Applied Ecology and Evolution II: Epidemiology and the SIR Model, Zoonoses, Antibiotic Resistance, Climate Change, Threats to Biodiversity and Invasive Species
1. Epidemiology: the SIR model, R₀ and herd immunity
The SIR model (Kermack and McKendrick, 1927) divides a host population of size N into Susceptible, Infectious and Recovered (immune) classes: dS/dt = −βSI/N, dI/dt = βSI/N − γI, dR/dt = γI, where β is the transmission rate and γ the recovery rate, so the mean infectious period is 1/γ. The basic reproduction number R₀ is the average number of secondary infections one infectious individual causes in a wholly susceptible population; here R₀ = β/γ. With β = 0.3 per day and an infectious period of 10 days, R₀ = 0.3 × 10 = 3. An infection invades only if R₀ > 1, and an epidemic grows only while the effective reproduction number R_e = R₀ × S/N exceeds 1: with R₀ = 4 and 60 % of the population immune, R_e = 4 × 0.4 = 1.6 and cases are still rising.
An epidemic turns over when S/N falls below 1/R₀. Vaccination that keeps the immune fraction above the herd-immunity threshold p_c = 1 − 1/R₀ keeps R_e below 1, protecting even the unvaccinated: for R₀ = 3, p_c = 1 − 1/3 = 0.667, so 66.7 % must be immune. If the vaccine protects only a fraction E of those vaccinated, the coverage needed is V_c = (1 − 1/R₀)/E; for R₀ = 5 and E = 0.9, V_c = 0.8/0.9 = 0.889, or 88.9 %. When 1 − 1/R₀ exceeds E, elimination by that vaccine alone is impossible. Highly transmissible infections such as measles have R₀ values commonly quoted in the range of about 12 to 18, which is why their thresholds exceed 90 %.
- Density-dependent transmission (βSI) rises with host density, so there is a threshold density below which an infection cannot persist — the logic of culling and of the critical community size for measles. Frequency-dependent transmission (βSI/N), typical of sexually transmitted and vector-borne infections, has no such threshold.
- Incidence is the rate of new cases; prevalence is the proportion infected at a time. A long infectious period raises prevalence at a given incidence.
- Microparasites (viruses, bacteria, protozoa) are modelled by host class as above; macroparasites (helminths, ticks) by the number of parasites per host, whose aggregated (negative binomial) distribution means most parasites live in a few hosts.
- Virulence evolution: in the trade-off view, a pathogen that replicates faster transmits more per unit time but shortens the infectious period by killing or sickening the host, so an intermediate virulence often maximises R₀; the attenuation of myxoma virus in Australian rabbits fits this.
2. Zoonotic diseases and spillover
A zoonosis is an infection naturally transmitted from vertebrate animals to people. Most emerging infectious diseases of humans are zoonotic, with wildlife reservoirs prominent among them. Transmission can be direct (bites, contact with body fluids), through food, or through vectors such as mosquitoes, ticks and fleas. Spillover needs a chain of events: the pathogen must be present and shed by the reservoir, reach people, and be able to infect and establish in them. Land-use change — deforestation, agricultural expansion into forest, livestock intensification, the wildlife trade — raises contact between reservoirs, domestic animals and people and is a major driver of emergence; the One Health approach treats human, animal and environmental health together for this reason.
| Disease | Agent and reservoir | Route to people |
|---|---|---|
| Rabies | lyssavirus; domestic dogs are the main source of human cases in India, with wild carnivores and bats as other reservoirs | bites |
| Nipah virus disease | henipavirus; fruit bats of the genus Pteropus | food contaminated by bats, pigs as intermediate hosts, then person to person |
| Kyasanur Forest Disease | a tick-borne flavivirus recognised in Karnataka in 1957; small mammals as reservoirs, monkeys as amplifying hosts | bites of Haemaphysalis ticks in forest |
| Plague | the bacterium Yersinia pestis; wild rodents | bites of infected fleas |
| Lyme disease | the bacterium Borrelia burgdorferi; rodents such as the white-footed mouse in North America | bites of Ixodes ticks |
| Japanese encephalitis | a flavivirus; wading birds as reservoirs, pigs as amplifiers | Culex mosquitoes; humans are dead-end hosts |
3. Antibiotic resistance as evolution
Antibiotic resistance is natural selection that can be watched in real time. Resistant variants arise by mutation or arrive by horizontal gene transfer — conjugation (plasmids, often carrying several resistance genes at once), transformation (uptake of free DNA) and transduction (transfer by bacteriophages) — and an antibiotic then kills or halts the susceptible cells, so the resistant ones increase. Resistance genes long predate clinical use: they occur in environmental bacteria and in permafrost samples thousands of years old, because many antibiotics are natural products of microbes.
| Mechanism | How it works | Example |
|---|---|---|
| Enzymatic inactivation | an enzyme destroys or modifies the drug | β-lactamases that open the β-lactam ring of penicillins |
| Target modification | the drug’s target is altered so the drug no longer binds | MRSA: the mecA gene encodes PBP2a, a penicillin-binding protein with low affinity for β-lactams |
| Efflux pumps | membrane pumps expel the drug | tetracycline efflux; multidrug pumps in Gram-negative bacteria |
| Reduced permeability | fewer or altered porins let less drug in | porin loss in Gram-negative bacteria |
Resistance often carries a fitness cost in the absence of the drug, so reducing use can slow or reverse its spread — but compensatory mutations frequently reduce the cost, and resistance then persists. Selection is strongest where drugs are used heavily: in hospitals, in livestock production and in the environment around manufacturing effluent. Worked example of haploid selection: a resistant strain at frequency 0.01 with twice the growth of susceptible cells under treatment multiplies its odds by 2 each generation; after 5 generations the odds are (0.01/0.99) × 2⁵ = 0.323, so its frequency is 0.323/1.323 = 0.244. Stewardship — using antibiotics only when needed, at the right dose and duration — aims to reduce this selection pressure.
4. Climate change: causes, consequences, adaptation and mitigation
Causes: the greenhouse gases carbon dioxide, methane and nitrous oxide absorb outgoing infrared radiation and warm the lower atmosphere. Atmospheric CO₂ was about 280 ppm before industrialisation and has been above 400 ppm since the mid-2010s, mainly from burning fossil fuels and secondarily from land-use change; methane comes from wetlands, livestock, rice paddies, landfills and fossil-fuel extraction, and nitrous oxide largely from fertilised soils. Methane and nitrous oxide are far more potent per molecule than CO₂ but are present at much lower concentrations. The IPCC’s Sixth Assessment Report put global surface temperature in 2011–2020 at about 1.1 °C above 1850–1900 and attributed the warming unequivocally to human influence.
| Response | What is observed | Example |
|---|---|---|
| Range shifts | species move poleward and upslope; mountain-top species run out of space | upslope shifts of plants and birds in the Himalaya and the Alps |
| Phenology | earlier flowering, leaf-out, breeding and migration in spring | earlier flowering in long-term records of many regions |
| Trophic mismatch | interacting species shift at different rates | great tits whose chicks hatch after the peak of winter-moth caterpillars |
| Coral bleaching | heat stress makes corals expel their symbiotic algae (zooxanthellae) | repeated mass bleaching of the Great Barrier Reef and Indian Ocean reefs |
| Ocean acidification | absorbed CO₂ lowers seawater pH and carbonate saturation | surface ocean pH has fallen by about 0.1 since pre-industrial times; shell-building organisms are stressed |
| Temperature-dependent sex ratios | warmer nests skew sex ratios | sea turtles, whose warmer nests produce more females |
Adaptation of species to climate change happens through plasticity (shifting timing within a generation), evolutionary change (heritable shifts in phenology or tolerance, possible in species with short generations and large populations) and movement; conservation can help by protecting corridors and climate refugia, reducing other stresses, and, controversially, by assisted migration of species beyond their current range. Mitigation reduces the cause: cutting emissions through renewable energy and efficiency, and enhancing sinks through forest protection and restoration — REDD+ pays for reduced emissions from deforestation and forest degradation. The Paris Agreement (2015) aims to hold warming well below 2 °C above pre-industrial levels and to pursue efforts to limit it to 1.5 °C.
5. Threats to biodiversity: habitat loss, pollution and invasive species
The major threats are often summarised as HIPPO — Habitat loss, Invasive species, Pollution, (human) Population and Overharvesting — with climate change now added. Habitat loss and change is the largest single threat on land: conversion to agriculture, fragmentation into small, isolated patches that support smaller populations and suffer edge effects, and degradation. Pollution acts through toxicity and through altered nutrients. Persistent, fat-soluble pollutants undergo biomagnification, rising in concentration at each trophic level: DDT residues in top predators caused eggshell thinning and population crashes of raptors such as the peregrine falcon. In South Asia, residues of the veterinary drug diclofenac in livestock carcasses caused kidney failure in vultures that fed on them, and populations of three Gyps species fell by more than 95 %. Nutrient run-off causes eutrophication: algal blooms, oxygen depletion when they decompose, and fish kills.
An invasive species is a non-native species that establishes, spreads and causes ecological or economic harm. Invasion proceeds through stages — transport, introduction, establishment and spread — and most species fail at each; Williamson’s tens rule is the rough generalisation that about one in ten passes each stage, so of 1000 imported species about 100 appear in the wild, about 10 establish and about 1 becomes a pest. Success rises with propagule pressure (the number and frequency of individuals released). Explanations for success include the enemy release hypothesis (freedom from the natural enemies of the native range), evolution of increased competitive ability (EICA, reallocating resources from defence to growth once enemies are absent), novel weapons (allelochemicals to which native plants are not adapted) and empty niches or disturbance. India’s notorious invaders include Lantana camara in forests, Prosopis juliflora in arid lands, water hyacinth Eichhornia crassipes in wetlands, Parthenium hysterophorus in croplands and pastures, and Mikania micrantha in the north-east and the Western Ghats; the African catfish Clarias gariepinus threatens native fish.
Key takeaways
- SIR: R₀ = β/γ = transmission rate × infectious period; an infection invades if R₀ > 1 and grows while R_e = R₀S/N > 1.
- Herd-immunity threshold 1 − 1/R₀; with vaccine efficacy E the coverage needed is (1 − 1/R₀)/E; density-dependent transmission has a threshold host density, frequency-dependent does not.
- Zoonoses spill over from reservoirs such as bats, rodents and dogs, and land-use change drives emergence; the dilution effect can link biodiversity to lower risk.
- Resistance evolves by mutation and horizontal gene transfer under selection by the drug; β-lactamases, target change (mecA in MRSA), efflux and reduced permeability are the mechanisms.
- Climate change shifts ranges poleward and upslope, advances phenology, causes mismatches, bleaching and acidification; HIPPO names the threats, and the tens rule, enemy release, EICA and novel weapons describe invasions.
Practice questions (16)
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.
In an SIR model the transmission rate is β = 0.3 per day and the mean infectious period is 10 days. The herd-immunity threshold, as a percentage to one decimal place, is ____.
Numerical answer — type the value.
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Answer: 66.7
R₀ = β × infectious period = 0.3 × 10 = 3, and p_c = 1 − 1/R₀ = 1 − 1/3 = 0.667 = 66.7 %. Answering 33.3 gives 1/R₀, the susceptible fraction at which the epidemic turns over, not the immune fraction needed.An infection has R₀ = 5, and a vaccine protects 90 % of those who receive it. The minimum vaccination coverage needed to prevent sustained transmission, as a percentage to one decimal place, is ____.
Numerical answer — type the value.
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Answer: 88.9
The immune fraction must reach 1 − 1/5 = 0.8; with 90 % efficacy the coverage needed is 0.8/0.9 = 0.889 = 88.9 %. Answering 80 ignores vaccine failure, and 72 multiplies by the efficacy instead of dividing.An infection has R₀ = 4, and 60 % of the population is currently immune. The effective reproduction number, to one decimal place, is ____.
Numerical answer — type the value.
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Answer: 1.6
R_e = R₀ × S/N = 4 × 0.4 = 1.6, still above 1, so cases keep rising; the threshold for this infection is 1 − 1/4 = 75 % immune. Multiplying by the immune fraction instead gives 2.4.In the basic SIR model, which statements are correct?
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Answer: A — R₀ equals the transmission rate multiplied by the mean infectious period; B — An epidemic begins to decline once the susceptible fraction falls below 1/R₀; C — Vaccinating a fraction 1 − 1/R₀ of the population with a perfect vaccine prevents sustained transmission
R₀ = β/γ = β × (1/γ). dI/dt < 0 once R₀S/N < 1, and immunising 1 − 1/R₀ keeps R_e below 1. With R₀ < 1 each case causes fewer than one new case on average, so introductions die out whatever the population size.Culling a wildlife reservoir to lower host density is expected to eliminate an infection only if
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Answer: A — transmission is density-dependent, so that R₀ falls below 1 at low host density
With density-dependent transmission (βSI) R₀ is proportional to host density, so there is a threshold density below which the infection cannot persist. With frequency-dependent transmission (βSI/N) contact rates do not fall with density, so culling does not lower R₀ — and it can even spread infection by disrupting host behaviour.Which pairings of a zoonotic disease with its reservoir or vector are correct?
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Answer: A — Nipah virus — Pteropus fruit bats; B — Kyasanur Forest Disease — Haemaphysalis ticks; C — Plague — rodents and their fleas
Nipah is carried by Pteropus bats, KFD by Haemaphysalis ticks with monkeys as amplifiers, and plague by rodents and fleas. Japanese encephalitis is carried by Culex mosquitoes from birds and pigs; humans are dead-end hosts, so it does not pass from person to person.A resistant bacterial strain is at frequency 0.01. Under antibiotic treatment it grows twice as fast per generation as the susceptible strain (haploid selection). Its frequency after 5 generations, to three decimal places, is ____.
Numerical answer — type the value.
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Answer: 0.244
With relative fitness 2, the odds p/(1 − p) double each generation: (0.01/0.99) × 2⁵ = 0.0101 × 32 = 0.323, so p = 0.323/1.323 = 0.244. Multiplying the frequency itself by 32 gives 0.32, which ignores that the susceptible cells also still grow.Methicillin resistance in Staphylococcus aureus (MRSA) is mainly due to
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Answer: A — the mecA gene, encoding a penicillin-binding protein with low affinity for β-lactams
MRSA carries mecA, which encodes PBP2a; the cell-wall enzyme keeps working because β-lactams bind it poorly — target modification. Porins belong to the outer membrane of Gram-negative bacteria, which S. aureus lacks, and bacteria do not make antibodies.Which statements about the evolution of antibiotic resistance are correct?
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Answer: A — Resistance genes can spread between species on plasmids by conjugation; B — Resistance often carries a fitness cost when the antibiotic is absent; C — Compensatory mutations can allow resistance to persist after antibiotic use stops
Plasmid conjugation moves resistance across species; resistance is often costly without the drug, but compensatory mutations can remove the cost. The antibiotic selects variants that already exist or arrive by gene transfer — the Lamarckian idea that the drug makes each cell become resistant is the misconception.Great tits in the Netherlands now often hatch their chicks after the spring peak of the caterpillars they feed on, because the caterpillars have advanced their timing more than the birds. This is an example of
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Answer: A — phenological (trophic) mismatch
When interacting species shift their seasonal timing at different rates, the consumer’s peak demand no longer matches the resource peak — a phenological or trophic mismatch. A range shift is a change in where a species lives, not when it breeds.Which of the following are well-documented biological consequences of recent climate change?
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Answer: A — Shifts of species ranges upslope and towards the poles; B — Earlier spring flowering and breeding; C — Mass bleaching of coral reefs
Range shifts, advancing spring phenology and heat-driven coral bleaching are all widely recorded. The ocean absorbs CO₂, which forms carbonic acid, so surface pH has fallen by about 0.1 since pre-industrial times — acidification, not a rise in pH.Which of these is a mitigation measure rather than an adaptation measure?
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Answer: A — Paying to reduce emissions from deforestation (REDD+)
Mitigation reduces the cause — greenhouse-gas emissions or their accumulation — and REDD+ does that by keeping forest carbon out of the atmosphere. Corridors, assisted migration and refugia help species cope with change that is already happening, which is adaptation.An introduced plant grows larger and more vigorously than in its native range, where specialist insects feed on it; none of those insects came with it. The hypothesis this most directly supports is
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Answer: A — the enemy release hypothesis
Escape from the natural enemies of the native range is enemy release; EICA extends it by proposing that the plant then evolves to shift resources from defence to growth. Novel weapons concern allelochemicals, the tens rule the attrition across invasion stages, and biotic resistance works against invaders, not for them.According to Williamson’s tens rule, of 1000 species imported into a region, about how many would be expected to become established?
Numerical answer — type the value.
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Answer: 10
About one in ten passes each stage: 1000 imported → about 100 appear in the wild → about 10 establish → about 1 becomes a pest. Answering 100 stops one stage early, and 1 is the number expected to become a pest.Which of the following are invasive alien plants that cause serious ecological problems in India?
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Answer: A — Lantana camara; B — Prosopis juliflora; C — Eichhornia crassipes
Lantana (from tropical America) invades forests, Prosopis juliflora (from Central and South America) arid lands and grasslands, and water hyacinth (from South America) wetlands. Teak is native to peninsular India and South-East Asia, so it is not an alien invader here.Populations of three Gyps vulture species in South Asia fell by more than 95 % within little more than a decade. The main cause was
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Answer: A — residues of the veterinary drug diclofenac in the livestock carcasses they ate
Vultures feeding on carcasses of cattle treated with diclofenac suffered kidney failure; the decline slowed after the drug was banned for veterinary use. DDT-driven eggshell thinning is the classic cause of raptor declines elsewhere, but it does not explain this collapse of scavengers.