mathematics

Patrick Holt Leslie

Patrick Holt Leslie 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 Patrick Holt Leslie rather than just read about it. In short: Patrick Holt Leslie (1900 – June 1972) nickname "George" was a Scottish physiologist best known for his contributions to population dynamics, including the development of the Leslie matrix, a mathematical tool widely used in ecological and demographic studies. Career Leslie was born in 1900 near Edinburgh, Scotland.

Key takeaways

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

Reference excerpt

Patrick Holt Leslie (1900 – June 1972) nickname "George" was a Scottish physiologist best known for his contributions to population dynamics, including the development of the Leslie matrix, a mathematical tool widely used in ecological and demographic studies.

Career Leslie was born in 1900 near Edinburgh, Scotland. He pursued his education at Christ Church, Oxford, where he earned a bachelor's degree in physiology in 1921. However, due to a serious lung disease, he was unable to complete his medical studies. Following this, Leslie worked as an assistant in bacteriology in the Department of Pathology for several years. In 1935, Leslie joined the Bureau of Animal Population, a research center established by Charles Elton at Oxford. He had no formal training in advanced mathematics and lived a fairly quiet and somewhat secluded life partly due to his past illness. During World War II, the bureau shifted its focus to controlling rat and mouse populations in grain silos. Leslie's pioneering work in population studies began with calculating the intrinsic rate of increase for voles, Microtus agrestis, using age-specific birth and death rates with methods originally developed by Alfred J. Lotka, a method previously applied only to humans. He later extended these calculations to other species like brown rats, Orkney voles, and flour beetles. In 1945, Leslie published his seminal work in Biometrika, titled "On the Use of Matrices in Certain Population Mathematics". This paper introduced the Leslie matrix, a mathematical model for studying population dynamics. The method simplifies computations of population growth parameters, such as R0 (net reproductive rate) and R1 (intrinsic growth rate), particularly with modern computational tools capable of analyzing eigenvalues and eigenvectors. After the war, Leslie expanded the application of his matrix method to study the growth rates of various animal species, including birds and beetles. He worked on the statistical methods for marking and recapturing live-trapped small rodents, utilizing field data from Dennis and Helen Chitty on voles, with applications beyond rodents. Second, he conducted groundbreaking studies on stochastic equations to better understand predator-prey and interspecies relationships, contrasting these with simpler deterministic models. This work was supported by J.C. Gower's programming expertise on Rothamsted Research's computer. From 1948, Leslie collaborated closely with Thomas Park of the University of Chicago, who studied competition between Tribolium flour beetles. Leslie developed equations that successfully modeled and explained the intricate outcomes of these experiments. He earned the honorary Doctor of Science at Oxford based on the results of his extensive research. Leslie retired in 1967, the same year that the Bureau of Animal Population was integrated into Oxford's Department of Zoology following Charles Elton's retirement. Leslie died in 1972.

Bibliography Leslie, P. H. (November 1945). "On the Use of Matrices in Certain Population Mathematics". Biometrika. 33 (3): 183–212. doi:10.2307/2332297. JSTOR 2332297. Leslie, P. H. (December 1948). "Some Further Notes on the Use of Matrices in Population Mathematics". Biometrika. 35 (3/4): 213–245. doi:10.2307/2332342. JSTOR 2332342. Leslie, P. H. (June 1958). "A Stochastic Model for Studying the Properties of Certain Biological Systems by Numerical Methods". Biometrika. 45 (1/2): 16–31. doi:10.2307/2333042. JSTOR 2333042. Leslie, P. H.; Gower, J. C. (December 1960). "The Properties of a Stochastic Model for the Predator-Prey Type of Interaction Between Two Species". Biometrika. 47 (3/4): 219. doi:10.2307/2333294. JSTOR 2333294.

References

Worked examples

Example 1 — a first encounter with Patrick Holt Leslie

Start with the simplest possible case. Write down what Patrick Holt Leslie 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 Patrick Holt Leslie 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 Patrick Holt Leslie 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 Patrick Holt Leslie

In research: Patrick Holt Leslie 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 Patrick Holt Leslie 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: Patrick Holt Leslie is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1900 births, 1972 deaths, 20th-century British statisticians, so understanding it makes those chapters shorter.
In everyday life: Look for Patrick Holt Leslie 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 Patrick Holt Leslie in 20 minutes

Read the reference excerpt below once, without taking notes.
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Frequently asked questions

What is Patrick Holt Leslie in simple terms?

Why does Patrick Holt Leslie 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 Patrick Holt Leslie?

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 Patrick Holt Leslie.