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Minimum viable population

Minimum viable population is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Minimum viable population rather than just read about it. In short: Minimum viable population (MVP) is a lower bound on the population of a species, such that it can survive in the wild. This term is commonly used in the fields of biology, ecology, and conservation biology.

Minimum viable population — main illustration
Minimum viable population — illustration

Key takeaways

  • Minimum viable population belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Minimum viable population to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Minimum viable population from memory before moving on to harder problems.

Reference excerpt

Minimum viable population (MVP) is a lower bound on the population of a species, such that it can survive in the wild. This term is commonly used in the fields of biology, ecology, and conservation biology. MVP refers to the smallest possible size at which a biological population can exist without facing extinction from natural disasters or demographic, environmental, or genetic stochasticity. The term "population" is defined as a group of interbreeding individuals in similar geographic area that undergo negligible gene flow with other groups of the species. Typically, MVP is used to refer to a wild population, but can also be used for ex situ conservation (Zoo populations).

Estimation There is no unique definition of what constitutes a sufficient population for the continuation of a species, because whether a species survives will depend to some extent on random events. Thus, any calculation of a minimum viable population (MVP) will depend on the population projection model used. A set of random (stochastic) projections might be used to estimate the initial population size needed (based on the assumptions in the model) for there to be, (for example) a 95% or 99% probability of survival 1,000 years into the future. Some models use generations as a unit of time rather than years in order to maintain consistency between taxa. These projections (population viability analyses, or PVA) use computer simulations to model populations using demographic and environmental information to project future population dynamics. The probability assigned to a PVA is arrived at after repeating the environmental simulation thousands of times.

Extinction

Small populations are at a greater risk of extinction than larger populations due to small populations having less capacity to recover from adverse stochastic (i.e. random) events. Such events may be divided into four sources:

Demographic stochasticity Demographic stochasticity is often only a driving force toward extinction in populations with fewer than 50 individuals. Random events influence the fecundity and survival of individuals in a population, and in larger populations, these events tend to stabilize toward a steady growth rate. However, in small populations there is much more relative variance, which can in turn cause extinction. Environmental stochasticity Small, random changes in the abiotic and biotic components of the ecosystem that a population inhabits fall under environmental stochasticity. Examples are changes in climate over time and the arrival of another species that competes for resources. Unlike demographic and genetic stochasticity, environmental stochasticity tends to affect populations of all sizes. Natural catastrophes An extension of environmental stochasticity, natural disasters are random, large scale events such as blizzards, droughts, storms, or fires that directly reduce a population within a short period of time. Natural catastrophes are the hardest events to predict, and MVP models often have difficulty factoring them in. Genetic stochasticity Small populations are vulnerable to genetic stochasticity, the random change in allele frequencies over time, also known as genetic drift. Genetic drift can cause alleles to disappear from a population, and this lowers genetic diversity. In small populations, low genetic diversity can increase rates of inbreeding, which can result in inbreeding depression, in which a population made up of genetically similar individuals loses fitness. Inbreeding in a population reduces fitness by causing deleterious recessive alleles to become more common in the population, and also by reducing adaptive potential. The so-called "50/500 rule", where a population needs 50 individuals to prevent inbreeding depression, and 500 individuals to guard against genetic drift at-large, is an oft-used benchmark for an MVP, but 2014 guidance indicates this rule is not applicable across a wide diversity of taxa.

Application MVP does not take external intervention into account. Thus, it is useful for conservation managers and environmentalists; a population may be increased above the MVP using a captive breeding program or by bringing other members of the species in from other reserves. There is naturally some debate on the accuracy of PVAs, since a wide variety of assumptions are generally required for forecasting; however, the important consideration is not absolute accuracy but the promulgation of the concept that each species indeed has an MVP, which at least can be approximated for the sake of conservation biology and Biodiversity Action Plans. There is a marked trend for insularity, surviving genetic bottlenecks, and r-strategy to allow far lower MVPs than average. Conversely, taxa easily affected by inbreeding depression –having high MVPs – are often decidedly K-strategists, with low population densities occurring over a wide range. An MVP of 500 to 1,000 has often been given as an average for terrestrial vertebrates when inbreeding or genetic variability is ignored. When inbreeding effects are included, estimates of MVP for many species are in the thousands. Based on a meta-analysis of reported values in the literature for many species, Traill et al. reported concerning vertebrates "a cross-species frequency distribution of MVP with a median of 4,169 individuals (95% CI = 3,577–5,129)."

See also Effective population size Inbreeding depression Human population Metapopulation Rescue effect

References

Illustrations

Minimum viable population: A graphical representation of population growth over total population. K is the carrying capacity, and MVP is minimum viable population.
A graphical representation of population growth over total population. K is the carrying capacity, and MVP is minimum viable population.
Minimum viable population: In 1912, the Laysan duck had an effective population size of seven adults at most.
In 1912, the Laysan duck had an effective population size of seven adults at most.

Worked examples

Example 1 — a first encounter with Minimum viable population

Start with the simplest possible case. Write down what Minimum viable population claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Minimum viable population before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Minimum viable population ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Minimum viable population

In research
Minimum viable population appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Minimum viable population in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Minimum viable population is common in secondary-school and first-year university syllabi. It links to neighbouring topics Biostatistics, Ecological metrics, Environmental terminology, so understanding it makes those chapters shorter.
In everyday life
Look for Minimum viable population outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Minimum viable population in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Minimum viable population means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Minimum viable population out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Minimum viable population in simple terms?

Minimum viable population (MVP) is a lower bound on the population of a species, such that it can survive in the wild. This term is commonly used in the fields of biology, ecology, and conservation biology.

Why does Minimum viable population matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Minimum viable population?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Minimum viable population.

Tags

  • Biostatistics
  • Ecological metrics
  • Environmental terminology
  • Habitat

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