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Population Growth

Population Growth

Population size is dynamic, increasing with birth rates and immigration, and decreasing with death rates and emigration. In ideal conditions with unlimited resources, populations can increase exponentially, which plots as a J-shaped growth rate curve of population size against time. This type of curve is characteristic of newly-introduced invasive species, or populations that have suffered catastrophic declines and are rebounding.

Genetic Drift

Genetic Drift

Natural selection—probably the most well-known evolutionary mechanism—increases the prevalence of traits that enhance survival and reproduction. However, evolution does not merely propagate favorable traits, nor does it always benefit populations.

Modeling with Differential Equations

Modeling with Differential Equations

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...

Hardy-Weinberg Principle

Hardy-Weinberg Principle

Diploid organisms have two alleles of each gene, one from each parent, in their somatic cells. Therefore, each individual contributes two alleles to the gene pool of the population. The gene pool of a population is the sum of every allele of all genes within that population and has some degree of variation. Genetic variation is typically expressed as a relative frequency, which is the percentage of the total population that has a given allele, genotype or phenotype.

Mutation, Gene Flow, and Genetic Drift

Mutation, Gene Flow, and Genetic Drift

In a population that is not at Hardy-Weinberg equilibrium, the frequency of alleles changes over time. Therefore, any deviations from the five conditions of Hardy-Weinberg equilibrium can alter the genetic variation of a given population. Conditions that change the genetic variability of a population include mutations, natural selection, non-random mating, gene flow, and genetic drift (small population size).

What is Population Genetics?

What is Population Genetics?

A population is composed of members of the same species that simultaneously live and interact in the same area. When individuals in a population breed, they pass down their genes to their offspring. Many of these genes are polymorphic, meaning that they occur in multiple variants. Such variations of a gene are referred to as alleles. The collective set of all the alleles within a population is known as the gene pool.

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Related Experiment Video

Updated: Mar 5, 2026

Following the Dynamics of Structural Variants in Experimentally Evolved Populations

Following the Dynamics of Structural Variants in Experimentally Evolved Populations

Published on: February 3, 2023

Evolutionary dynamics on any population structure.

Benjamin Allen^1,2,3, Gabor Lippner^3,4, Yu-Ting Chen^2,3,5

¹Department of Mathematics, Emmanuel College, Boston, Massachusetts, USA.

|March 30, 2017

Summary

This summary is machine-generated.

Evolutionary game dynamics in structured populations are complex. This study reveals that cooperation thrives in populations with strong pairwise connections, offering a new solution for weak selection scenarios.

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Area of Science:

Evolutionary biology
Game theory
Network science

Background:

Population structure significantly influences evolutionary trajectories.
Understanding evolutionary game dynamics in general structured populations is computationally challenging.
Existing mathematical solutions are limited to specific population structures with uniform connectivity.

Purpose of the Study:

To develop a general solution for evolutionary game dynamics in structured populations under weak selection.
To investigate how varying population structures impact the evolution of cooperation.
To provide a method applicable to any arbitrary graph or network structure.

Main Methods:

Utilizing coalescence times of random walks on graphs.
Analyzing diverse population structures to assess their propensity to favor cooperation.
Employing graph surgery techniques to study the effects of small structural changes on evolutionary outcomes.

Main Results:

A novel solution for weak selection in evolutionary games on arbitrary graphs is presented.
Cooperation is found to flourish most in populations characterized by strong pairwise ties.
The study demonstrates how network topology influences evolutionary stability and cooperation levels.

Conclusions:

The developed method provides a computationally tractable approach to studying evolutionary game dynamics in complex networks.
Strong local interactions and dense local neighborhoods are key drivers for the evolution of cooperation.
Findings have implications for understanding social behavior and designing robust social structures.