Fenchel's Law is a regularity in population ecology

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. It is the study of how the population sizes of species living together in groups change over time and space....

 regarding how exponential population growth is related to the body size of the organism. It was first described by the Danish

Denmark

Denmark is a Scandinavian country in Northern Europe. The countries of Denmark and Greenland, as well as the Faroe Islands, constitute the Kingdom of Denmark . It is the southernmost of the Nordic countries, southwest of Sweden and south of Norway, and bordered to the south by Germany. Denmark...

 marine ecologist

Marine biology

Marine biology is the scientific study of organisms in the ocean or other marine or brackish bodies of water. 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 classifies species based on the environment rather...

 Tom Fenchel

Tom Fenchel

Tom Michael Fenchel 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, Fenchel's Law. He holds PhD and D.Sc...

. 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

Unicellular organism

A unicellular organism, also known as a single-celled organism is an organism that consists of only one cell, in contrast to a multicellular organism that consists of multiple cells. Historically simple single celled organisms have sometimes been referred to as monads Prokaryotes, most protists,...

s, one for poikilotherm

Poikilotherm

A poikilotherm is an organism whose internal temperature varies considerably. It is the opposite of a homeotherm, an organism which maintains thermal homeostasis. Usually the variation is a consequence of variation in the ambient environmental temperature...

s and one for homeotherm

Homeotherm

Homeothermy is thermoregulation that maintains a stable internal body temperature regardless of external influence. This temperature is often, though not necessarily, higher than the immediate environment...

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.