Application of Boolean algebra in the Depiction of Life Pattern of Animals and Environmental Effects

Application of Boolean algebra in the Depiction of Life Pattern of Animals and Environmental Effects !

In writing the life patterns of animals and various arthropods much information needs to be brought together, relating not only to the morphological states but also including statements about the speed of development, limiting conditions, steady states and alter­native possibilities.

image source: c14608526.r26.cf2.rackcdn.com

Such relationships can only be stated concisely if the printed sentence is replaced by a symbol. This can be done by the help of Boolean algebra as follows (Hohn, I960; Clarke 1973).

First of all one must have symbols to represent the major morphological changes in the development of the animal: z can stand for zygote, meaning the fertilized egg of the animal; e for embryonic development; I for larva, meaning the post-embryonic to pre-adult stage of the life cycle; a for adult, meaning the body form the animal has during the reproductive cycles of the life history. The life pattern is terminated by death, indicated by d Written at the end of the symbols. Thus the stages in the life pattern of an arthropod or any animal with indirect development could be indicated thus:

z e I a d … (i)

The symbols written in sequence without punctuation indicating that the events they represent follow one another in the order stated. Where it is necessary to recognize more stages in the life history extra terms can be introduced, as for example, in endopterygote insects where, if p stands for pupa, the symbolic representa­tion would be

z e I p a d. ………. (ii)

If more than one larval stage needs to be recognized terms can be introduced thus:

z e n m c f o a d ……… (iii)

for the Euphausiacea (Crustacea, Malacostraca) where n = nauplius, m = metanauplius, c=calyptopsis larva, ƒ =furcilia larva, o=cyrtopia larva and a = adult.

Where names have not been given to the larval forms a se­quence of larval stages could be designated:

l₁ l₂ l₃ l₄ l₅ l₆ l₇ l₈ etc.

Each of the stages so named has properties which must be taken into account: these can be indicated by a symbol which can be written as subscript to the appropriate stage. Since all these pro­perties must be present they are enclosed in a bracket and as they are all of equal importance the symbols are separated by a full stop.

This system of notation says all must occur; all are of equal value to the animal. These properties and their symbols are: g for growth, dƒ for differentiation, r for reproduction, and dp for diapause.

Thus a larval stage may exhibit growth and differentiation and would be symbolized thus:

l (g-df)

Or growth only

lg

Or be a resting diapause stage

l dp

A sequence of larval stages showing these events could be symbolized thus:

l₁ (g.dƒ) l₂ (g) l₃ (dp) p a d

An entire life history of an endopterygote could be written thus:

z e (dƒ) l (g.dƒ) p (dƒ dp dƒ) a (g.r) d

Where l (g.dƒ) indicates that in larval development growth and differentiation occur together, but in the pupal stage the absence of stops in the term of (dƒ dp dƒ ) indicates that these events, differen­tiation, diapause and differentiation must occur in the sequence.

Further, the rates of development and tolerances of physical conditions for each stage differ; they may be symbolically repre­sented thus: T— temperature in degrees centigrade, R. H— relative humidity and P=photoperiod, the number of hours of light and dark in a day to which the stage is subjected.

The limits of tempe­rature are indicated by an integral sign with the figures written the upper limit at the top, the lower at the bottom of the sign, and the photoperiod by the number of hours light/number of hours dark.

Thus a larval period may be written indicating that larval growth and differentiation normally take place within a temperature range 10 —3(J°C, a relative humidity 20-90%, a photoperiod of 16 hours daylight and 8 hours dark­ness. If necessary the shape of the developmental curves for tem­perature can be written following the integral. For a pupa with diapause, the diapause conditions can be written following the symbol in subscript thus:

The formula for a complete life history of the tropical bug Dysdercus intermedins, a serious pest on cotton in Africa, can be written thus:

D = duration of instar in days,

Pr = pre-copulatory period in days,

Pro = pre-oviposition period in days,

I. O =inter-oviposition period in days.