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Antlions organize themselves systematically in response to the
environments where they find themselves.
Individuals attempt to regularize their own pit locations according to
nearby pits and the borders of the living space, and this structure is
affirmed by a statistical test on the uniformity of their distribution.
Using a Monte Carlo simulation of 10,000 randomly distributed patterns
of the same number of pits as observed from each trial, a typical
distribution of the distance to the nearest neighbor was determined.
The distance to the nearest neighbor is approximately independent for
each pit, so a Cram\'er-von Mises statistical test was applied to the
observed distributions, resulting in striking evidence that these pit %'
dsitributions do not conform to a uniformly random independent
distribution of each pit, with all (except one) distributions of
antlions having $p<0.05.$
As a result of the statistical analysis procedure, during which the
settlement patterns of antlions in a given trial were compared to a
completely random settlement, a clear correlation was shown between the
settlement patterns of the antlions. However, for an effective
conclusion to be drawn about the antlions settlement patterns as a group
and the modes of communication that they may rely on the settlement
patterns of individual antlions (such as average pit depth, pit width,
and the rate of reclusive and cannibalism) had to be examined first.
With this in mind, several clear patterns were observed throughout
various trial sizes and communication conditions. For starters, a clear
increase in the reclusive population as trial size decreased was
observed in every obstacle condition, as the amount of reclusive
increased from one ($24\times24$) to two ($12\times12$) during the trail
erasure trial. The same results are shown across the trial with fake
pits, where the number of reclusive antlions increased from one to four,
and the obstacle trial, where the amount of reclusive antlion increased
from zero to three. In summary, the number of reclusive antlions
increased by an average of 2.333 antlions, or an increase of 233.3\%,
which marks quite a significant change. This change indicates that the
introduction of various obstacles and interference in other modes of
communication can change the natural settlement patterns of the
antlions, as a significantly larger number of reclusive antlions were
observed during trials with artificial pits, indicating that the density
of pits in a given area affects how antlions settle the territory. This
analysis makes biological sense, as by regulating the density of
antlions in a given territory the organisms can reduce intraspecies
competition, which in turn helps the species reproduce more as a whole,
thereby explaining the phenomenon. Along with this, a dramatic change
in the cannibalistic nature of the antlions was noticed once various
obstacles were introduced, as it was noted in the previous study that
the number of cannibalized antlions increased by an average of 13.9785\%
when the trial size was reduced with no obstacles or communication
interference. This differs from the trend in cannibalism noted
throughout the following trials, as the data clearly shows how the rate
of cannibalism tended to decrease across various trials, with the
exception of the first two trials where pits were removed, as shown by
graph 1. This indicates that the antlions' cannibalistic nature is
affected by environmental conditions such as changes in terrain and
other obstacles, which could be a response to an interrupted
communication pattern that results in a closer settlement, which intern
would increase the contact between each antlion, thereby leading to more
cannibalism. Finally, along with a trend in reclusivity and cannibalism,
a trend was noticed in the average pit depth across all trials, as it
decreased as trial size decreased throughout the study, regardless of
the obstacles introduced (Graph 1). This indicates that the size of
pits made by antlions is independent of the mechanisms that govern how
they settle, as the study was able to alter all of the settlement
patterns of the antlions through the introduction of obstacles except
for the average pit depth, which maintained a constant pattern through
the introduction of obstacles and the original trial from a previous
year. This indicates that the average pit depth does not depend on their
settlement pattern of the antlion community as a whole, but rather is
dependent on factors such as time and available resources.
Following the analysis of individual pit patterns, a large scale
analysis of the settlement pattern of the antlion groups as a whole was
conducted in order to determine how the introduction of various
obstacles and environmental conditions altered the group settlement
patterns of the antlions. During this analysis, several key patterns
emerged from the antlions distribution. For starters, the average
nearest neighbor remained relatively constant across all trials and
environmental conditions, except for when a series of fake pits were
introduced to the environment, as the average nearest neighbor ranged
from 2.1-3.9 (graph 2) for all trials except the $24\times24$ trial with fake
pits, where the average nearest neighbor increased to 8.7. Furthermore,
the nearest neighbor varied the most across the fake pit trial, as it
decreased by about 5.5 inches, which differed from the trial with trail
erasure where the nearest neighbor decreased by about 1.95 inches, and
the trial where obstacles were introduced, during which nearest neighbor
reminds constantly. This indicated that the spatial distribution of the
antlions is most likely dependent on several environmental conditions,
each of which has a varying impact on the antlions patterns. Another
settlement pattern that became clear throughout the trial was shown in
the Voronoi diagrams, pictured below, which illustrate the settlement of
every pit in a trial and show the “territory” occupied by each antlion.
Based on the aforementioned Voronoi diagrams, and statistical analysis,
it can be effectively concluded that the antlions maintain a non-random
distribution pattern across all trial sizes and environmental
conditions, as the antlions near the middle of the habitat maintain
about five neighbors at all times, a principal that is clearly shown by
examining the centermost pit in the Voronoi diagrams, as the territory
occupied by each antlion almost always makes a pentagon shape. Finally,
a closer examination of the Voronoi diagrams illustrates how the
antlions tended to maintain a constant pattern across both changes in
environment and changes in habitat size, as the average territory
occupied by each antlion remains statistically constant throughout all
trial sizes and environmental conditions, indicating that the antlions
distribute in a way that maintains a constant proportion between each
pit, thereby reducing cannibalism and competition.
Based on the settlement patterns of the antlions on both, an individual
and group scale several conclusions can be drawn about the environment's
impact on the settlement patterns of the insect along with the
mechanisms that antlions use to settle in a non-random pattern. With
this in mind, one of the most evident patterns in the data was the
impact of fake pits on the antlions settlement, as when fake pits were
introduced to the environment the rate of cannibalism and reclusivity
among the antlion population increased significantly, as shown by graph
1. Along with this, the Vovrinoi diagrams illustrate how the antlions
tended to space themselves away from fake pits when settling,
represented by the abnormally high average nearest neighbor during this
trial, as the average nearest neighbor increased significantly during
the trial with fake pits, as shown by graph 1. This indicates that the
settlement pattern of the antlions is highly dependent on the existence
of pits around them, as by introducing fake pits into the environment
the natural non-random distribution of the antlions was disturbed the
most, thereby showing that the pits and deformities in terrain that
antlions come into contact with influence where they settle the most.
This principle makes biological sense, as by spacing themselves away
from one another the antlions are allowing for an equal spread of
resources, thereby helping the species as whole progress more
efficiently. Along with this the increase in reclusivity and cannibalism
observed during this trial also indicates that the presence of pits
influences the settlement patterns of the insect, as the sharp increase
in extreme behavior patterns indicates that the antlions are attempting
to adapt to the introduction of a new environmental extreme. With this
in mind, it can be concluded that antlions rely on the density of pits
in a given region to settle, as well as the density of trails
surrounding a given region, as the interference with these two
environmental conditions disrupted the antlions the most.
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