Chapter 4
Evolutionary Simulation
But we really know little about the minds of the lower an-
imals. It cannot be supposed, for instance, that male birds
of paradise or peacocks should take such pains in erecting,
spreading, and vibrating their beautiful plumes before the fe-
males for no purpose. We should remember the fact given on
excellent authority in a former chapter, that several peahens,
when debarred from an admired male, remained widows dur-
ing a whole season rather than pair with another bird (Charles
Robert Darwin [23, p. 490]).
4.1 Simulation of sexual selection
Why does the peacock have such wastefully beautiful feathers?
Why did the zebra develop such a striped pattern?
Biologists are divided in their opinions regarding the excessive beauty of
certain animals. Does it fulfill a function of distinguishing individuals, of pro-
moting mutual grooming, of protecting the body from harmful insects, or of
adjusting the body temperature? Perhaps the aesthetics are a handicap?
Researchers conceive that such wonderful patterns mig ht be unsuitable for
adaptation. The maintenance of beauty requires ener gy (cost) and prevents
the animal from hiding effectively when discovered by predators. The feathers
of a peacock do not provide an advantage when running away from a threat.
Even Darwin was troubled by this problem when building arguments for
his theory of evolution. Why did evolution produce certain traits (behavioral
and physical characteristics) that are seemingly detrimental to individuals?
In this chapter, we present several hypotheses explaining this, together with
verification expe riments based on genetic algorithms (GAs).
4.1.1 Sexual selection in relation to markers, handicaps, and
parasites
In the following paragraphs, let us consider the difference in opinion be-
tween Darwin and Wallace in reg ard to the striped pattern of the zebra.
73
74 Agent-Based Modeling and Simulation with Swarm
The z e bra is conspicuously s tripe d, and stripes on the open plains
of South Africa cannot afford any protection. Here we have no ev-
idence of sexual selection, as throughout the whole group of the
Equidae the sexes are identical in colour. Nevertheless he who at-
tributes the white and dark vertical stripes on the flanks of various
antelopes to sexual selection, will probably extend the same view
to the Royal Tiger and beautiful Zebra. [23, p. 302]
It may be thought that such extremely conspicuous markings as
those o f the zebra would be a great danger in a country abounding
with lions, leo pards, and other beasts of prey; but it is not so.
Zebras usually go in bands , and are so swift and wary that they
are in little danger during the day. It is in the evening, or on
moonlight nights, when they go to drink, that they are chiefly
exp osed to attack; and Mr. Francis Galton, who has s tudied these
animals in their native haunts, assures me, that in twilight they are
not at all conspicuous, the stripes of white and black so merging
together into a gray tint that it is very difficult to see them at a
little dis tance. [123, p. 220]
Being the subject of “a delicate ar rangement [13],” Wallace is famous in a
paradoxical sense (one of his achievements in biology was the proposal of the
Wallace boundary found in biota). He and Darwin independently and almost
simultaneously devised the theory of evolution by natural selection, and the
paper sent by Wallace from the Malay Archipelago surprised the slow writer
Darwin. Eventua lly, both papers were presented simultaneously in 1858 at the
Linnean Society after Darwin had made “minor adjustments” in relevant parts
of his paper.
In On the Origin of Species, Da rwin argues that a female chooses a mate
after seeing a display of ma rvelous plumage and unusual, outlandish body
movements [21A]. B e ing chosen by the opposite sex in this way is known as
“elimination through sexual selection” or simply “sexual selection.”
The law of battle for the possessio n of the fema le appears to prevail
throughout the whole great class of mammals. Most naturalists will
admit that the greater size, strength, courage, and pugnaci ty of the
male, his special weapons of offence, as well as his special means
of defence, have been acquired or modified through that form of
selection which I have called sexual. This does not depend on any
supe riority in the general struggle for life, but on certain individ-
uals of one sex, generally the male, being succe ssful in conquering
other males, and leaving a larger number of offspring to inherit
their superiority than do the less successful males. [23, ch. XVIII]
Fisher supp orted the theory of sexual selection proposed by Darwin
(Fig. 4.1). In a seminal work entitled The Genetical Theory of Natural Se-
Evolutionary Simulation 75
FIGURE 4.1: The sexual selection.
lection, Fisher presented an adequate explanation of the female animal pref-
erences described by Da rwin in his theory [36A]. The premise of Fisher’s the-
ory is that successful achievement generates further successful achievement,
resulting in positive feedback with the potential for explosive growth. For ex-
ample, if the preference for a long tail becomes increasing ly successful, the
tails of males in later generations will become longer, and females will prefer
the males with even lo nger tails. This results in the development of yet longer
tails and a preference for long tails in females. Since success depends on the
rate of occurrence, the process progresses in a self-reinforcing manner.
The optimal strategy is that practiced by the majority, and mimicking the
actions adopted by most individuals is thus preferable. Therefore, selection
based on a long tail and the preference for a long tail pr ogress together. The
appearance of males and the preference in females for a certain appearance
evolve hand-in-hand in such a way that they reinforce each other. This process
is considere d to have eventually given ris e to the extraordinary tail feathers
of the peacock, and explains why the evolution and preference of a certain
appearance often exceeds a moderate level and bec omes a runaway process [21,
p. 284]. Such rapid growth is referred to as “the runaway effect” by Fisher.
In contrast, Wallace adopted the point of view that coloration is ultimately
derived from “protective colors and marks.” This idea about protective colors
explains both concealing coloration (which hides the body by deceiving the
eyes of an adversary) and conspicuous coloration. In other words, Wallace
points out that although it might appe ar at first sight that the colo ration of
some animals is extremely no ticeable, this coloration is in fact concealing in
the natural habitat of the animal. Examples supporting this view include the
zebra, the tiger, a nd the giraffe, which blend seamlessly into their respective
native environments. In addition, inedible animals that use bright colora tion as
a warning, and animals that mimic such colo ration, ar e in e xcellent agreement
with this explanation. Furthermore, colored ma rkings distinguish individuals
76 Agent-Based Modeling and Simulation with Swarm
FIGURE 4.2: The handicap principle.
of the same species, which serves as an aid fo r social animals (such as ants and
bees) to stay together or to recognize potential partners. The bright coloration
of various birds can also be explained in this way [21, pp. 176–178].
Although all the details about coloration as proposed by Wallace do not
necessarily hold true, and despite the large number of demonstrated coun-
terexamples, the general outline of Wallace’s argument is well constructed,
and has been adopted as a fundamental viewpoint in Darwinian theory .
Conversely, the “handica p principle” propo sed by the Israeli biologist
Amotz Zahavi accounts for the seemingly paradoxical existence of animals
that pay an extraordinarily high cost for their appearance. With its extrava-
gant feathers, the pea c ock makes a statement that it can afford its beautiful
appearance, since its nourishment is plentiful and its agility and stamina elim-
inate the risk of being discovered by predators. Thus, the peacock is in a supe-
rior position even with the disadvantage imposed by this handicap (Fig. 4.2).
In the same manner, bucks with extraordinary horns make a statement that
despite their handicap, their nourishment is sufficient and they are strong
enough to win a fight.
Why does the gazelle reveal itself to a predator that might not
otherwise sp ot it? Why does it waste time and energy jumping up
and down (stotting) instead of running away as fast as it can? The
gazelle is signaling to the predator that it has seen it; by “wasting”
time and by jumping high in the air rather than bounding away,
it demonstrates in a reliable way that it is able to outrun the
wolf. [130, pp. xiii–xiv]
A third theory that emphasizes the role of parasites was recently proposed,
sparking controversy. This theory was developed by the animal behaviorist
Hamilton, and resembles the ha ndicap principle. Using the male’s feathers as
a clue, a female assumes that she is choosing a partner with superior genes. A
male’s genes determine its immunological resistance to parasitic agents (bac-
Evolutionary Simulation 77
FIGURE 4.3: The parasite principle.
teria, viruses, and parasites), since maintaining large be autiful feathers is diffi-
cult if the body has been severely damaged by parasites. Therefore, choosing a
male w ith spectacular feathers equals choosing that with strong resistance to
parasites (and hence strong capability; Fig. 4.3). Although, up to this p oint,
Hamilton’s theo ry shares the same line of thought as the handicap theory,
it differs drastically from the latter in the following sens e. While predators
in Zahavi’s theory are more or less known, new parasites constantly emerge,
and the parasites themselves are extremely dive rse. Therefore, a consider-
ably strong e r resilience must be maintained than that necessary for avoiding
predators. The magnificence of a male’s feathers clearly shows its resilience
against current parasites, and the female wishes to obta in this information
by all means possible. Hence, the feathers of the peacock have acquired this
extravagance, which also appeals to the female.
To verify his theory, Ha milton investigated se veral species of birds (Passer-
iformes living in North America) in terms of their resistance to parasites, by
ranking on a six-level scale the plumage and the song complexity of males.
The results were subsequently compared with research data on the concentra-
tion of trematodes and protozoans in the blood of these birds, and a correla-
tion with assigned ranks was investigated. Unsurprisingly, species with more
extravagant feathers and mo re complex songs also had greater resilience to
parasites. Investigating the feathers o f the females, the cor relation was almost
indistinguishable from that observed in ma les. Hamilton’s parasite hypothesis
was thus considered to be verified. However, a number of problems with this
exp e riment have been pointed out, and the debate continues.
We now turn our attention to the use of GAs in sexual selection research.
4.1.2 The Kirkpatrick model
Mark Kirkpa trick [69] studied a mathematical model of sexual selection
based o n population genetics. In this model, each individual car ries two types
of genes denoted T (traits, features) and P (pre ferences), and each gene has
a pair of alleles (T
0
, T
1
and P
0
, P
1
, r e sp e c tively). P encodes the preference
of a female with respect to trait T of a male such that females carrying P
i
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