The four maxims of ecology

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

M = nm̅;   ∫dm < 0;   ∇ • M → 0

(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 = H/n =

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 = ∂/∂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 = ∂/∂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 → ∞; > 0

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

LAW 3: The law of diversity
A → 0; FM

LAW 4: The law of reproduction
[(dm̅/dt ≤ 0) ∧ ( > 0)] ⇒ [(dn/dt ≥ 0) ∧ (dA/dt > 0)]

dU = Mdt = δQ - dH; M > 0
Biology is “the study of those systems that can replace their internal energy” (See explanation of terms and variables).

pdt + mdt = dh + du = δq; m > 0
Ecology is “the study of the processes systems use to replace their internal energy” (See explanation of terms and variables).

The Gibbs-Duhem equation governs all biological energy:
m̅μ = dS = dU + dH - Σi μi(dvi - dmi)
The Euler equation governs all biological activity:
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.

All biological populations are subject to the three constraints of:

(a) constant propagation,
0 =  T0dP < P’ = N’p̅’
;
(b) constant size,
0 =  T0dM < M’ = N’m̅’ ( = R’)
;
(c) constant equivalence,
0 =  T0dS < S’ = N’s̅’
.