Ricker model

Key takeaways

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

Reference excerpt

The Ricker model, named after Bill Ricker, is a classic discrete population model which gives the expected number N t+1 (or density) of individuals in generation t + 1 as a function of the number of individuals in the previous generation,

N t + 1 = N t e r ( 1 − N t k ) . {\displaystyle N_{t+1}=N_{t}e^{r\left(1-{\frac {N_{t}}{k}}\right)}.\,}

Here r is interpreted as an intrinsic growth rate and k as the carrying capacity of the environment. Unlike some other models like the Logistic map, the carrying capacity in the Ricker model is not a hard barrier that cannot be exceeded by the population, but it only determines the overall scale of the population. The Ricker model was introduced in 1954 by Ricker in the context of stock and recruitment in fisheries. The model can be used to predict the number of fish that will be present in a fishery. Subsequent work has derived the model under other assumptions such as scramble competition, within-year resource limited competition or even as the outcome of source-sink Malthusian patches linked by density-dependent dispersal. The Ricker model is a limiting case of the Hassell model which takes the form

N t + 1 = k 1 N t ( 1 + k 2 N t ) c . {\displaystyle N_{t+1}=k_{1}{\frac {N_{t}}{\left(1+k_{2}N_{t}\right)^{c}}}.}

When c = 1, the Hassell model is simply the Beverton–Holt model.

See also Population dynamics of fisheries

Notes

References Brännström A and Sumpter DJ (2005) "The role of competition and clustering in population dynamics" Archived 11 July 2007 at the Wayback Machine Proc Biol Sci., 272(1576): 2065–72. Bravo de la Parra, R., Marvá, M., Sánchez, E. and Sanz, L. (2013) Reduction of discrete dynamical systems with applications to dynamics population models. Math Model Nat Phenom. 8(6). pp 107–129 Geritz SA and Kisdi E (2004). "On the mechanistic underpinning of discrete-time population models with complex dynamics". J Theor Biol., 21 May 2004;228(2):261–9. Marvá, M., Sánchez, E., Bravo de la Parra, R., Sanz, L. (2009). Reduction of slow–fast discrete models coupling migration and demography. J Theor Biol.. 258(371-379). Noakes, David L. G. (Ed.) (2006) Bill Ricker: an appreciation シュプリンガー・ジャパン株式会社, ISBN 978-1-4020-4707-7. Ricker, W. E. (1954) Stock and Recruitment Journal of the Fisheries Research Board of Canada, 11(5): 559–623. doi:10.1139/f54-039 Ricker, W. E. (1975) Computation and Interpretation of Biological Statistics of Fish Populations. Bulletin of the Fisheries Research Board of Canada, No 119. Ottawa.

Illustrations

Worked examples

Example 1 — a first encounter with Ricker model

Start with the simplest possible case. Write down what Ricker model 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 Ricker model 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 Ricker model 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 Ricker model

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

How to study Ricker model in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Ricker model 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 Ricker model out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Ricker model in simple terms?

The Ricker model, named after Bill Ricker, is a classic discrete population model which gives the expected number N t+1 (or density) of individuals in generation t + 1 as a function of the number of individuals in the previous generation, N t + 1 = N t e r ( 1 − N t k ) . {\displaystyle N_{t+1}=N_{…

Why does Ricker model 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 Ricker model?

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 Ricker model.