concept

evolution

Evolution is the process by which species change over time through mechanisms like natural selection, adaptation, and ecosystem dynamics.
54 related articles · 6 formulas

Description

Biological evolution is the change in heritable characteristics of populations over generations. Its main mechanisms: mutations (DNA changes), gene recombination during sexual reproduction, gene flow (exchange of individuals between populations), genetic drift (random fluctuations in gene variant frequencies), and natural selection. Natural selection directs evolution: traits that increase fitness (the ability to survive and reproduce) gradually spread. Population separation (geographic barriers) can lead to speciation.

History

The idea of species transformation dates back to antiquity, but scientific substantiation emerged in the 19th century. Charles Darwin and Alfred Russel Wallace independently formulated the concept of natural selection; Darwin published it in 1859 in 'On the Origin of Species.' Gregor Mendel discovered the laws of heredity in 1865, which later formed the basis of genetics. In the early 20th century, the synthesis of Mendelism and Darwinism led to the formation of the synthetic theory of evolution (S.S. Chetverikov, J.B.S. Haldane, R. Fisher, S. Wright). The discovery of the DNA structure (1953) and the development of molecular biology provided a direct mechanism for heredity and mutations.

How it works

The evolutionary process is based on four main factors: mutations, recombination, genetic drift, and natural selection. Mutations randomly change the DNA sequence; most are neutral or harmful, but some confer an advantage. Recombination during meiosis shuffles paternal and maternal chromosomes, creating new allele combinations. Genetic drift causes random changes in allele frequencies, especially in small populations. Natural selection increases the frequency of alleles that enhance fitness in a given environment. Mathematically, this is described by the Hardy-Weinberg law, which shows equilibrium in the absence of evolutionary forces. Speciation often occurs through geographic isolation, where accumulated differences lead to reproductive incompatibility.

In practice

Understanding evolution helps create vaccines against rapidly mutating viruses and explains bacterial resistance to antibiotics. Plant and animal breeding is accelerated evolution under human control.

Fun fact

The octopus eye and the human eye are structured very similarly but developed independently — this is an example of convergent evolution: similar conditions produce similar solutions.

Concept graph →

Formulas

$$P(t) = e^{-\Gamma t}$$
Survival probability decays exponentially with time.
What is in the formula
P(t)variableSurvival probability at time t — probability
tvariableTime — time second
ΓvariableDecay rate (inverse lifetime) — decay rate per second
e^{-\sqrt{r_pt}}e^{-r_dt} · 2511.07785
\frac{dδn}{dt}=-\frac{g}{χ}δn · 2606.30521
$$M_{\rm ext} = M_{\rm int} + A$$
Observed magnitude equals intrinsic magnitude plus extinction.
What is in the formula
M_{\rm ext}variableObserved apparent magnitude — apparent magnitude
M_{\rm int}variableIntrinsic apparent magnitude — apparent magnitude
AvariableExtinction in magnitudes — extinction
m_{\rmext}=m_{\rmint}+r_b*e · 2606.06593v1
$$\tau = \frac{1}{\lambda}$$
The lifetime is the reciprocal of the decay rate constant.
What is in the formula
\tauvariablelifetime — lifetime second
\lambdavariabledecay rate constant — decay rate per second
τ_{γ}=\frac{1}{λ_{γ}} · 2606.31185
$$\dot{\theta} = F(\theta) - \theta$$
Evolution of a state driven by expected increment minus current value.
What is in the formula
θvariableState vector — state vector
F(θ)variableExpected increment function — increment function
˙operatorDerivative with respect to time — time derivative
\dot{\theta}=f(\theta)-\theta · 2607.01148
$$P_{\text{new}} = P_{\text{old}} \left(1 - \frac{\Delta E}{E}\right)^{-1/2}$$
Period increases when rotational energy is extracted.
What is in the formula
P_newvariablenew rotation period — period second
P_oldvariableold rotation period — period second
ΔEvariableenergy lost from rotation — energy joule
Evariableinitial rotational energy — energy joule
p_{{new}}=p_{{old}}(1-f)^{-1/2},\quadδ\logp=-\frac{1}{2}\log_{10}(1-f) · 2607.07781
$$\phi_i = -n_i v - K_{zz} n_{\text{tot}} \frac{\partial X_i}{\partial z} - D_i \left[ \frac{\partial n_i}{\partial z} + n_i \left( \frac{1}{H_i} + \frac{1+\alpha_T}{T} \frac{dT}{dz} \right) \right]$$
Flux of species includes advection, eddy diffusion, and molecular diffusion.
What is in the formula
\phi_ivariablevertical flux of species i — particle flux metre per second per square metre
n_ivariablenumber density of species i — number density per cubic metre
vvariablebulk vertical velocity — velocity metre per second
K_{zz}variableeddy diffusion coefficient — eddy diffusion coefficient square metre per second
n_{\text{tot}}variabletotal number density — number density per cubic metre
X_ivariablemole fraction of species i — mole fraction
zvariablealtitude — altitude metre
D_ivariablemolecular diffusion coefficient of species i — diffusion coefficient square metre per second
H_ivariablescale height of species i — scale height metre
\alpha_Tvariablethermal diffusion factor — thermal diffusion factor
Tvariabletemperature — temperature kelvin
\frac{\partial}{\paroperatorderivative with respect to altitude — partial derivative
\frac{d}{dz}operatortotal derivative with respect to altitude — total derivative
φ_i=-n_iv-k_{zz}n_{{tot}}\frac{\partialx_i}{\partialz}-d_i[\frac{\partialn_i}{\partialz}+n_i(\frac{1}{h_i}+\frac{1+α_t}{t}\frac{dt}{dz})] · 2607.15204

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