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| -rw-r--r-- | poster2.tex | 2 | ||||
| -rw-r--r-- | src/analysis2-bu.i | 135 | ||||
| -rw-r--r-- | src/analysis2.i | 2 |
3 files changed, 137 insertions, 2 deletions
diff --git a/poster2.tex b/poster2.tex index c812fae..58af014 100644 --- a/poster2.tex +++ b/poster2.tex @@ -102,6 +102,6 @@ \image poster2/img4.i %\incl{Experiment Notes}{src/notes2.i} \image poster2/img5.i -{\spacing105\incl{Data Analysis}{src/analysis2.i}} +{\spacing105\incl{Data Analysis}{src/analysis2-bu.i}} \incl{Conclusion}{src/conc.i} \supereject\end diff --git a/src/analysis2-bu.i b/src/analysis2-bu.i new file mode 100644 index 0000000..ff6b1dc --- /dev/null +++ b/src/analysis2-bu.i @@ -0,0 +1,135 @@ +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. diff --git a/src/analysis2.i b/src/analysis2.i index cd7cba9..ff6b1dc 100644 --- a/src/analysis2.i +++ b/src/analysis2.i @@ -8,7 +8,7 @@ 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%' +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 $p<0.05.$ |