The four maxims of ecology

MAXIM 1: The maxim of dissipation
[Darwin's theory of competition]

∫dm < 0; ∇• M → 0; M = nm̅

(A) Any entity that can lift a weight will be prevented from so doing; and/or (B) can be put to use for the same purpose. (C) No entity can lift a weight indefinitely.

Explanation

MAXIM 2:The maxim of number

∇• H = δW = Pdt = nh̅

The number of progeny produced depends upon the number of progenitors maintained.

Explanation

MAXIM 3:The maxim of succession
[Darwin's theory of evolution]

∇ x M = ∂m̅/∂t - ∂n/∂t

The rate at which progeny is produced depends upon the rate at which competition occurs.

Explanation

MAXIM 4:The maxim of apportionment

∇ x H = ∂m̅/∂t - ∂n/∂t - ∂V/∂t

The bioactivity of a biological population is subject to increase from an initial value for one or more of three reasons: (a) increases in mass; (b) decreases in competition. All other increases are due to (c) the essential development of the entity or species.

Explanation

 

G  O    T  O    C  O  N  S  T  R  A  I  N  T  S

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

dU = Mdt = δQ - dH
Biology is “the study of those thermodynamic systems that can replace their internal energy”.

pdt + mdt = dh + du
Ecology is “the study of the exact processes by which a thermodynamic system replaces its internal energy”.

The Gibbs-Duhem equation:
m̅μ = m̅dS = dU + dH - Σi μi(dvi - dmi)
The Euler equation:
μ = dS = (∂S/∂U)V,Ni dU + (∂S/∂V)U,Ni dV + Σi (∂S/∂ui)U,V,{Nj≠i} dui + Σi (∂S/∂vi)U,V,{Nj≠i} dvi.

The three constraints: constant propagation, P > 0 = ∫0T dP; constant size, R > 0 = ∫0T dR; constant equivalence, W > 0 = ∫0T dW.