Populations inherit variation and change across generations. An individual changing during life is a different process.
By the end: Distinguish evolutionary change, development, acclimation, and a change in population size.
This course assumes high-school biology and basic arithmetic. It introduces inheritance and population models before using them to assess evolutionary explanations. The probability course is not a prerequisite. Numerical examples and hypothetical trees are teaching constructions, not measurements of a particular species.
Follow heritable differences
Evolution concerns change in heritable characteristics of populations across generations. A population is a set of organisms whose reproduction and movement connect them in the context being studied. One useful measurement is allele frequency: the fraction of gene copies at a particular location that carry a particular variant.
A genome is the full genetic material of an organism. In cellular organisms, a gene is a DNA sequence involved in a functional product; a locus is a genomic position or region. Alleles are alternative versions at a locus. A phenotype is a measurable characteristic of an organism, influenced by its genes and environment. DNA sequence differences can affect traits, have little effect in a given environment, or interact with other genetic differences. Evolution is not limited to visible changes in body shape.
Follow a population through reproduction
To decide whether a population evolved, connect the organisms counted at one time with reproduction and inheritance at a later time. A photograph of large adults beside small juveniles shows different life stages, not necessarily an inherited difference between generations. A useful comparison records a defined inherited characteristic at comparable stages. For example, count alleles among breeding adults in one generation and among their adult descendants in the next. The organisms need not look different for their allele frequencies to differ.
Consider a constructed population of ten haploid organisms, each with one copy of a particular locus. Four carry A and six carry a. Suppose the next generation again contains ten organisms, but six carry A and four carry a. The A frequency changed from four divided by ten, or 40%, to six divided by ten, or 60%. The population did not grow. The change concerns the composition of inherited copies, not the number of organisms or the amount of change experienced by any individual.
The same population size, different inherited shares
Constructed haploid genealogy; each circle is one organism and one locus copy. Paths show parentage, not expected fitness. The last two parents leave no offspring. Spacing and path lengths are schematic, not biological time or distance.
One possible history is that each of the four A parents leaves offspring counts of two, two, one, and one. Together they contribute six A copies. The six a parents together contribute four copies, perhaps because two leave no descendants and four leave one each. These counts produce the observed endpoint without changing any parent's allele during its life. They do not establish why contributions differed. A consistent effect of a heritable trait on reproduction would support selection; unequal realized contributions can also arise by chance.
Equal expected reproductive contribution does not mean every parent must leave exactly one descendant. Imagine repeating reproduction many times under identical conditions in which neither allele affects success. The average A contribution can match its starting share even though individual repetitions give different counts. Genetic drift concerns those realized sampling changes. Selection concerns differences in expected contribution associated with inherited variation under specified conditions. The same population can experience both, so observing six A descendants does not let us assign the entire change to one mechanism.
Population boundaries also affect the question. Two neighboring ponds might contain different frequencies while exchanging some breeding individuals. Counting one pond describes local change; pooling both describes change across the combined population. A visitor that never breeds can alter the organisms visible during a survey without contributing copies to local descendants. Before calling a difference gene flow, ask whether inherited material entered the recipient population. Before comparing generations, ask whether both surveys sampled the same biological population rather than different mixtures of residents and visitors.
An observation boundary is not always a breeding boundary
Survey situation
Copies entering local descendants
Interpretation
A visitor passes through without breeding or transfer
None from that visitor
Presence alone is not gene flow
A migrant contributes gametes to local offspring
Inherited migrant copies
Gene flow can change the local pool
A survey includes more visitors in its second sample
Not specified by the survey
An apparent frequency change may be a sampling difference
Constructed contrasting situations. Movement, observation, and genetic contribution are separate measurements; the table does not estimate their frequencies in nature.
Use the lineage comparison to trace each offspring copy backward to a parent. Then imagine exchanging the allele labels while keeping every parent and offspring connection unchanged. The connections still describe reproduction, but the allele totals change because the labels identify which inherited differences are being tracked. This separates a genealogy from a claim about adaptive value. An inherited history explains where copies came from. To explain an advantage, we would also need evidence about trait effects and reproduction in the environment where the organisms lived.
Use the right denominator
In a simple diploid organism, most autosomal loci have two copies, one inherited from each parent. A population of 100 such organisms has 200 copies at the locus. If 20 organisms are AA, 40 are Aa, and 40 are aa, there are 80 copies of A. Its frequency is 80/200 = 0.4, not the fraction of organisms carrying at least one A.
A population can double in size while preserving every allele frequency. Conversely, the frequency of A can rise while the total population shrinks. Frequency, absolute abundance, and the fraction of organisms expressing a phenotype answer different questions. Decide what was counted before interpreting a graph.
Keep copies, organisms, and traits separate
A diploid count starts with organisms but ends with copies at one specified locus. Two copies per organism does not mean two copies of every possible allele. AA contributes two A copies, Aa contributes one A and one a, and aa contributes two a copies. First add the organisms to find population size. Then multiply that total by two to find the denominator for this autosomal locus. Finally add the A contributions. Using these separate steps prevents a carrier count from silently becoming an allele count.
For the original example, 20 AA organisms contribute 40 A copies. The 40 Aa organisms contribute another 40, and the 40 aa organisms contribute none. There are 80 A copies among 200 total copies, so A frequency is 40%. There are instead 60 organisms carrying A among 100 organisms, so the carrier fraction is 60%. If A is completely dominant for a defined color trait, those same 60 organisms express its associated phenotype under the assumed conditions. That phenotype count still does not make the allele frequency 60%.
Now compare two smaller constructed populations. The first contains two AA and eight aa organisms. The second contains four Aa and six aa organisms. Both contain ten organisms and four A copies among twenty locus copies, so both have A frequency 20%. Their carrier fractions differ, at 20% and 40%. Under complete dominance, their corresponding phenotype fractions differ too. The allele frequency does not specify how copies are paired inside organisms. Genotype counts preserve information that disappears when we summarize the population with one frequency.
Equal allele frequencies can hide different pairings
Constructed populations. Each pair is one diploid organism, and each labeled circle is one locus copy. Geometry is schematic. Both panels have the same A frequency, but not the same genotype or carrier frequencies.
The converse ambiguity also matters. Among ten organisms, four AA plus six aa gives four A carriers and eight A copies. Four Aa plus six aa gives the same four carriers but only four A copies. Thus a 40% carrier fraction can coexist with either 40% or 20% A frequency in these examples. If we only observe a dominant phenotype, we cannot distinguish AA from Aa. Additional genetic information or justified population assumptions would be needed to recover the allele count. Appearance alone cannot supply the missing copies.
Frequency changes need equally careful units. Suppose a haploid population goes from 40 A organisms among 100 to 30 among 50. A abundance falls by ten organisms, while its frequency rises from 40% to 60%. That rise is twenty percentage points. Relative to the original 40%, it is a 50% proportional increase, because twenty divided by forty is one half. Reporting only that A increased leaves unclear whether it concerns count, percentage points, or proportional change in frequency.
Recalculate the paired populations by counting a rather than A. Each has sixteen a copies out of twenty, but the fractions carrying a need not match the A carrier fractions. In the first population eight of ten organisms carry a; in the second all ten do. Carrier categories overlap because an Aa organism carries both alleles. Allele frequencies at this two-allele locus sum to one, whereas the two carrier fractions can sum to more than one. The denominators are valid, but they answer different biological questions.
The numerator determines which question you answer
Quantity in the 100-organism example
Numerator
Denominator
Result
A allele frequency
80 A copies
200 locus copies
40%
A carrier fraction
60 AA or Aa organisms
100 organisms
60%
a carrier fraction
80 Aa or aa organisms
100 organisms
80%
A-associated phenotype, if completely dominant
60 expressing organisms
100 organisms
60%
Constructed counts of 20 AA, 40 Aa, and 40 aa. The phenotype row additionally assumes complete dominance and the stated environment. Carrier fractions overlap because Aa carries both alleles.
Work through the mechanism
Count copies at one diploid locus
AA individuals contribute two A copies; Aa individuals contribute one. The denominator includes both copies from all individuals.
Genotype
Organisms
A copies
AA
20
40
Aa
40
40
aa
40
0
Total
100
80 of 200
A and a name two variants, not superior and inferior forms.
Use counts to test competing explanations
The displayed frequency equation is a counting identity, not a model of the cause of change. It converts genotype counts into a share of locus copies. It contains no reproduction rate, movement rate, or probability of mutation. Therefore, getting the arithmetic right is necessary but does not establish natural selection. To reason about causes, construct different histories that produce the same measured endpoint. If several histories fit, identify the observations that would distinguish them rather than choosing whichever history sounds most adaptive.
Start again with a haploid population containing 40 A and 60 a organisms. One possible next generation contains 60 A and 40 a because the two types contribute unequally to descendants. In a deterministic teaching example, A has expected contribution 1.5 offspring per starting organism, while a has two thirds of an offspring per starting organism. Multiplying gives 60 and 40 expected descendants. Expected offspring counts can be fractional per parent because they average across possible outcomes. Actual descendants are whole organisms, and finite reproduction adds sampling variation.
A second history involves genetic input rather than different local reproduction. Suppose residents contribute fifty locus copies to a new pool, with A frequency 40%, and immigrants contribute fifty copies, with A frequency 80%. Residents contribute twenty A copies and immigrants forty, making sixty among one hundred. The same 60% endpoint now comes from mixing. The weights describe inherited contributions to the resulting pool. Fifty visitors who leave no genetic descendants would not justify using a fifty-copy immigrant contribution, even if they made up half the organisms observed.
Genetic contributions can reproduce the same endpoint
Constructed contribution mixture, not arrival counts. Each symbol represents five inherited locus copies, not five diploid organisms. The pools and their spacing are schematic; symbol counts encode the stated copy totals exactly.
A third possibility is neutral sampling. If each of one hundred offspring copies independently samples a parental copy from the initial 40% A pool, the expected A count is forty. Sixty is a possible realized count, although it is away from that expectation. This example does not claim all possible endpoints are equally probable or that drift is the best explanation for a measured jump. It shows why expectation and observation are different. Evaluating plausibility needs the population's reproductive sampling process and the uncertainty of the measurements.
Mutation creates another distinction between a copy's origin and its later frequency. A sequence change can create an A copy in an a lineage. Its descendants might then increase through selection, drift, or genetic exchange. Counting more A later does not reveal when the first A appeared, whether it arrived from another population, or what caused it to spread. None of the arithmetic examples requires mutations to arise because organisms need A. Environmental conditions can affect molecular processes without specifying a useful future sequence change in advance.
Compare the three histories in the table before adding a causal label to the frequency change. Parentage and genetic contribution help distinguish mixing from local descent. Repeated reproductive comparisons under specified conditions can test an expected advantage. Sampling design and population size help assess drift and measurement uncertainty. These are requests for evidence, not instructions for an experiment. A genuine population can combine all of these processes. The comparison narrows what the counts establish and identifies what they leave unresolved.
One endpoint does not identify one cause
History starting at 40% A
How 60% could result
Evidence to distinguish it
Unequal expected contribution
40 A × 1.5 = 60; 60 a × 2/3 = 40
Reproductive comparisons under specified conditions
Genetic contribution mixture
50 × 0.4 + 50 × 0.8 = 60 A among 100
Ancestry and genetic input from outside
Neutral independent sampling
60 A is possible; expected count is 40 among 100
Population sampling model, replication, and measurement uncertainty
Constructed alternative histories. Their endpoint arithmetic agrees, but the table does not assign them equal probabilities or claim that any one occurred in a real population.
Separate change within a life from change across generations
A muscle growing with exercise, a seedling developing leaves, and an organism acclimating to heat are changes within a life. They do not by themselves demonstrate evolution of the population. The capacity for such responses can itself be heritable and shaped by past evolution.
Evolution has no general goal of becoming larger, stronger, more complex, or morally better. Descendants inherit workable modifications under particular histories and environments. Natural selection is one mechanism of evolutionary change; mutation, genetic drift, and gene flow also matter. A change in frequency alone does not identify which mechanism caused it.
Separate environmental responses from inherited change
A phenotype depends on inheritance and developmental conditions. Consider a constructed plant example in which a genotype produces leaves averaging four centimeters in one environment and six centimeters in another. Moving plants can change their measured leaves without changing allele frequencies. Such a response is called phenotypic plasticity. Acclimation is a within-life adjustment to conditions; development includes changes as an organism grows and matures. Neither a new environment nor a new life stage, by itself, demonstrates an inherited population change.
Suppose two successive generations have the same genotype proportions, but the first grows in a dry environment and the second in a moist one. Mean leaf length might differ entirely because conditions changed. Conversely, two generations can have different allele frequencies yet similar mean leaves if environmental effects oppose genetic effects. A measured trait difference and a genetic difference are therefore separate observations. Comparison under similar conditions helps assess inherited effects, but parental environmental effects can complicate the interpretation.
The schematic shows two genotypes with different responses to the same environmental contrast. In the constructed values, genotype X produces lengths of four and six centimeters, while genotype Y produces five and five. Under the first condition Y has longer leaves; under the second X does. The crossing responses show why a genotype cannot be assigned one permanent phenotypic rank. They do not show reproductive fitness. Longer leaves could increase, decrease, or have no effect on reproductive contribution depending on resources and other conditions that the length measurements do not specify.
A phenotype ranking can reverse with conditions
Constructed phenotype values, not empirical plant measurements. Vertical positions use a linear centimeter scale; the environmental categories are not a continuous scale. Connecting segments aid comparison and do not predict intermediate conditions. Leaf length is not a measure of fitness.
Even if longer leaves improve reproduction in one setting, that result would not establish why those leaves originally evolved. A present benefit tests a current functional claim. Historical adaptation requires evidence that heritable differences contributed to reproduction in the relevant past population. An inherited structure might acquire a new use after it already exists, or remain because other linked effects matter. Distinguish a record of descent from an explanation of selective history. A plausible account of what a plant needed cannot substitute for those missing historical observations.
For guided practice, imagine that a survey reports taller plants after a warm year. Ask first whether the same plants grew taller or a later generation differed. Next ask whether ages, sampling locations, and growing conditions match. Then ask what inherited characteristic was actually measured. If no genetic or inheritance evidence exists, the supported statement concerns observed height, not a demonstrated allele-frequency change. If genetic change is documented, you still need reproductive and movement evidence to distinguish selection from drift and gene flow rather than treating warmth as a complete explanation.
Try a second case in which every genotype count doubles from one generation to the next. A table might change from 20 AA, 40 Aa, and 40 aa to 40 AA, 80 Aa, and 80 aa. A copies double from eighty to one hundred sixty, but total locus copies double from two hundred to four hundred. The frequency remains 40%. This is population growth without a frequency change at the measured locus. Other inherited characteristics elsewhere in the genome might still have changed.
Doubling every genotype preserves this allele frequency
Count
Earlier generation
Later generation
AA organisms
20
40
Aa organisms
40
80
aa organisms
40
80
All organisms
100
200
A copies
80
160
All locus copies
200
400
A frequency
40%
40%
Constructed diploid generations. A abundance doubles while A frequency stays constant at this locus. Other loci and other inherited characteristics are not measured by this comparison.
Exercises
Count copies, not carriers
A diploid population contains 10 AA, 20 Aa, and 70 aa individuals. Find the A frequency and the fraction of carriers.
Hint
Heterozygotes carry one A; AA individuals carry two.
Worked answer
Quantity
Count
Fraction
A gene copies
40 of 200
20%
Individuals carrying A
30 of 100
30%
A copy frequency is not a carrier frequency.
There are 2 × 10 + 20 = 40 A copies out of 200, so frequency is 20%. Thirty of the hundred individuals carry A, so the carrier fraction is 30%. The two quantities have different numerators and denominators.
A shrinking population
A haploid population changes from 1,000 cells, 100 carrying A, to 200 cells, 80 carrying A. Did A increase?
Hint
Specify whether you mean abundance or frequency.
Worked answer
Generation
A count
Total
A frequency
Earlier
100
1,000
10%
Later
80
200
40%
An increasing frequency need not mean an expanding population.
Its count fell from 100 to 80, but frequency rose from 10% to 40%. This is a frequency increase despite a decline in absolute abundance. If these are successive generations and A is inherited, the change is evolutionary, but these counts alone do not distinguish selection from drift or migration.
Sources and further reading
The explanations and exercises are complete without these optional links. The references cover inheritance, population mechanisms, and evidence for ancestry. Source annotations distinguish textbook explanations, secondary history, and a primary paper whose bibliographic identity alone was checked. The examples are constructed teaching models, not empirical estimates or professional decision advice.
Genetic variation, allele frequencies, and the Hardy-Weinberg reference model. Its closing claim about any genotype deviation implying evolution is too broad: sampling, subdivision, and nonrandom pairing can produce departures without an allele-frequency change. Our lessons distinguish the random-union calculation from stability across generations.