1.1 Population biology

Population biology studies groups of organisms of the same species living in defined areas, their abundance, structure, genetic composition, interactions and changes through time.

1.2 Population

A population is a group of individuals of the same species occupying a defined area at a particular time and potentially connected by reproduction or gene flow.

1.3 Species as biological units

Species are lineages of organisms that maintain identity through reproductive, ecological and evolutionary processes. No single species concept solves every biological case.

1.4 Biological species concept

The biological species concept emphasizes actual or potential interbreeding within species and reproductive isolation from other such groups.

1.5 Morphological species concept

Morphological approaches distinguish species using consistent differences in form and structure. They are useful for fossils and many field identifications but can be complicated by sexual dimorphism and cryptic species.

1.6 Phylogenetic perspective

Phylogenetic approaches recognise separately evolving lineages using shared ancestry and diagnosable differences.

1.7 Ecological properties

Species occupy ecological niches involving resources, environmental tolerances and interactions. Ecological differentiation can contribute to coexistence and divergence.

1.8 Population attributes

Density, dispersion, age structure, sex ratio, birth rate, death rate, immigration and emigration describe populations rather than single organisms.

1.9 Gene pool

The gene pool is the total collection of alleles in a population. Evolutionary processes change allele and genotype frequencies through generations.

2.1 Meaning of variation

Variation refers to differences among individuals or populations in genetic, morphological, physiological, behavioural or other traits.

2.2 Genetic variation

Genetic variation arises from mutation, recombination, segregation and movement of alleles among populations.

2.3 Mutation

Mutation generates new sequence variants. Although mutation rates at individual loci may be low, mutation is the ultimate source of new alleles.

2.4 Recombination

Meiosis reshuffles existing variation through independent assortment and crossing over, generating new combinations of alleles.

2.5 Phenotypic variation

Observed phenotype reflects genotype, environment and their interaction. Not every phenotypic difference is heritable.

2.6 Continuous variation

Quantitative traits can show a broad range of values because multiple genes and environmental factors contribute.

2.7 Discontinuous variation

Some traits form distinct categories, often where major genetic differences strongly determine phenotype.

2.8 Heritable variation

Natural selection produces evolutionary change only when phenotypic differences are associated with heritable differences.

2.9 Measuring variation

Means, variances, frequency distributions and allele frequencies can describe variation quantitatively.

3.1 Allele frequency

Allele frequency is the proportion of copies of a particular allele among all copies of that locus in the population.

3.2 Genotype frequency

Genotype frequency is the proportion of individuals carrying a particular genotype.

3.3 Hardy-Weinberg principle

For a two-allele autosomal locus under ideal assumptions, allele frequencies p and q satisfy p+q=1 and expected genotype frequencies are p², 2pq and q².

3.4 Assumptions

The ideal model assumes random mating with respect to the locus, very large population size, and absence of selection, mutation and migration affecting allele frequencies.

3.5 Purpose of equilibrium model

Hardy-Weinberg equilibrium provides a null expectation. Departures can motivate investigation of population structure, nonrandom mating, selection, migration, sampling or other processes.

3.6 Estimating allele frequencies

Allele frequencies can be calculated directly from genotype counts by counting two alleles per diploid individual.

3.7 Estimating recessive allele frequency

If a recessive phenotype corresponds exactly to aa and equilibrium assumptions are justified, q can be estimated as the square root of q².

3.8 Heterozygosity

Expected heterozygosity under the two-allele equilibrium model is 2pq and is highest when p and q are both 0.5.

3.9 Limitations

Real populations can violate multiple assumptions simultaneously; Hardy-Weinberg calculations are models, not claims that nature is static.

4.1 Definition

Natural selection is differential survival or reproductive success associated with heritable phenotypic differences.

4.2 Requirements

Selection requires variation, differences in reproductive contribution related to that variation, and heritability of relevant differences.

4.3 Fitness

Evolutionary fitness concerns relative contribution of genotypes or phenotypes to subsequent generations in a particular environment.

4.4 Directional selection

Directional selection favours phenotypes toward one end of a distribution and can shift the population mean.

4.5 Stabilizing selection

Stabilizing selection favours intermediate phenotypes relative to extremes and can reduce phenotypic variance.

4.6 Disruptive selection

Disruptive selection can favour contrasting phenotypes relative to intermediates under appropriate ecological conditions.

4.7 Balancing selection

Balancing processes can maintain multiple alleles, for example when heterozygotes have an advantage or selection varies across space or time.

4.8 Frequency-dependent selection

Fitness can depend on how common or rare a phenotype is.

4.9 Sexual selection

Differences in mating success can cause evolutionary change through competition for mates or mate choice.

4.10 Selection and environment

Fitness is context-dependent; a trait advantageous in one environment may be neutral or disadvantageous in another.

5.1 Genetic drift

Genetic drift is random change in allele frequencies caused by finite sampling of gametes and individuals across generations.

5.2 Population size

Drift is generally stronger in small populations because sampling error is proportionally larger.

5.3 Founder effect

A new population founded by few individuals can have allele frequencies that differ by chance from the source population.

5.4 Population bottleneck

A sharp reduction in population size can remove genetic variation and alter allele frequencies by chance.

5.5 Gene flow

Gene flow is movement of alleles among populations through migration and reproduction.

5.6 Mutation and migration

Mutation introduces new alleles, while migration can introduce alleles already present elsewhere.

5.7 Nonrandom mating

Assortative mating and inbreeding alter genotype proportions and can increase homozygosity without necessarily changing allele frequencies directly.

5.8 Interaction among forces

Selection, drift, mutation and gene flow operate simultaneously; observed change reflects their combined effects.

6.1 Meaning

An adaptation is a heritable feature shaped by natural selection because it contributed to reproductive success in relevant ancestral environments.

6.2 Adaptation versus acclimatization

Adaptation is an evolutionary population-level outcome; acclimatization is a reversible or developmental response within an individual's lifetime.

6.3 Structural adaptations

Morphological traits such as body form, leaf structure or protective features can influence performance in particular environments.

6.4 Physiological adaptations

Water conservation, temperature regulation, salt balance and metabolic specialisations illustrate physiological adaptation.

6.5 Behavioural adaptations

Foraging, migration, mating and defensive behaviours can influence survival and reproduction.

6.6 Trade-offs

Adaptations involve constraints and costs. Improving one function can reduce performance in another.

6.7 Local adaptation

Populations can evolve differences suited to local conditions when selection overcomes homogenising effects of gene flow.

6.8 Testing adaptation

A plausible adaptive story is not sufficient; comparative, experimental, genetic and ecological evidence is required.

6.9 Exaptation

A feature that evolved in one context can later be co-opted for another function.

7.1 Reproductive isolation

Reproductive isolation consists of barriers that reduce gene exchange between diverging populations.

7.2 Prezygotic barriers

Barriers before fertilisation include habitat, temporal, behavioural, mechanical and gametic isolation.

7.3 Postzygotic barriers

After fertilisation, hybrids may show reduced viability, fertility or later-generation performance.

7.4 Geographic isolation

Physical separation can reduce gene flow and permit populations to diverge through selection, drift and mutation.

7.5 Ecological isolation

Populations using different habitats or resources may encounter one another less often and experience different selection.

7.6 Temporal isolation

Differences in breeding or flowering time can reduce mating between populations.

7.7 Behavioural isolation

Divergent courtship signals or mate preferences can reduce interbreeding.

7.8 Mechanical and gametic barriers

Morphological incompatibility or failure of gametes to unite can prevent successful fertilisation.

7.9 Reinforcement

Where hybrids have low fitness, selection can favour traits that reduce interbreeding between diverged populations.

8.1 Hybridization

Hybridization is reproduction between individuals from genetically differentiated populations or species, producing mixed ancestry.

8.2 Hybrid zones

Hybrid zones are geographic regions where differentiated populations meet and interbreed.

8.3 Introgression

Repeated backcrossing can transfer alleles from one population or species into another.

8.4 Outcomes

Hybridization may produce low-fitness offspring, stable hybrid zones, adaptive introgression, lineage fusion or, in some contexts, new evolutionary lineages.

8.5 Plants and hybridization

Hybridization and changes in chromosome number have played important roles in plant evolution.

8.6 Isolation breakdown

Environmental change, range shifts or altered behaviour can bring previously isolated groups into contact.

8.7 Genetic consequences

Hybridization can increase variation but can also threaten distinct small populations through genetic swamping.

8.8 Evolutionary significance

Gene exchange across lineage boundaries demonstrates that speciation can be a process rather than an instantaneous event.

9.1 Scope

The origin of life concerns how nonliving chemical systems gave rise to the earliest self-maintaining and evolving biological systems.

9.2 Chemical evolution

Scientific hypotheses consider formation and accumulation of organic molecules, emergence of compartmentalisation and systems capable of heredity and selection.

9.3 Prebiotic chemistry

Experiments show that some organic compounds can form under plausible nonbiological conditions, but no single experiment reconstructs the complete historical pathway.

9.4 Information and replication

Any early evolving system required mechanisms through which variants could persist and differ in reproductive success.

9.5 Compartmentalisation

Membrane-like compartments can concentrate molecules and separate internal chemistry from the environment.

9.6 RNA-world hypothesis

RNA is of interest because RNA molecules can store sequence information and some RNAs catalyse reactions.

9.7 Evidence and uncertainty

Origin-of-life research evaluates plausible mechanisms using chemistry, geology and biology; major historical details remain uncertain.

9.8 Origin of life versus evolution

Biological evolution describes change in reproducing populations once heredity and variation exist; it is conceptually distinct from the initial origin of life.

10.1 Speciation

Speciation is the evolutionary formation of distinct lineages that become reproductively or evolutionarily independent.

10.2 Allopatric speciation

Geographic separation can interrupt gene flow, allowing populations to diverge until reproductive isolation evolves.

10.3 Peripatric situations

Small peripheral populations may diverge under a combination of isolation, drift and local selection.

10.4 Parapatric divergence

Neighbouring populations can diverge despite limited gene flow when contrasting environments impose divergent selection.

10.5 Sympatric divergence

Reproductive isolation can evolve without geographic separation when ecological, genetic or behavioural processes strongly reduce gene exchange.

10.6 Polyploid speciation

In plants especially, chromosome-set changes can create rapid reproductive barriers.

10.7 Species boundaries

Speciation is often gradual; different species criteria may disagree during intermediate stages.

10.8 Evidence

Comparative genetics, morphology, ecology, behaviour and reproductive compatibility can provide evidence about divergence.

10.9 Extinction

Speciation adds lineages while extinction removes them; biodiversity reflects both processes through time.

11.1 Definition

Adaptive radiation is relatively rapid diversification of one ancestral lineage into multiple forms associated with different ecological opportunities.

11.2 Ecological opportunity

New habitats, reduced competition or availability of underused resources can permit diversification.

11.3 Key innovations

A novel trait can sometimes allow a lineage to exploit resources or habitats previously inaccessible.

11.4 Divergent selection

Different environments favour different phenotypes, increasing ecological and morphological divergence.

11.5 Isolation

Reduced gene flow among populations permits differences to accumulate.

11.6 Examples

Classic examples include diversification of island birds, cichlid fishes and several plant lineages, though each radiation has its own history.

11.7 Limits

Not every diverse lineage represents a single simple adaptive radiation; historical and phylogenetic evidence is required.

12.1 Plant evolutionary transitions

Plant evolution includes major transitions in life cycles, vascular tissues, seeds, pollen, flowers and fruits.

12.2 Early land plants

Colonisation of land required solutions to desiccation, support, reproduction and transport.

12.3 Vascular plants

Vascular tissues improved internal transport and mechanical support, contributing to larger terrestrial growth forms.

12.4 Seed evolution

Seeds protect embryos, provide stored resources and permit dormancy and dispersal.

12.5 Pollen

Pollen reduces dependence on free external water for transfer of male gametes in seed plants.

12.6 Gymnosperms

Gymnosperms possess seeds not enclosed within fruits and include several major living lineages.

12.7 Angiosperms

Flowering plants combine flowers, enclosed ovules and fruits with diverse pollination and dispersal systems.

12.8 Coevolution

Interactions with pollinators, herbivores, pathogens and dispersers can generate reciprocal selective pressures.

12.9 Diversification

Plant diversity reflects innovation, environmental change, geographic history, extinction and lineage-specific ecological opportunities.

13.1 Animal diversification

Animal evolution involved diversification of body plans, tissues, symmetry, feeding systems, locomotion and developmental patterns.

13.2 Multicellularity

Multicellular organisation enabled cell specialisation and larger integrated bodies.

13.3 Bilateral organisation

Bilateral symmetry is associated in many lineages with directional movement and concentration of sensory structures.

13.4 Invertebrate diversification

Arthropods, molluscs, annelids and other groups evolved distinctive body plans and ecological strategies.

13.5 Vertebrate origins

Vertebrate evolution involved innovations in support, sensory systems, circulation and locomotion.

13.6 Transition to land

Tetrapod ancestors evolved structural and physiological features that permitted increasing use of terrestrial environments.

13.7 Amniotes

The amniotic reproductive system reduced dependence on aquatic environments for embryonic development.

13.8 Birds and mammals

These lineages evolved distinctive combinations of endothermy, integument, reproduction and behaviour.

13.9 Evolutionary trees

Modern classification interprets similarities in the context of common ancestry rather than as a simple ladder of progress.

14.1 Humans as primates

Humans are primates and share common ancestry with other living primates; humans did not evolve from any modern ape species.

14.2 Hominin lineage

Hominins include humans and extinct lineages more closely related to humans than to chimpanzees.

14.3 Bipedalism

Habitual bipedal locomotion is a major feature of hominin evolution and involved changes in pelvis, spine, limbs and feet.

14.4 Brain and behaviour

Brain expansion, tool use, social learning and culture developed through complex evolutionary histories rather than a single linear sequence.

14.5 Genus Homo

The genus Homo includes multiple extinct species as well as Homo sapiens.

14.6 Dispersal

Hominin populations dispersed from Africa at different times, and genetic evidence reveals episodes of interaction among some lineages.

14.7 Modern human variation

Most human genetic variation occurs within populations, and human populations have remained connected by gene flow.

14.8 Evolution is branching

Human evolution is represented more accurately as a branching tree with coexistence and extinction than as a straight progression.

14.9 Evidence

Fossils, archaeology, comparative anatomy, dating methods and genetics contribute complementary evidence.

15.1 Meaning

Population dynamics examines changes in population size, density and structure through time.

15.2 Birth and death

Births add individuals and deaths remove them. Their balance contributes to natural population increase or decrease.

15.3 Immigration and emigration

Immigration adds individuals from elsewhere while emigration removes residents.

15.4 Population balance

For a defined interval, change can be represented as births plus immigration minus deaths minus emigration.

15.5 Per capita growth

Per capita rates express demographic events relative to population size, allowing comparison among populations.

15.6 Age structure

The proportions of pre-reproductive, reproductive and post-reproductive individuals influence future growth potential.

15.7 Sex ratio

Sex ratio can influence reproductive output depending on mating system and biology.

15.8 Dispersion

Individuals may be clumped, random or relatively uniform in space, affecting interactions and sampling.

15.9 Metapopulations

Some species exist as networks of local populations linked by dispersal, with local extinction and recolonisation.

15.10 Population regulation

Density-dependent and density-independent factors interact to shape abundance.

16.1 Exponential model

Under constant per capita growth and unlimited conditions, population change can be represented by dN/dt = rN.

16.2 Intrinsic rate

The parameter r is the per capita rate of increase under the model and combines contributions of birth and death rates.

16.3 Exponential solution

For continuous growth with constant r, N(t)=N0e^(rt).

16.4 Doubling time

For positive exponential growth, doubling time is ln(2)/r.

16.5 Logistic model

The logistic model incorporates density dependence: dN/dt = rN(1-N/K).

16.6 Carrying capacity

K represents the population size around which environmental limitation becomes strong in the simplified logistic model.

16.7 Growth maximum

In the basic logistic model, absolute population growth is greatest at N=K/2.

16.8 Model limitations

Natural populations experience changing environments, time lags, age structure, migration and species interactions, so simple models are approximations.

16.9 Discrete growth

Organisms with distinct breeding intervals may be modelled with discrete-time growth, often using finite rate λ.

16.10 Model selection

The biological life history and available data determine which population model is appropriate.

17.1 Density-dependent factors

Competition, disease and some forms of predation can intensify as population density increases.

17.2 Density-independent influences

Drought, storms, fires or extreme temperatures can affect populations without effects scaling simply with density.

17.3 Resource limitation

Food, water, nutrients, light, nesting sites and space can constrain growth.

17.4 Competition

Individuals may compete within species or with other species for limiting resources.

17.5 Predation

Predators can alter prey abundance, behaviour and population cycles.

17.6 Disease and parasitism

Transmission and impact of pathogens or parasites can depend on host density, environment and host condition.

17.7 Climate

Temperature and rainfall influence survival, reproduction, resource availability and geographic distribution.

17.8 Habitat change

Habitat loss, fragmentation and degradation alter carrying conditions and movement.

17.9 Human activities

Harvesting, pollution, introductions, conservation and land-use change can alter demographic rates.

17.10 Stochasticity

Random environmental and demographic events are especially important in small populations.

18.1 Microevolution

Microevolution is change in allele frequencies within populations through mutation, selection, drift and gene flow.

18.2 Population divergence

When populations experience different evolutionary forces and reduced gene flow, genetic differences can accumulate.

18.3 Ecology and evolution

Environmental conditions influence selection, while evolutionary change can alter ecological interactions.

18.4 Demography and evolution

Population size and structure affect drift, selection efficiency and availability of genetic variation.

18.5 Conservation implications

Small isolated populations may face demographic risk, inbreeding and loss of genetic diversity.

18.6 Evolutionary rescue

Rapid adaptive change can sometimes improve persistence under environmental change, but it is not guaranteed and depends on variation and demographic conditions.

18.7 Unified view

Species, populations, genes, environments and demographic processes form an interacting evolutionary system.

Counting Alleles from Genotypes

Hardy-Weinberg Expected Counts

From Recessive Phenotype to Carrier Frequency

Selection Coefficients

Relative fitness values can be scaled so that the highest genotype fitness is 1. The selection coefficient is commonly written s=1−w for a genotype with relative fitness w. Thus w=0.8 corresponds to s=0.2 under that scaling. This does not mean 20% of individuals must literally die; fitness can reflect total reproductive contribution.

Mean Fitness Concept

If genotype frequencies are known, mean relative fitness can be calculated as the sum of each genotype frequency multiplied by its relative fitness. This weighted average helps predict genotype contributions after selection. The exact biological interpretation depends on when in the life cycle frequencies and fitness are measured.

Finite Rate of Increase

Per Capita Change

Logistic Growth at Different Densities

The factor (1−N/K) describes the simple density-dependent reduction in per capita growth. When N is very small relative to K, the factor is near 1 and logistic growth resembles exponential growth. At N=K, the factor is zero. If N temporarily exceeds K in the mathematical model, the factor becomes negative and population size tends to decline.

Maximum Logistic Increment

The product N(1−N/K) is maximised at N=K/2. Therefore the basic logistic model predicts greatest absolute increase at half the carrying capacity. This result is mathematical and should not be applied uncritically to populations with age structure, time lags or changing K.

Population Projection

Antibiotic Resistance as Natural Selection

Within a microbial population, genetic variants can differ in susceptibility to an antibiotic. Treatment creates a selective environment in which susceptible cells contribute less to subsequent generations while resistant variants can survive and reproduce. The antibiotic does not intentionally create resistance because bacteria need it; rather, selection changes the frequencies of variants. Mutation and horizontal gene transfer can supply resistance determinants, while selection changes their representation.

Pesticide Resistance

Pest populations can similarly evolve resistance when heritable variants survive control measures disproportionately. Repeated use of the same mode of action can impose strong selection. Integrated pest management seeks, among other goals, to reduce conditions that consistently favour the same resistance mechanisms.

Industrial Melanism as a Selection Illustration

Changes in environmental background can alter predation risk for differently coloured organisms. Where colour is heritable, differential survival and reproduction can change phenotype and allele frequencies. The important lesson is not the particular colour but the interaction between heritable variation and changing environment.

Founder Effect on an Island

If a few individuals colonise an island, they carry only a sample of the source population's alleles. Even before selection acts, the new population can differ genetically because of sampling. Subsequent small population size can strengthen drift, while novel ecological conditions can impose new selection.

Bottleneck and Conservation

A population reduced by habitat destruction or catastrophic mortality can lose rare alleles by chance. If numbers later recover, census size may rebound faster than genetic diversity. This distinction between demographic recovery and genetic recovery is important in conservation biology.

Gene Flow and Local Adaptation

Suppose two plant populations occupy wet and dry habitats. Selection may favour different physiological traits, but pollen movement between sites continually introduces alleles from the other habitat. Local adaptation depends partly on the balance between divergent selection and homogenising gene flow.

Isolation and Speciation

A river, mountain, habitat discontinuity or geographic distance can reduce exchange between populations. Once isolated, mutation, drift and selection cause divergence. If secondary contact occurs later, the populations may interbreed freely, form a hybrid zone, or remain reproductively isolated. Geographic separation starts a process; it does not guarantee speciation.

Adaptive Radiation on Islands

Island systems can provide ecological opportunities and geographic separation. Descendants of a colonising lineage may specialise on different foods or habitats. If divergence is accompanied by reproductive isolation, multiple species can emerge. Phylogenetic evidence is required to demonstrate their common ancestry.

Plant Polyploidy

Whole-genome duplication changes chromosome number. In some plants, a polyploid lineage can become reproductively isolated from its diploid relatives because chromosome pairing in hybrids is disrupted. Polyploidy therefore provides a mechanism through which reproductive isolation can arise rapidly.

Human Adaptation

Human populations have experienced selection associated with diet, pathogens, climate and altitude, among other factors. These adaptations involve particular traits and histories and do not divide humanity into discrete biological ranks. Extensive shared ancestry and gene flow connect human populations.

Life Tables

A life table summarises survival and mortality across ages or stages. Cohort life tables follow a group born at approximately the same time, while static approaches infer age-specific patterns from a population sampled at one period under stronger assumptions. Life tables help identify stages where mortality is concentrated.

Survivorship Curves

Survivorship patterns are often described conceptually as Type I, II and III. Type I has relatively high survival until later life, Type II approximates a more constant mortality risk, and Type III has high early mortality with relatively few survivors reaching later stages. Real species can depart from idealised curves.

Age Structure and Growth

A population dominated by young pre-reproductive individuals can contain demographic momentum for future growth if survival and reproduction remain favourable. A population dominated by older post-reproductive individuals may decline even if current size appears large. Population size alone therefore provides incomplete demographic information.

Density and Sampling

Density estimates depend on the sampling method and spatial pattern. Quadrat sampling may suit sessile or slow-moving organisms; transects can describe change along environmental gradients; mark-recapture methods can estimate mobile animal abundance under specific assumptions. Clumped distributions increase sampling variance if too few sampling units are used.

Mark-Recapture Concept

In a simple two-sample model, a first sample is marked and released, then a second sample is collected. If marked individuals have mixed back into the population and marking does not alter survival or capture probability, the fraction marked in the second sample can estimate the fraction of the total population that was marked initially.

Density Dependence

As density rises, individuals can experience stronger competition for food, space or nesting sites; pathogen transmission can also increase. These effects can reduce per capita birth rate or increase death rate. Density dependence creates negative feedback that can contribute to population regulation.

Time Lags

Population response may lag behind changes in density. Resources can be depleted before reduced reproduction becomes apparent, or predator numbers may rise after prey have already increased. Time lags can generate oscillations rather than smooth logistic trajectories.

Population Cycles

Some populations fluctuate cyclically because of interactions among consumers and resources, delayed density dependence, seasonal forcing or other mechanisms. A repeating pattern alone does not identify its cause; demographic and ecological data are needed.

Metapopulation Dynamics

Habitat fragmentation can divide a species into local populations connected by dispersal. Some patches may become locally extinct while others are colonised. Regional persistence can therefore depend on both local population performance and movement among patches.

Source-Sink Concept

A source habitat produces enough successful reproduction to export individuals, while a sink may persist only because immigrants arrive from better habitats. Observing individuals in a habitat does not prove that the habitat supports a self-sustaining population.

1. National Universities Commission. Core Curriculum and Minimum Academic Standards for the Nigerian University System: Sciences. BIO 302 Population Biology and Evolution.
2. Futuyma, D. J. and Kirkpatrick, M. Evolution.
3. Freeman, S. and Herron, J. C. Evolutionary Analysis.
4. Hartl, D. L. and Clark, A. G. Principles of Population Genetics.
5. Ricklefs, R. E. and Relyea, R. Ecology: The Economy of Nature.
6. Begon, M., Townsend, C. R. and Harper, J. L. Ecology: From Individuals to Ecosystems.
7. Campbell, N. A. et al. Campbell Biology.
8. Ridley, M. Evolution.

Natural Selection as a Change in Representation

Consider a population containing two heritable phenotypes. If phenotype A leaves, on average, more surviving reproductive offspring than phenotype B under current conditions, the alleles contributing to A may increase in representation. The critical comparison is reproductive contribution, not whether individual A organisms live longer in every circumstance. An organism that survives for a long time but produces no descendants can have lower evolutionary fitness than one with a shorter life but greater successful reproduction.

Selection can operate at several life stages. Differential survival before reproduction is viability selection; differences in mating success contribute through sexual selection; differences in fecundity can alter representation through offspring number. The total evolutionary outcome combines these components. Measuring only adult survival can therefore miss important selection.

Relative Fitness and Allele-Frequency Change

Suppose genotypes AA, Aa and aa have frequencies before selection and relative fitness values wAA, wAa and waa. Multiplying each genotype frequency by its fitness gives its proportional contribution after selection before normalisation. Dividing by mean fitness converts these contributions into frequencies among survivors or reproductive contributors. Allele frequencies can then be recalculated.

This calculation is a model of one selection episode. Real populations may also experience mating structure, migration, mutation and drift during the same generation.

Selection Does Not Always Remove Variation

Directional selection can reduce some variants, but selection can also maintain polymorphism. If heterozygotes have higher relative fitness than either homozygote under a stable model, neither allele is necessarily eliminated because each allele gains an advantage when paired in heterozygotes. Spatially variable environments can also favour different alleles in different locations, while migration continually redistributes them.

Negative frequency-dependent selection offers another mechanism: a phenotype may gain an advantage when rare because predators, competitors or mates respond to frequency. As it becomes common, that advantage declines. Such feedback can preserve diversity.

Drift as Repeated Sampling

Imagine an idealised diploid population with only ten breeding individuals. Twenty allele copies are sampled into the next generation. Even if A has frequency 0.5, exactly ten A copies need not be transmitted. Chance can produce twelve, eight or another count. Repeating this process generation after generation makes allele frequencies fluctuate.

In a much larger population, random deviations still occur but constitute a smaller fraction of the gene pool. This is why effective population size strongly influences drift. Over long periods in isolated finite populations, drift can lead to fixation of one allele and loss of another even when the alleles have equal fitness.

Effective Population Size

Census size is the number of individuals counted, whereas effective population size concerns the number effectively contributing genes to subsequent generations under a population-genetic model. Unequal sex ratios, variation in reproductive success and fluctuations in population size can make effective size smaller than census size. Drift is more closely related to effective than simple census size.

This distinction matters in conservation. A population may contain many individuals yet have relatively few successful breeders. Management based only on head counts can therefore overestimate retained genetic diversity.

Gene Flow: Homogenisation and Innovation

Migration followed by reproduction moves alleles. When two populations have different allele frequencies, gene flow tends to reduce their genetic difference. However, incoming alleles can be beneficial in the receiving environment and spread through selection. Gene flow can therefore oppose local divergence while simultaneously providing useful variation.

The balance depends on migration rate and selection strength. Strong divergent selection can maintain local differences despite continuing gene flow, while extensive migration can swamp weak local adaptation.

Mutation-Selection Perspective

Mutation continuously introduces new variants, including deleterious ones. Selection can remove or reduce variants that lower reproductive success, while mutation reintroduces them. Population genetics often studies this balance quantitatively, although the exact equilibrium depends on dominance, mutation rate and fitness effects. The general lesson is that an allele's persistence need not mean it is advantageous.

Inbreeding and Genotype Frequencies

Inbreeding increases the probability that two alleles within an individual are identical by descent and generally increases homozygosity relative to random mating. By itself, nonrandom mating can change genotype frequencies without necessarily changing allele frequencies immediately. Its evolutionary importance becomes greater when homozygous genotypes differ in fitness.

Small isolated populations can experience both drift and inbreeding, but these are distinct concepts. Drift changes allele frequencies through sampling; inbreeding concerns mating among relatives and genotype associations.

Heritability and Evolutionary Response

For quantitative traits, phenotypic variation contains genetic and environmental components. Heritability describes, for a defined population and environment, the proportion of phenotypic variance associated with genetic variance under a specified definition. It is not a fixed property of a trait everywhere and does not state what proportion of an individual's phenotype is 'caused by genes.'

Selection on a quantitative phenotype can produce evolutionary response when relevant variation is heritable. Environmental change can alter both trait means and heritability estimates without genetic evolution.

Reaction Norms and Phenotypic Plasticity

A genotype can produce different phenotypes in different environments; this pattern is its reaction norm. Phenotypic plasticity can itself vary genetically and may be adaptive when environments vary predictably. Plasticity demonstrates why phenotype cannot be read as a direct copy of genotype.

Common-garden experiments raise individuals from different populations in similar conditions to reduce environmental differences, while reciprocal-transplant experiments compare performance in home and foreign environments. Together they can help distinguish genetic differentiation, plasticity and local adaptation.

Adaptation and Constraint

Natural selection works with inherited variation available in populations and with structures inherited from ancestors. Developmental architecture, physical laws and trade-offs constrain possible evolutionary paths. Therefore organisms are not expected to be perfectly engineered. A trait can be adequate for reproduction while carrying costs or historical compromises.

For example, allocating more energy to reproduction can reduce investment in growth, repair or future reproduction. Life-history evolution examines such trade-offs in age at maturity, offspring number, parental investment and lifespan.

Isolation as Reduced Gene Exchange

Reproductive isolation is best understood quantitatively as reduction in successful gene exchange. Barriers can be incomplete. Two populations may mate rarely, produce some fertile hybrids and still maintain substantial genetic differentiation because selection removes migrants or hybrids. Species formation therefore need not require an absolute barrier at every stage.

Prezygotic barriers act before a zygote forms and often prevent wasted reproductive effort. Postzygotic barriers act after fertilisation through hybrid inviability, sterility or reduced performance in later generations. Reinforcement can strengthen prezygotic discrimination where hybridisation is costly.

Hybrid Fitness and Hybrid Zones

A hybrid zone can persist when dispersal continually brings parental forms together even if hybrids have reduced fitness. Alternatively, hybrids may perform well in intermediate habitats. Genomic analysis can reveal that some regions cross species boundaries more readily than others, producing a mosaic history of gene flow and isolation.

Hybridization is especially prominent in plants, where self-fertilisation, vegetative reproduction and polyploidy can stabilise new genetic combinations. Nevertheless, not every plant hybrid becomes a new species; establishment and reproductive independence are required.

Origin-of-Life Reasoning without Overclaiming

Several problems must be solved in any scientific account of life's origin: production of building blocks, concentration and organisation of molecules, emergence of catalytic networks, compartment formation, information storage and sufficiently accurate replication with variation. Different hypotheses address different portions of this sequence.

Experiments that generate amino acids or nucleotide precursors under particular conditions demonstrate chemical possibility, not proof that the exact laboratory pathway occurred on early Earth. Scientific reasoning distinguishes plausibility, experimental support and historical certainty.

Speciation as Accumulated Divergence

In an allopatric scenario, a barrier divides a population. Once gene flow is greatly reduced, mutation introduces new variants independently, drift changes frequencies, and different environments can impose different selection. If reproductive incompatibilities accumulate, removal of the geographic barrier may no longer restore free interbreeding.

In sympatric scenarios, divergence must overcome ongoing opportunity for gene flow. Strong ecological differentiation, assortative mating or chromosome changes can create associations between habitat use and mate choice. Because the conditions are demanding, evidence for sympatric speciation requires careful exclusion of historical geographic separation.

Adaptive Radiation versus Ordinary Diversification

A lineage can become species-rich without every difference representing adaptation to distinct niches. To infer adaptive radiation, researchers examine phylogeny, timing, ecological differentiation and trait-function relationships. Rapid lineage accumulation plus ecological divergence provides stronger evidence than species number alone.

Extinction can obscure a radiation by removing intermediate forms. The living species are therefore an incomplete sample of historical diversity, which is why fossils and molecular phylogenies are valuable.

Plant Evolution: Alternation of Generations

Plants exhibit alternation between multicellular haploid gametophyte and diploid sporophyte generations. Across major land-plant lineages, the relative prominence and independence of these generations changed. Bryophyte life cycles feature a prominent gametophyte, whereas vascular plants have dominant sporophytes, and seed plants have highly reduced gametophytes.

This life-cycle perspective complements the study of structural innovations. Vascular tissue, heterospory, seeds, pollen, flowers and fruits each altered reproduction, dispersal or resource acquisition and contributed to diversification under appropriate ecological conditions.

Animal Evolution: Homology and Convergence

Homologous structures are similar because of common ancestry even if functions differ; analogous similarities can evolve independently under similar selective pressures. The forelimbs of tetrapods illustrate deep homology despite modification for walking, swimming or flight. Streamlined body forms in unrelated aquatic vertebrates can illustrate convergence.

Molecular phylogenetics tests relationships using sequence data, but genes can differ in evolutionary rate and history. Robust evolutionary trees often combine multiple genes with morphology, fossils and developmental evidence.

Human Evolution and Population Genetics

Genomic evidence supports an African origin for Homo sapiens and subsequent dispersal, while also revealing gene flow with some archaic hominin populations. This history is neither complete replacement everywhere nor a simple unbranched progression. Different genomic regions can preserve different aspects of population history.

Human genetic variation is shaped by migration, population size changes, drift and selection. Because gene flow has repeatedly connected populations, boundaries are gradual rather than discrete. Evolutionary biology therefore treats human variation as population history and adaptation, not a hierarchy of biological worth.

Demographic Rates and Time Scale

A birth rate expressed per year cannot be compared directly with one expressed per month without conversion. Population models require consistent units. Likewise, r in a continuous-time model has inverse-time units, while λ is a dimensionless multiplier per discrete interval. Confusing them produces incorrect projections.

Exponential Growth Derivation

The differential equation dN/dt=rN states that instantaneous change is proportional to current population size. Separating variables gives dN/N=r dt. Integrating from N₀ at time 0 to N at time t gives ln(N/N₀)=rt. Exponentiation yields N=N₀e^rt. The derivation shows exactly why constant r produces multiplicative rather than linear growth.

Logistic Growth Derivation and Interpretation

The logistic equation modifies exponential growth by multiplying rN by (1−N/K). At low N, this factor approaches one. As N approaches K, the factor approaches zero. The model therefore builds density dependence directly into per capita growth.

To see the maximum absolute growth, write growth as rN−(r/K)N², a downward-opening quadratic in N. Its vertex occurs at N=K/2. Substituting gives maximum growth rK/4. This result follows from the model's mathematical form, not from a universal biological law.

Carrying Capacity as a Dynamic Ecological Quantity

Although K is constant in the simplest logistic equation, real carrying conditions vary with rainfall, nutrient availability, habitat area, competitors, predators and human activity. Seasonal environments can therefore have changing effective carrying capacity. Treating K as a permanent number independent of environment misuses the model.

Demographic Stochasticity

Even when average birth and death probabilities are stable, the actual number of births and deaths in a small population fluctuates by chance. A small population can therefore decline to extinction through unlucky demographic sequences. This stochasticity weakens proportionally as population size increases, though environmental events can affect populations of any size.

Environmental Stochasticity

Environmental stochasticity arises when conditions such as rainfall, temperature or resource production vary unpredictably through time and affect many individuals simultaneously. Unlike demographic stochasticity, its impact does not vanish simply because the population is large. Correlated environmental effects can cause major population fluctuations.

Allee Effects

At very low density, some populations experience reduced per capita growth because individuals have difficulty finding mates, cooperative defence fails, pollination becomes inefficient or social functions break down. This positive density dependence at low abundance is called an Allee effect. It demonstrates that low density is not always equivalent to maximal per capita growth.

Harvesting and Population Growth

Removing individuals through harvest adds mortality. Sustainable management requires understanding reproduction, age structure, density dependence and environmental variability. A harvest level that appears sustainable during favourable years may be excessive during drought or after recruitment failure. Simple logistic calculations can illustrate principles but should not replace population-specific evidence.

Population Viability

Population viability concerns the probability of persistence over a defined period under specified demographic and environmental assumptions. Models can include age-specific survival, reproduction, catastrophes and density dependence. Their predictions are conditional on input data and should be accompanied by uncertainty.

Evolutionary Change during Population Decline

Declining populations experience both demographic and genetic processes. Drift becomes stronger, rare alleles can be lost, inbreeding may increase, and selection may change as environments deteriorate. These processes can interact: loss of variation can reduce future adaptive potential, while low fitness can accelerate demographic decline.

Evolutionary Rescue and Its Limits

If a population facing environmental deterioration contains or acquires variants that substantially improve fitness, selection can increase them quickly enough to contribute to recovery. This possibility is called evolutionary rescue. It requires sufficient variation, time and population size; severe decline can cause extinction before adaptation occurs.

Ecological Feedback from Evolution

Evolution can alter ecological processes on observable time scales. Changes in prey defence can affect predator abundance, changes in plant traits can alter herbivory, and resistance evolution can change disease or pest control. Ecology influences evolution through selection, while evolution can feed back to ecology through changed organismal traits.

Reading Evolutionary Graphs

When interpreting a graph, first identify axes, units and whether values are absolute or proportional. A rising allele-frequency line shows change in representation, not automatically selection; drift or migration could also produce change. A sigmoid population curve suggests logistic-like growth but does not prove a specific mechanism. Mechanistic conclusions require additional evidence.

Constructing a Scientific Evolutionary Explanation

A strong explanation begins with observed variation, identifies which part is heritable, specifies an environmental or reproductive difference that causes differential fitness, and predicts a change across generations. For speciation, add reduced gene flow and accumulation of reproductive barriers. For drift, explicitly state that change is stochastic rather than adaptive.

This structure avoids teleological language such as 'organisms changed so they could survive.' Instead say that variants differed in survival or reproduction and their frequencies consequently changed.

Hardy-Weinberg Problem 1

Hardy-Weinberg Problem 2

Carrier Estimation

Demographic Accounting Problem

Exponential Projection Problem

Finding r

Logistic Instantaneous Growth

Near Carrying Capacity

Discrete Decline

Mark-Recapture Problem

A Complete Evolutionary Chain

Evolutionary analysis can be organised as a chain. Mutation introduces new alleles; recombination reshuffles alleles into new genotypes; reproduction transmits them; selection causes systematic differences in reproductive contribution; drift causes stochastic frequency change; and gene flow transfers variants among populations. The resulting allele frequencies influence the variation available to future generations. No single force explains every evolutionary pattern.

At the phenotypic level, genotype interacts with environment. Selection therefore encounters organisms as integrated phenotypes, not naked alleles. If phenotypic differences are heritable and influence reproduction, genetic composition can change. If the difference is entirely environmental and is not transmitted through a heritable mechanism, selection on that difference alone does not produce the same genetic evolutionary response.

Species as Dynamic Lineages

The biological properties of species emerge from both cohesion and separation. Gene flow and shared ancestry can hold populations together, while geographic separation, divergent selection and reproductive barriers promote divergence. Species boundaries are often clear, but recently diverged lineages may occupy intermediate states in which some genes cross boundaries while others remain differentiated.

This dynamic perspective explains why different species concepts can disagree. A fossil lineage cannot be tested for mating compatibility; an asexual organism does not fit the biological species concept neatly; morphologically similar cryptic species may be genetically distinct. Biologists choose concepts and evidence appropriate to the organisms and question.

Variation at Multiple Biological Levels

Variation can be measured in DNA sequence, allele frequencies, protein properties, morphology, physiology, behaviour and life history. These levels are connected but not interchangeable. A DNA polymorphism may have no detectable phenotypic effect, while a quantitative phenotype may reflect hundreds of loci plus environment. Population biology therefore benefits from integrating molecular and organismal data.

Spatial variation is equally important. Allele frequencies can form clines across environmental gradients, populations can form discrete patches, and traits can vary with altitude, rainfall or temperature. A geographic pattern may reflect selection, isolation by distance, demographic history or several processes together.

Natural Selection and Causation

To demonstrate natural selection, it is not enough to show that a trait differs among environments. Evidence should connect phenotype to differential survival or reproduction and show that relevant variation is heritable. Experiments, longitudinal observations, genetic analyses and comparative studies can contribute different pieces of this causal argument.

Selection can be strong yet produce little long-term response if heritable variation is scarce. Conversely, abundant variation can persist if selection is weak, variable or balanced by other forces. Evolutionary outcome depends on both the strength of selection and the genetic architecture of traits.

Adaptation in Changing Environments

An adaptation reflects past selection, but environments continue to change. A trait once advantageous may become less useful or even costly. Climate change, habitat alteration and novel species interactions can therefore create mismatch between inherited traits and current conditions. Populations can respond through plasticity, movement or evolution, subject to constraints.

Rapid environmental change is especially challenging when generation times are long or populations are small. Evolution requires heritable variation and successful reproduction; demographic collapse can remove the opportunity for adaptation.

Isolation, Hybridization and the Continuum of Divergence

Population divergence can be viewed as a continuum from freely interbreeding populations to strongly isolated species. Early in divergence, gene flow may remain extensive. Later, ecological differentiation, mate choice, chromosome changes or genetic incompatibilities can reduce exchange. Secondary contact tests how far isolation has progressed.

If hybrids are fit and reproduce with parental populations, divergence can be partly reversed through introgression. If hybrids have low fitness, selection may strengthen prezygotic isolation. If hybrids exploit a distinct niche or chromosome changes create reproductive separation, hybridization can contribute to new lineage formation.

Evolution of Plants as Responses to Terrestrial Challenges

Terrestrial life exposes plants to desiccation, gravity, variable water supply and the challenge of moving gametes without an aquatic medium. Cuticles, protected reproductive structures, vascular tissues, roots, pollen and seeds addressed different components of these challenges during plant evolutionary history. Flowers and fruits later created additional opportunities for interactions with animals and other dispersal agents.

These innovations did not appear because plants consciously faced problems. Variants that improved performance under particular conditions left descendants, and lineages accumulated modifications. Evolutionary explanations should always preserve this population-level causal direction.

Evolution of Animals and Ecological Opportunity

Animal diversification reflects innovations in development, feeding, locomotion, sensory biology and reproduction. Predation can create selection for defence and detection; new feeding structures can open resources; locomotor innovations can permit colonisation of new habitats. Yet extinction repeatedly removes lineages, so living diversity represents survivors of a much larger evolutionary history.

Convergent evolution is strong evidence that similar environmental problems can favour similar functional solutions. However, convergence does not erase ancestry. Wings of birds and insects both enable flight but arose through different structural histories; evolutionary analysis separates functional similarity from homology.

Human Evolution in Population Context

Human evolution includes anatomical, behavioural and demographic change. Bipedalism predates the largest increases in brain size, showing that familiar human features did not arise simultaneously. Different hominin species overlapped in time, and some interacted genetically. The fossil record therefore supports mosaic and branching evolution.

Modern human genetic patterns also reflect recent population history. Founder events, expansions and migrations affect allele frequencies. Local selection can produce geographic differences at particular loci, while continuing gene flow maintains extensive shared variation. Population genetics is thus essential for interpreting human diversity accurately.

From Individual Events to Population Equations

Every term in a population equation represents events experienced by individuals. Births occur through reproduction, deaths through mortality, immigration through arrival and emigration through departure. Mathematical models aggregate these events to reveal overall trajectories. The simplification makes comparison and prediction possible but can hide age, sex, spatial and environmental differences.

For example, two populations can have identical r values yet differ greatly in age structure. One may have high birth and death rates, another low rates. A single summary parameter therefore answers a limited question and should be interpreted with supporting demographic information.

Exponential Growth as a Benchmark

Unlimited exponential growth cannot continue indefinitely in a finite environment, but the model remains useful. It describes early phases of some population expansions, provides a benchmark for comparison and clarifies the consequence of constant proportional growth. Its accelerating curve arises because a fixed proportion of a growing base is itself an increasing number.

Linear growth, by contrast, adds a constant number per unit time. Confusing linear and exponential change leads to serious prediction errors. If 100 individuals are added annually, the increment remains 100; if a population grows by 10% annually, the numerical increment grows as the population grows.

Logistic Growth and Ecological Feedback

The logistic model introduces feedback through density. At low abundance, resources are assumed sufficiently available for near-exponential growth. As density increases, per capita growth falls linearly in the simplest formulation. The resulting S-shaped curve approaches K. Real populations may overshoot, oscillate or encounter changing K, but the model provides a foundation for thinking about regulation.

Density dependence can act through many mechanisms rather than a mysterious 'carrying capacity force.' Competition can reduce food intake, disease can spread more efficiently, territories can become scarce, or waste can accumulate. Identifying the actual mechanism is an empirical ecological task.

Population Growth and Evolutionary Feedback

Population density can alter selection. At high density, competition may favour efficient resource use; at low density, mate-finding traits may become important. Conversely, evolution can change demographic parameters: improved disease resistance can increase survival, while altered reproductive timing can change generation length. Ecology and evolution can therefore influence one another dynamically.

Population Biology in Conservation

Conservation decisions require both demographic and genetic information. Protecting habitat can increase carrying conditions; connecting habitat patches can facilitate dispersal; maintaining sufficiently large breeding populations can reduce drift and inbreeding. However, connectivity can also spread disease or disrupt strong local adaptation, so management requires species-specific evidence.

Rare species are not all rare for the same reason. Some naturally occur at low density over large areas, some occupy tiny specialised habitats, and others have recently declined from former abundance. Population trends, reproductive rates and threats must be evaluated rather than assuming rarity alone reveals extinction risk.

How to Answer Quantitative Examination Questions

First identify what the symbols mean and ensure units are consistent. For Hardy-Weinberg questions, determine whether the problem supplies allele frequencies, genotype counts or a recessive phenotype frequency. For demographic questions, distinguish continuous r from discrete λ. For logistic questions, write N, r and K before substitution. For mark-recapture, state the assumptions that make the estimator meaningful.

After calculating, interpret biologically. A result of r=0.08 year⁻¹ means positive instantaneous per capita growth under the continuous model; it is not simply '8 individuals per year.' A Hardy-Weinberg carrier frequency is an expected population proportion under assumptions, not a certainty about a particular person.

How to Evaluate an Evolutionary Claim

Ask five questions. What is the observed pattern? What evolutionary mechanism is proposed? What evidence distinguishes that mechanism from alternatives? What assumptions are being made? What prediction follows? For example, a geographic allele-frequency difference might be caused by selection, drift or demographic history. Evidence of a functional advantage in the local environment strengthens selection as an explanation but population history must still be considered.

Course Integration

Population Biology and Evolution brings genetics, ecology, physiology, behaviour and systematics together. Genetics supplies inheritance and variation; ecology supplies environmental interactions and demographic context; physiology explains functional performance; behaviour influences mating and survival; systematics reconstructs lineage relationships. Evolution provides the historical process connecting these fields.

The NUC learning outcomes therefore form one coherent sequence: understand natural selection, recognise evolutionary histories, explain adaptation, use mathematical models to predict genetic and demographic change, and identify factors responsible for population dynamics. A student who can connect these tasks has moved beyond memorising evolutionary vocabulary to analysing biological populations scientifically.