Fenchel's Law is a regularity in
population ecology
Population ecology is a sub-field of ecology that deals with the dynamics of species populations and how these populations interact with the environment (biophysical), environment, such as birth rate, birth and death rates, and by immigration an ...
regarding how exponential population growth is related to the body size of the organism. It was first described by the
Danish marine ecologist
Marine biology is the scientific study of the biology of marine life, organisms that inhabit the sea. Given that in biology many phyla, families and genera have some species that live in the sea and others that live on land, marine biology clas ...
Tom Fenchel
Tom Michael Fenchel (born 19 March 1940, in Copenhagen) is a Danish marine ecologist and professor first at the University of Aarhus, later at the University of Copenhagen. He is a highly cited scientist and known for, among other things, Fenche ...
. It contends that species with larger body sizes tend to have lower rates of population growth. More exactly, it states that the maximum rate of reproduction decreases with body size at a power of a quarter of the body mass
Fenchel's law may be expressed as an allometric equation:
:
,
where r is the intrinsic rate of natural population growth, a is a constant that has 3 different values (one for
unicellular organism
A unicellular organism, also known as a single-celled organism, is an organism that consists of a single cell, unlike a multicellular organism that consists of multiple cells. Organisms fall into two general categories: prokaryotic organisms and ...
s, one for
poikilotherm
A poikilotherm () is an animal (Greek ''poikilos'' – 'various', 'spotted', and ''therme'' – 'heat') whose internal temperature varies considerably. Poikilotherms have to survive and adapt to environmental stress. One of the most important s ...
s and one for
homeotherm
Homeothermy, homothermy, or homoiothermy () is thermoregulation that maintains a stable internal body temperature regardless of external influence. This internal body temperature is often, though not necessarily, higher than the immediate envir ...
s), and W is the average body mass of the organism. This means that if a species ''A'' has a body mass 10 times that of species B, then the maximum population growth rate of ''A'' will be one-half that of species B.
[Ginzburg, L.R. & Colyvan, M. (2004) Ecological Orbits: how planets move and populations grow. Oxford University Press, New York ]
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Population ecology