science

Matrix population models

Matrix population models is a science 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 Matrix population models rather than just read about it. In short: Matrix population models are a specific type of population model that uses matrix algebra. Population models are used in population ecology to model the dynamics of wildlife or human populations.

Key takeaways

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

Reference excerpt

Matrix population models are a specific type of population model that uses matrix algebra. Population models are used in population ecology to model the dynamics of wildlife or human populations. Matrix algebra, in turn, is simply a form of algebraic shorthand for summarizing a larger number of often repetitious and tedious algebraic computations. All populations can be modeled

N t + 1 = N t + B − D + I − E , {\displaystyle N_{t+1}=N_{t}+B-D+I-E,}

where:

Nt+1 = abundance at time t+1 Nt = abundance at time t B = number of births within the population between Nt and Nt+1 D = number of deaths within the population between Nt and Nt+1 I = number of individuals immigrating into the population between Nt and Nt+1 E = number of individuals emigrating from the population between Nt and Nt+1 This equation is called a BIDE model (Birth, Immigration, Death, Emigration model). Although BIDE models are conceptually simple, reliable estimates of the 5 variables contained therein (N, B, D, I and E) are often difficult to obtain. Usually a researcher attempts to estimate current abundance, Nt, often using some form of mark and recapture technique. Estimates of B might be obtained via a ratio of immatures to adults soon after the breeding season, Ri. Number of deaths can be obtained by estimating annual survival probability, usually via mark and recapture methods, then multiplying present abundance and survival rate. Often, immigration and emigration are ignored because they are so difficult to estimate. For added simplicity it may help to think of time t as the end of the breeding season in year t and to imagine that one is studying a species that has only one discrete breeding season per year. The BIDE model can then be expressed as:

N t + 1 = N t , a × S a + N t , i × R i × S i {\displaystyle N_{t+1}=N_{t,a}\times S_{a}+N_{t,i}\times R_{i}\times S_{i}}

where:

Nt,a = number of adult females at time t Nt,i = number of immature females at time t Sa = annual survival of adult females from time t to time t+1 Si = annual survival of immature females from time t to time t+1 Ri = ratio of surviving young females at the end of the breeding season per breeding female In matrix notation this model can be expressed as:

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Matrix population models

Start with the simplest possible case. Write down what Matrix population models claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, 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 Matrix population models 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 Matrix population models 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 Matrix population models

In research: Matrix population models appears in science 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 Matrix population models 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: Matrix population models is common in secondary-school and first-year university syllabi. It links to neighbouring topics Population dynamics, Population models, so understanding it makes those chapters shorter.
In everyday life: Look for Matrix population models 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.

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Matrix population models in 20 minutes

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

Frequently asked questions

What is Matrix population models in simple terms?

Matrix population models are a specific type of population model that uses matrix algebra. Population models are used in population ecology to model the dynamics of wildlife or human populations.

Why does Matrix population models matter?

Because it connects several science 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 Matrix population models?

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 Matrix population models.