Infinite Population
Infinite Population - Related Videos
01:28
Introduction to Infinite Series
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2026
An infinite series is the sum of an infinite sequence of terms. Instead of adding only a fixed number of values, the addition continues without end. To make sense of this process, mathematicians examine partial sums, which are running totals formed by adding the first few terms of the series. If these partial sums approach a fixed number, the infinite series is said to converge. If they do not approach a finite value, the series diverges.The water tank example illustrates convergence through...
01:28
Infinitely Repeated Games
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2025
An infinitely repeated game is a scenario where players repeatedly engage in the same game without a predetermined end. This concept is crucial in understanding long-term interactions in various fields of the social sciences, including economics and international relations. Examples: Firms Setting Prices: Companies continuously adjust prices. Trade Negotiations: Countries consistently negotiate trade terms. Tit-for-Tat Strategy Cooperative Start: Players begin with a cooperative action,...
07:28
A Contusive Model of Unilateral Cervical Spinal Cord Injury Using the Infinite Horizon Impactor
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Cited by 46 •
2012
A reliable and repeatable way to produce a cervical unilateral spinal cord injury using the Infinite Horizon impactor is described. The method takes advantage of a custom designed frame and clamp to stabilize the spine. The standardized procedure and biomechanical injury parameters result in sufficient and sustained injuries.
01:29
Improper Integrals: Infinite Intervals
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2026
An integral is classified as improper due to an infinite interval when at least one of its limits of integration extends to positive or negative infinity. In such cases, the region under the curve is unbounded, and standard techniques for evaluating definite integrals are not directly applicable. Instead, the improper integral is defined through a limiting process that allows one to determine whether the accumulated area remains finite despite the infinite domain.Application to Exponential...
14:47
Population Growth - Student Protocol
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2019
Exponential Population Growth Model ExpandNOTE: In these experiments you will use computer software to simulate different types of growth models. HYPOTHESES: The experimental hypothesis might be that if we increase either R, the reproductive rate or the initial population size, NT, that this will increase the population size after 10 generations in an exponential growth model compared to unmanipulated control populations. The null hypothesis may be that populations of different R and initial...
FAQs
The model removes every process that could change frequencies: random mating determines reproductive pairing, while selection, mutation, and migration are absent. Because the population is treated as effectively unlimited, sampling error also disappears. Under these combined conditions, allele and genotype frequencies remain stable across generations, allowing inheritance patterns to be examined without evolutionary forces altering the result.
Genetic drift results from chance fluctuations associated with sampling individuals in a finite population. An Infinite Population model excludes that sampling error, so random changes in allele frequencies do not occur from one generation to the next. This distinction lets researchers separate predictable effects of selection, mutation, or migration from frequency changes that would otherwise arise purely through chance.
The central difference is whether random sampling can change allele frequencies. In the idealized model, unlimited population size prevents drift and keeps frequencies constant when other evolutionary forces are absent. Finite populations can experience chance fluctuations, so their allele frequencies may change even without selection, mutation, or migration. The comparison clarifies which patterns reflect population size.
A departure indicates that at least one simplifying condition may not hold. Natural selection can favor some inherited variants, mutation can introduce changes, migration can move variants between populations, and finite population size can produce drift. Examining which of these processes is consistent with the observed change helps researchers interpret departures from the theoretical expectation.
Researchers can first treat the model's stable allele and genotype frequencies as a theoretical expectation under random mating and absent evolutionary forces. They can then compare population-genetics observations with that expectation. Differences provide a starting point for investigating population structure, inheritance, selection, migration, mutation, or drift rather than assuming that every change has the same cause.
Its main practical value is diagnostic. If frequencies remain consistent with the model, the population may show no detectable departure from the specified assumptions in the analysis. If frequencies change, the discrepancy directs attention toward selection, migration, mutation, or drift. In this way, the idealized system provides a baseline for interpreting evolutionary patterns in real populations.
The model simplifies population genetics by holding several conditions constant, making the expected inheritance pattern easier to determine. Real populations may depart from those conditions, especially through finite size and associated drift or through other evolutionary forces. Comparing real data with the simplified expectation helps isolate biological processes that would be harder to recognize when all factors vary simultaneously.