factor limiting the growth of a population?

(a)Competition for food among individuals
(b)Predation pressure
(c)A sudden, large-scale forest fire
(d)Spread of a contagious disease through the population

Ans: (c). A sudden, large-scale forest fire's impact does not depend on population density, unlike food competition, predation and disease spread, which are all density-dependent.

UPSC Prelims 2019

Q: Consider the following characteristics:

Small body size
Long lifespan
Minimal parental care
Late age at sexual maturity

Which of the above are typically associated with "r-selected" (r-strategist) species?

(a)1 and 3 only
(b)2 and 4 only
(c)1, 2 and 3 only
(d)1, 2, 3 and 4

Ans: (a) 1 and 3 only. Long lifespan and late maturity (2 and 4) are characteristics of K-selected species, not r-selected species.

UPSC Prelims 2017

Q: With reference to the Demographic Transition Model, "Stage 2" is best characterised by —

(a)High birth rate and high death rate, with slow population growth
(b)High birth rate and rapidly falling death rate, producing rapid population growth
(c)Falling birth rate and low death rate, with slowing population growth
(d)Low birth rate and low death rate, with near-zero population growth

Ans: (b). High birth rate combined with a rapidly falling death rate (due to improved healthcare and sanitation) produces the phase of most rapid population growth ("Early Expanding" stage).

11. Mains PYQs

Mains GS-III 2020

Q: Explain the concept of "carrying capacity" and discuss its relevance to India's development planning and sustainable resource management. (250 words)

Model Answer Framework

Introduction — define K: Open with a crisp definition — carrying capacity (K) is the maximum population an environment can sustain indefinitely given available resources, without degrading the resource base.
- Note it is dynamic, not fixed — set by resources, space, predation, disease, competition and waste-assimilation limits.
Body — determinants & the technology debate: Explain how K can be raised by technology and lowered by degradation.
- Green Revolution raised India's food carrying capacity, averting Malthusian famine despite ~4× population growth since 1951.
- Malthusian vs Boserupian framing — pressure either outstrips resources or drives innovation.
Body — relevance to India's planning: Anchor with concrete Indian examples.
- NITI Aayog / state carrying-capacity studies for fragile Himalayan hill states (post-2013 Uttarakhand floods) and Char Dham pilgrimage caps.
- Urban carrying capacity, groundwater over-extraction (Punjab), and EIA thresholds.
Modern extension: Link to Planetary Boundaries (Rockström, 2009) and Ecological Footprint vs Biocapacity as scientific successors to a single K number; stress consumption patterns matter as much as headcount.
Conclusion: Sustainable development = keeping resource use within a dynamic, technology-augmented carrying capacity; align with SDGs and India's LiFE (Lifestyle for Environment) mission.

250 words · 15 marks

Mains GS-III 2018

Q: Discuss the Demographic Transition Model. In which stage is India currently placed, and what are the implications for India's demographic dividend? (200 words)

Model Answer Framework

Introduction — the model: Define DTM as the shift from high-birth/high-death to low-birth/low-death regimes as societies industrialise, driving predictable population change.
Body — the five stages: Summarise each with birth/death trends.
- Stage 1 High Stationary → 2 Early Expanding (rapid growth) → 3 Late Expanding → 4 Low Stationary → 5 Declining.
Body — India's placement: Locate India in late Stage 3 moving to Stage 4 (TFR ~2.0, NFHS-5, at replacement).
- Regional heterogeneity: southern/western states near Stage 4–5 (Kerala, TN) vs some northern states still Stage 2–3 (Bihar, UP).
Body — demographic dividend implications: A time-bound window of a bulging working-age population.
- Requires skilling, job creation, health & education investment to convert into growth; else "demographic burden".
- Prepare for later ageing (Stage 4–5) — pensions, healthcare.
Conclusion: India's dividend window is finite (roughly to ~2040s); realising it depends on human-capital policy now, not demography alone.

200 words · 12.5 marks

Mains GS-III 2016

Q: "Malthusian predictions of population outpacing food supply have repeatedly been deferred by technology, yet ecological limits remain real." Critically examine this statement with reference to the concepts of ecological footprint and biocapacity. (250 words)

Model Answer Framework

Introduction — Malthus's thesis: State it — population grows geometrically, food only arithmetically, forcing positive/preventive checks.
Body — why predictions were deferred: Argue technology repeatedly raised the food ceiling.
- Boserup: population pressure induces innovation; Green Revolution and synthetic fertilisers averted mass famine.
- Ehrlich's Population Bomb (1968) forecasts largely did not materialise.
Body — yet limits are real (footprint vs biocapacity): Reframe limits ecologically, not just in food terms.
- Ecological Footprint > Biocapacity globally since ~1970s; humanity now uses ~1.7 Earths/year (Earth Overshoot Day advancing).
- Overshoot is masked by drawing down natural capital (aquifers, forests, fisheries, climate stability).
Body — critical synthesis: Technology defers food scarcity but not ecological limits; consumption patterns (rich-world footprint) matter more than raw headcount.
- Link to Planetary Boundaries (Rockström, 2009) as the scientific successor to Malthusian limits.
Conclusion: Neither pure Malthusian doom nor techno-optimism holds; sustainability needs both innovation and demand-side restraint within biocapacity.

250 words · 15 marks

15-Minute Revision Box

Rapid Revision — Carrying Capacity & Population Growth

Carrying Capacity (K)

Maximum population a habitat can sustain indefinitely; determined by resources, space, predation, disease, competition, waste accumulation.
Dynamic, not fixed — raised by technology/conservation, lowered by habitat degradation.

Growth Models

Exponential (J-curve): dN/dt = rN, unlimited resources, unrealistic long-term.
Logistic (S-curve): dN/dt = rN(1−N/K), Verhulst (1838); phases: Lag → Exponential → Deceleration → Stationary; growth fastest at N=K/2 (basis of MSY).

Regulating Factors

Density-dependent — food, predation, disease, competition (negative feedback toward K).
Density-independent — storms, floods, fires, drought (same impact regardless of density).

r vs K Strategists

r-strategists: many small offspring, little care, short life, unstable habitats (insects, rodents, weeds, bacteria).
K-strategists: few large offspring, extensive care, long life, stable habitats (elephants, whales, humans, tigers).

Demographic Transition Model (5 stages)

1 High Stationary → 2 Early Expanding (rapid growth) → 3 Late Expanding → 4 Low Stationary → 5 Declining.
India: TFR ~2.0 (NFHS-5); moving from Stage 3 toward Stage 4; most populous nation since 2023 (~1.45 billion, 2025-26).

Malthus vs Modern Debate

Malthus (1798): population geometric, food arithmetic → positive/preventive checks.
Boserup: population pressure drives innovation; Green Revolution raised K; Ehrlich's Population Bomb (1968) largely averted.
Modern view: Planetary Boundaries framework (Rockström, 2009) — technology defers but does not eliminate ecological limits.

Quick Facts

Ecological Footprint vs Biocapacity — global overshoot since early 1970s; ~1.7 Earths/year used.
Earth Overshoot Day 2025 — around 24 July (Global Footprint Network, provisional).
St. Matthew Island reindeer: 29 (1944) → ~6,000 (1963) → 42 (1966) — classic overshoot-crash case study.
Global population ~8.2 billion (2025); UN projects peak ~10.3 billion mid-2080s.

Term	Key Fact
Exponential growth	dN/dt = rN, J-shaped
Logistic growth	dN/dt = rN(1−N/K), S-shaped
Fastest growth	At N = K/2 (basis of MSY)
DTM stages	5 — High Stationary to Declining
India TFR	2.0 (NFHS-5, 2019-21)
Overshoot Day 2025	~24 July (GFN)

Metric	Value
World population (2025)	~8.2 billion
Projected peak	~10.3 bn (mid-2080s)
India population	~1.45 bn (most populous)
India TFR (NFHS-5)	2.0 (replacement)
Global demand	~1.7 Earths/year
Overshoot Day 2025	≈ 24 July
Logistic eqn.	Verhulst, 1838
r/K selection	MacArthur & Wilson, 1967

Topic 03: Carrying Capacity & Population Growth

Table of Contents

Conceptual Clarity — Why this Topic Matters

1. Carrying Capacity — Concept, Determinants & Dynamics

Factors Determining Carrying Capacity

Resource Availability

Space & Territory

Predation Pressure

Disease & Parasites

Competition

Waste & Self-Pollution

Carrying Capacity Is Dynamic, Not Fixed

2. Conceptual Clarity — Population Growth Models (Exponential vs Logistic)

Exponential Growth — J-shaped Curve

Logistic Growth — S-shaped (Sigmoid) Curve

Four Phases of the Logistic Curve

Where Is Growth Rate Fastest?

3. Density-Dependent vs Density-Independent Factors

Density-Dependent Factors Negative Feedback

Density-Independent Factors No Feedback

4. r-Selected vs K-Selected Species

5. Human Population Growth — Demographic Transition Model

India's Population Trajectory

6. Malthusian Theory vs Modern Carrying-Capacity Debates

Malthusian Theory (Thomas Malthus, 1798)

Why Malthus's Simple Prediction Failed to Materialise Globally

Modern Carrying-Capacity Debate

7. Ecological Footprint vs Biocapacity

Ecological Footprint Demand

Biocapacity Supply

Earth Overshoot Day

8. Case Studies — Overshoot & Carrying-Capacity Debates

St. Matthew Island Reindeer Crash (1944-1966)

India / Global Carrying-Capacity Debates

9. Current Affairs Link (2024–2026)

10. Prelims PYQs

11. Mains PYQs

Model Answer Framework

Model Answer Framework

Model Answer Framework

15-Minute Revision Box

Rapid Revision — Carrying Capacity & Population Growth

Carrying Capacity (K)

Growth Models

Regulating Factors

r vs K Strategists

Demographic Transition Model (5 stages)

Malthus vs Modern Debate

Quick Facts