Aiming the “unreasonable effectiveness of mathematics” at ecological theory

Ginzburg, Lev; Jensen, Christopher X. Jon; Yule, Jeffrey V.

doi:10.1016/j.ecolmodel.2007.05.015

Cited by 15 publications

(11 citation statements)

References 44 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By contrast, geometric or exponential growth of populations described by the above equations should not be called a "law" but rather provides an example of what the philosopher W.V.o. Quine called a "limit myth" (Quine, 1960), along the lines of the concept of an idealized perfect pendulum in classical mechanics (see Ginzburg et al, 2007). Essentially no populations exhibit exponential growth (just as no pendula in nature really fit the assumptions of a frictionless simple pendulum), but no ecologist can pretend to understand how populations behave unless he or she grasps exponential growth as a conceptual hook on which to hang our understanding of more complex dynamics.…”

Section: Newtonian Physics and Statementioning

confidence: 97%

IJEE Soapbox

Holt

2009

Israel J Ecol Evol

View full text Add to dashboard Cite

Section: Newtonian Physics and Statementioning

confidence: 97%

IJEE Soapbox

Holt

2009

Israel J Ecol Evol

View full text Add to dashboard Cite

“…Results range from Fussmann, Weithoff & Yoshida's (2005) finding of no evidence for predator dependence at naturally occurring densities of rotifers (see also Fussmann Weithoff & Yoshida, 2007) to Mills & Lacan's (2004) claim to have shown ratio-dependent predation by an egg parasitoid wasp. The past decade has also seen several new publications by Ginzburg and collaborators, which argued against analyses that did not find ratio dependence and reinterpreted many of the recent findings of predator dependence as being ratio dependence (Jensen & Ginzburg, 2005;Ginzburg, Jensen & Yule, 2007;Jensen, Jeschke & Ginzburg, 2007;Ginzburg & Jensen, 2008). This altered view of empirical results was summarized in a new book by Arditi & Ginzburg (2012;henceforth AG12), which returns to the arguments of AG89, and interprets subsequent work in light of those arguments.…”

Section: (2) Controversy In the 1990smentioning

confidence: 99%

“…In the case of ratio dependence, there is a continuing campaign by its authors to promote ratio dependence as the appropriate baseline form for functional responses. This 'pro-ratio' campaign is the central argument in AG12 and several of their other recent studies (Jensen & Ginzburg, 2005;Ginzburg et al, 2007;Jensen et al, 2007). Such a campaign would be relatively innocuous if the ideas were not widely accepted in the broader community.…”

Section: (5) the Status Of 'Ratio Dependence' In Current Ecological Tmentioning

confidence: 99%

Why ratio dependence is (still) a bad model of predation

Abrams

2014

Biological Reviews

View full text Add to dashboard Cite

The history of the idea that predation rates are functions of the ratio of prey density to predator density, known as ratio dependence, is reviewed and updated. When the term was introduced in 1989, it was already known that higher predator abundance often reduced an individual predator's average intake rate of prey. However, the idea that this effect was a universally applicable inverse proportionality was new. That idea was widely criticized in many articles in the early 1990s, and many of these criticisms have never been addressed. Nevertheless, ratio dependence seems to be gaining in popularity and is the subject of a recent monograph by the originators. This article revisits the most important objections to this theory, and assesses to what extent they have been answered by the theory's proponents. In this process, several new objections are raised. The counterarguments begin with the lack of a plausible, generally applicable mechanism that could produce ratio dependence. They include the fact that ratio dependence is a special case of predator‐density effects, which, in turn, are only one of many non‐prey species effects that influence the consumption rate of a particular prey. The proclaimed simplicity advantage of ratio dependence is at best small and is outweighed by its disadvantages; it predicts biologically implausible phenomena, and cannot easily be extended to describe multi‐species systems, trait‐mediated interactions, coevolution, and a number of other important ecological phenomena. Any potential small simplicity advantage disappears with corrections to remove unrealistic low‐density dynamics caused by ratio dependence. The frequent occurrence of strong predator dependence does not make ratio dependence a better ‘default’ model of predation than prey dependence, and empirical studies of the full range of non‐prey species effects on the consumption rates of predators are needed.

show abstract

“…Science progresses when it bonds with mathematics, and population ecology is the strongest of the subdisciplines of ecology in its mathematical development (Ginzburg et al ). The key to all of this is that there is a mathematics of populations, developed largely by human demographers followed by population ecologists.…”

Section: Successes In Population Ecologymentioning

confidence: 99%

One hundred years of population ecology: Successes, failures and the road ahead

KREBS

2015

Integrative Zoology

View full text Add to dashboard Cite

Population ecology is the most mature of the three subdisciplines of ecology partly because it has a solid mathematical foundation and partly because it can address the primary questions of distribution and abundance with experimental protocols. Yet there is much left to do to integrate our population knowledge into community and ecosystem ecology to help address the global issues of food security and the conservation of biodiversity. Many different approaches are now being developed to bring about this integration and much more research will be necessary to decide which if any will be most useful in achieving our goals of explaining the changes we see in the distribution and abundance of animals and plants. Food web ecology would appear to be the best approach at present because it uses the detailed information of the population ecology of particular species in combination with data on consumer-resource interactions to apply to the applied problems of biodiversity conservation, food security, pest management and disease prevention. If we can use our understanding of population ecology to address the practical problems of our time in a creative way, we will benefit both the human population and the Earth's biodiversity. Much remains to be done.

show abstract

Aiming the “unreasonable effectiveness of mathematics” at ecological theory

Cited by 15 publications

References 44 publications

IJEE Soapbox

IJEE Soapbox

Why ratio dependence is (still) a bad model of predation

One hundred years of population ecology: Successes, failures and the road ahead

Contact Info

Product

Resources

About