The rate of evolution

The rate of evolution is a measurement of the change in an evolutionary lineage over time.

The method for measuring the rate of evolution can be illustrated by work done by MacFadden on horse teeth: horse teeth are classic materials in the study of evolution.

The rate of evolution is measured as follows:

Suppose that a character has been measured at two times, t₁ and t₂ ; t₁ and t₂ are expressed as times before the present in millions of years.

The time interval between the two samples can be written as:Dt = t₁ - t₂,

which is 1 million years if t₁ = 15.2 and t₂ =14.2 The average value of the character is defined as x₁ in the earlier sample and x₂ in the later sample; we then take natural logarithms of x₁ and x₂ (the natural logarithm is the log to base e where e = 2.718, and it is symbolized by ln ).

The evolutionary rate (r) then is

r = (ln(x₂) - ln(x₁)) / Dt

The rate of evolution is measured in 'darwins'.

Haldane (pictured opposite) defined a 'darwin' as a unit to measure evolutionary rates; one darwin is a change in the character by a factor of e in one million years.

The formula above for r gives the rate in darwins provided that the time interval is in millions of years.

• Evolution Means Change In Living Things By Descent With Modification
• Living Things Show Adaptations
• A Short History Of Evolutionary Biology

• Inheritance Is Caused By DNA Molecules, Which Are Physically Passed From Parent To Offspring
• DNA Structurally Encodes Information Used To Build The Body's Proteins
• Information In DNA Is Decoded By Transcription And Translation
• Large Amounts Of Non-Coding DNA Exist In Some Species
• Mutational Errors May Occur During DNA Replication
• Rates Of Mutation Can Be Measured
• Diploid Organisms Inherit A Double Set Of Genes
• Genes Are Inherited In Characteristic Mendelian Ratios
• Darwin's Theory Would Probably Not Work If There Was A Non-Mendelian Blending
• Mechanism Of Heredity

• We Distinguish Three Possible Theories Of The History Of Life
• On A Small Scale, Evolution Can Be Observed In Action
• Evolution Can Also Be Produced Experimentally
• Interbreeding And Phenotypic Similarity Provide Two Concepts Of Species
• Ring "Species" Show That The Variation Within A Species Can Be Extensive Enough To Produce A New Species
• New, Reproductively Distinct Species Can Be Produced Experimentally
• Small-Scale Observations Can Be Extrapolated Over The Long Term
• Groups Of Living Things Have Homologous Similarities
• Different Homologies Are Correlated, And Can Be Hierarchically Classified
• Fossil Evidence Exists For The Transformation Of Species
• The Order Of The Main Groups In The Fossil Record Suggests They Have Evolutionary Relationships
• Summary Of The Evidence For Evolution
• Creationism Offers No Explanation Of Adaptation
• Modern "Scientific Creationism" Is Scientifically Untenable

• In Nature, There Is A Struggle For Existence
• Natural Selection Operates If Some Conditions Are Met
• Natural Selection Explains Both Evolution And Adaptation
• Natural Selection Can Be Directional, Stabilizing, Or Disruptive
• Variation In Natural Populations Is Widespread
• Organisms In A Population Vary In Reproductive Success
• New Variation Is Generated By Mutation And Recombination
• New Variation Created By Recombination And Mutation Is Random With Respect To The Direction Of Adaptation

• Population Genetics Is Concerned With Genotype And Gene Frequencies
• An Elementary Population Genetic Model Has Four Main Steps
• Genotype Frequencies In The Absence Of Selection Go To The Hardy-Weinberg Equilibrium
• We Can Test, By Simple Observation, Whether Genotypes In A Population Are At The Hardy-Weinberg Equilibrium
• The Hardy-Weinberg Theorem Is Important Conceptually, Historically, In Practical >Research, And In The Workings Of Theoretical Models
• The Simplest Model Of Selection Is For One Favored Allele At One Locus
• The Model Of Selection Can Be Applied To The Peppered Moth
• Pesticide Resistance In Insects Is An Example Of Natural Selection
• Fitnesses Are Important Numbers In Evolutionary Theory And Can Be Estimated By Three Main Methods
• Natural Selection Operating On A Favored Allele At A Single Locus Is Not Meant To Be A General Model Of Evolution
• A Recurrent Disadvantageous Mutation Will Evolve To A Calculable Equilibrial Frequency
• Heterozygous Advantage
• The Fitness Of A Genotype May Depend On Its Frequency
• Subdivided Populations Require Special Population Genetic Principles

• The Frequency Of Alleles Can Change At Random Through Time In A Process Called Genetic Drift
• A Small Founder Population May Have A Non-Representative Sample Of The Ancestral Population's Genes
• One Gene Can Be Substituted For Another By Random Drift
• Hardy-Weinberg "Equilibrium" Assumes The Absence Of Genetic Drift
• Neutral Drift Over Time Produces A March To Homozygosity
• A Calculable Amount Of Polymorphism Will Exist In A Population Because Of Neutral Mutation
• Population Size And Effective Population Size

• Random Drift And Natural Selection Can Both Hypothetically Explain Molecular Evolution
• Rates Of Molecular Evolution And Amounts Of Genetic Variation Can Be Measured
• Rates Of Molecular Evolution Are Arguably Too Constant For A Process Controlled By Natural Selection
• The Molecular Clock Shows A Generation Time Effect
• The Nearly Neutral Theory
• Evolutionary Rate And Functional Constraint
• Conclusion And Comment: The Neutralist Paradigm Shift
• Genomic Sequences Have Led To New Ways Of Studying Molecular Evolution
• Conclusion: 35 Years Of Research On Molecular Evolution

• Mimicry In Papilio Is Controlled By More Than One Genetic Locus
• Genotypes At Different Loci In Papilio Memnon Are Coadapted
• Mimicry In Heliconius Is Controlled By More Than One Gene, But They Are Not Tightly Linked
• Two-Locus Genetics Is Concerned With Haplotype Frequencies
• Frequencies Of Haplotypes May Or May Not Be In Linkage Equilibrium
• Human HLA Genes Are A Multilocus Gene System
• Linkage Disequilibrium Can Exist For Several Reasons
• Two-Locus Models Of Natural Selection Can Be Built
• Hitch-Hiking Occurs In Two-Locus Selection Models
• Selective Sweeps Can Provide Evidence Of Selection In DNA Sequences
• Linkage Disequilibrium Can Be Advantageous, Neutral, Or Disadvantageous
• Wright Invented The Influential Concept Of An Adaptive Topography
• The Shifting Balance Theory Of Evolution

• Climatic Changes Have Driven The Evolution Of Beak Size In One Of Darwin's Finches
• Quantitative Genetics Is Concerned With Characters Controlled By Large Numbers Of Genes
• Variation Is First Divided Into Genetic And Environmental Effects
• Variance Of A Character Is Divided Into Genetic And Environmental Effects
• Relatives Have Similar Genotypes, Producing The Correlation Between Relatives
• Heritability Is The Proportion Of Phenotypic Variance That Is Additive
• A Character's Heritability Determines Its Response To Artificial Selection
• Strength Of Selection Has Been Estimated In Many Studies Of Natural Populations
• Relations Between Genotype And Phenotype May Be Non-Linear, Producing Remarkable Responses To Selection
• Stabilizing Selection Reduces The Genetic Variability Of A Character
• Characters In Natural Populations Subject To Stabilizing Selection Show Genetic Variation
• Levels Of Genetic Variation In Natural Populations Are Imperfectly Understood
• Conclusion

• Natural Selection Is The Only Known Explanation For Adaptation
• Pluralism Is Appropriate In The Study Of Evolution, Not Of Adaptation
• Natural Selection Can In Principle Explain All Known Adaptations
• New Adaptations Evolve In Continuous Stages From Pre Existing Adaptations, But The Continuity Takes Various Forms
• Genetics Of Adaptation
• Three Main Methods Are Used To Study Adaptation
• Adaptations In Nature Are Not Perfect
• How Can We Recognize Adaptations?

• What Entities Benefit From The Adaptations Produced By Selection?
• Natural Selection Has Produced Adaptations That Benefit Various Levels Of Organization
• Another Sense Of "Unit Of Selection" Is The Entity Whose Frequency Is Adjusted Directly By Natural Selection
• The Two Senses Of "Unit Of Selection" Are Compatible; One Specifies The Entity That Generally Shows Phenotypic Adaptations, The Other The Entity Whose Frequency Is Generally Adjusted By Natural Selection

• The Existence Of Sex Is An Outstanding, Unsolved Problem In Evolutionary Biology
• There Are Two Main Theories In Which Sex May Have A Short-Term Advantage
• Conclusion: It Is Uncertain How Sex Is Adaptive
• The Theory Of Sexual Selection Explains Many Differences Between Males And Females
• The Sex Ratio Is A Well Understood Adaptation
• Different Adaptations Are Understood In Different Levels Of Detail

• In Practice Species Are Recognized And Defined By Phenetic Characters
• Several Closely Related Species Concepts Exist
• Isolating Barriers
• Geographic Variation Within A Species Can Be Understood In Terms Of Population Genetic And Ecological Processes
• "Population Thinking" And "Typological Thinking" Are Two Ways Of Thinking About Biological Diversity
• Ecological Influences On The Form Of A Species Are Shown By The Phenomenon Of >Character Displacement
• Some Controversial Issues Exist Between The Phenetic, Biological, And Ecological >Species Concepts
• Taxonomic Concepts May Be Nominalist Or Realist
• Conclusion

• How Can One Species Split Into Two Reproductively Isolated Groups Of Organisms?
• A Newly Evolving Species Could Theoretically Have An Allopatric, Parapatric, Or Sympatric Geographic Relation With Its Ancestor
• Reproductive Isolation Can Evolve As A By-Product Of Divergence In Allopatric Populations
• The Dobzhansky-Muller Theory Of Postzygotic Isolation
• An Interim Conclusion: Two Solid Generalizations About Speciation
• Reinforcement
• Some Plant Species Have Originated By Hybridization
• Speciation May Occur In Non-Allopatric Populations, Either Parapatrically Or Sympatrically
• Parapatric Speciation
• Sympatric Speciation
• The Influence Of Sexual Selection In Speciation Is One Current Trend In Research
• Identification Of Genes That Cause Reproductive Isolation Is Another Current Trend In Research
• Conclusion

• Phylogenies Express The Ancestral Relations Between Species
• Phyogenies Are Inferred From Morphological Characters Using Cladistic Techniques
• Homologies Provide Reliable Evidence For Phylogenetic Inference, And Homoplasies Provide Unreliable Evidence
• Homologies Can Be Distinguished From Homoplasies By Several Criteria
• Derived Homologies Are More Reliable Indicators Of Phylogenetic Relations Than Are Ancestral Homologies
• The Polarity Of Character States Can Be Inferred By Several Techniques
• Some Character Conflict May Remain After Cladistic Character Analysis Is Complete
• Molecular Sequences Are Becoming Increasingly Important In Phylogenetic Inference, And They Have Distinct Properties
• Several Statistical Techniques Exist To Infer Phylogenies From Molecular Sequences
• Molecular Phylogenetics In Action
• Several Problems Have Been Encountered In Molecular Phylogenetics
• Paralogous Genes Can Be Used To Root Unrooted Trees
• Molecular Evidence Successfully Challenged Paleontological Evidence In The Analysis Of Human Phylogenetic Relations
• Unrooted Trees Can Be Inferred From Other Kinds Of Evidence, Such As Chromosomal Inversions In Hawaiian Fruitflies
• Conclusion

• Biologists Classify Species Into A Hierarchy Of Groups
• There Are Phenetic And Phylogenetic Principles Of Classification
• There Are Phenetic, Cladistic, And Evolutionary Schools Of Classification
• A Method Is Needed To Judge The Merit Of A School Of Classification
• Phenetic Classification Uses Distance Measures And Cluster Statistics
• Phylogenetic Classification Uses Inferred Phylogenetic Relations
• Evolutionary Classification Is A Synthesis Of Phenetic And Phylogenetic Principles
• The Principle Of Divergence Explains Why Phylogeny Is Hierarchical
• Conclusion

• Species Have Defined Geographic Distributions
• Ecological Characteristics Of A Species Limit Its Geographic Distribution
• Geographic Distributions Are Influenced By Dispersal
• Geographic Distributions Are Influenced By Climate, Such As In The Ice Ages
• Local Adaptive Radiations Occur On Island Archipelagos
• Species Of Large Geographic Areas Tend To Be More Closely Related To Other Local Species Than To Ecologically Similar Species Elsewhere In The Globe
• Geographic Distributions Are Influenced By Vicariance Events, Some Of Which Are Caused By Plate Tectonic Movement
• The Great American Interchange
• Conclusion

• Fossils Are Remains Of Organisms From The Past And Are Preserved In Sedimentary >Rocks
• Geological Time Is Divided Into A Series Of Eras, Periods, And Epochs
• The Cambrian Explosion
• Evolution Of Land Plants
• Vertebrate Evolution
• Human Evolution
• Macroevolution May Or May Not Be An Extrapolated Form Of Microevolution

• Our Expanding Knowledge Of Genome Sequences Is Making It Possible To Ask, And Answer, Questions About The Evolution Of Genomes
• The Human Genome Documents The History Of The Human Gene Set Since Early Life
• The History Of Duplications Can Be Inferred In A Genomic Sequence
• Genome Size Can Shrink By Gene Loss
• Symbiotic Mergers, And Horizontal Gene Transfer, Between Species Influence Genome Evolution
• The X/Y Sex Chromosomes Provide An Example Of Evolutionary Genomic Research At The Chromosomal Level
• Genome Sequences Can Be Used To Study The History Of Non-Coding DNA
• Conclusion

• Changes In Development, And The Genes Controlling Development, Underlie Morphological Evolution
• The Theory Of Recapitulation Is A Classic Idea (Largely Discredited) About The Relation Between Development And Evolution
• Humans May Have Evolved From Ancestral Apes By Changes In Regulatory Genes
• Many Genes That Regulate Development Have Been Identified Recently
• Modern Developmental Genetic Discoveries Have Challenged And Clarified The Meaning On Homology
• The Hox Gene Complex Has Expanded At Two Points In The Evolution Of Animals
• Changes In The Embryonic Expression Of Genes Are Associated With Evolutionary Changes In Morphology
• Evolution Of Genetic Switches Enables Evolutionary Innovation, Making The System More "Evolvable"
• Conclusion

• Rates Of Evolution Can Be Expressed In "Darwins," As Illustrated By A Study Of Horse Evolution
• Why Do Evolutionary Rates Vary?
• The Theory Of Punctuated Equilibrium Applies The Theory Of Allopatric Speciation To Predict The Pattern Of Change In The Fossil Record
• What Is The Evidence For Punctuated Equilibrium And For Phyletic Gradualism?
• Evolutionary Rates Can Be Measured For Non-Continuous Character Changes, As Illustrated By A Study Of "Living Fossil" Lungfish
• Taxonomic Data Can Be Used To Describe The Rate Of Evolution Of Higher Taxonomic Groups
• Conclusion

• Coevolution Can Give Rise To Coadaptations Between Species
• Coadaptation Suggests, But Is Not Conclusive Evidence Of, Coevolution
• Insect-Plant Coevolution
• Coevolutionary Relations Will Often Be Diffuse
• Parasite-Host Coevolution
• Coevolution Can Proceed In An "Arms Race"
• The Probability That A Species Will Go Extinct Is Approximately Independent Of How Long It Has Existed
• Antagonistic Coevolution Can Have Various Forms, Including The Red Queen Mode
• Both Biological And Physical Hypotheses Should Be Tested On Macroevolutionary Observations

• The Number Of Species In A Taxon Increases Durings Phases Of Adaptive Radiation
• Causes And Consequences Of Extinctions Can Be Studied In The Fossil Record
• Mass Extinctions
• Distributions Of Extinction Rates May Fit A Power Law
• Changes In The Quality Of The Sedimentary Record Through Time Are Associated With Changes In The Observed Extinction Rate
• Species Selection
• One Higher Taxon May Replace Another, Because Of Chance, Environmental Change, Or Competitive Replacement
• Species Diversity May Have Increased Logistically Or Exponentially Since The Cambrian, Or It May Have Increased Little At All
• Conclusion: Biologists And Paleontologists Have Held A Range Of Views About The Importance Of Mass Extinctions In The History Of Life