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Recent Posts

The more they remain the same the more they change

John Ray, the English naturalist and scientist, produced the first ever biologically-relevant definition of ‘species’. He was trying to classify plants and in 1686 wrote: In order that an inventory of plants may be begun and a classification (divisio) of them correctly established, we must try to discover criteria of some sort for distinguishing what [...]

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Can we escape evolution?

Although the word ‘constraint’ often has a negative connotation in ordinary language, it is how scientists and mathematicians operate. One of the first and most effective uses of a scientific-mathematical constraint came in the seventeenth centruy from the Frenchman Pierre de Fermat (of ‘Fermat’s last theorem’ fame). Natural philosophers of his day wondered what path [...]

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Geography and the Gibbs energy

The ‘Gibbs energy’ is invariably difficult to explain to those who don’t know what it is. And despite its importance, it was only at the end of the nineteenth century that Max Rubner, the German physicist and physiologist, at last convinced other scientists that the energy that biological organisms use in metabolic processes exactly equals [...]

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Circumambulations: what are they, and why are they relevant to biology?

So what is a circumambulation, and why is it relevant to biology and evolution? Brian Charlesworth wrote in his book Evolution in age-structured populations (Cambridge University Press, 1994) that: “… the concept of generation time is a rather arbitrary one”. He then lists several alternatives. It is surely rather strange that something so fundamental to [...]

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“Engeny” in biology and ecology. What is it and why should we bother to measure it?

ENGENY (see definition) is how we measure Darwinian competition and evolution. It is important to correctly quantify this because as Theodosius Dobzhansky said with the title of his 1973 paper, Nothing in Biology Makes Sense Except in the Light of Evolution (March 1973 edition of American Biology Teacher). A really big issue is, of course, [...]

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The four laws of biology

brassica rapa experiment

LAW 1: The law of existence
n >= 1; δW = (δQ - dU) > 0; m → ∞; m̅ > 0

LAW 2: The law of equivalence
(δW1 = δW2) ∧ (δW2 = δW3) ⇒ (δW1 = δW3)

LAW 3: The law of diversity
A ⇒ 0; F ⇒ M

LAW 4: The law of reproduction
dA/dt > 0; dm̅/dt < 0; m̅ > 0; dn/dt >= 0

The four maxims of ecology

brassica rapa experiment

MAXIM 1: The maxim of dissipation
[Darwin's theory of competition]
∫dm < 0; ∇• M → 0; M = nm̅

MAXIM 2: The maxim of number
∇• H = δW = Pdt = nh̅

MAXIM 3: The maxim of succession
[Darwin's theory of evolution]
∇ x M = ∂m̅/∂t - ∂n/∂t

MAXIM 4: The maxim of apportionment
∇ x H = ∂m̅/∂t - ∂n/∂t - ∂V/∂t