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Appendix
Title: Effects of worker size on the dynamics of fire ant tunnel construction
Short Title: Fire ant worker size and tunnel construction
Nick Gravish1, Mateo Garcia1, Nicole Mazouchova2, Laura Levy2, Paul B. Umbanhowar3,
Michael A. D.Goodisman2, and Daniel I. Goldman1
1
School of Physics
Georgia Institute of Technology
Atlanta, GA 30332
2
School of Biology
Georgia Institute of Technology
Atlanta, GA 30332
3
Department of Mechanical Engineering
Northwestern University
Evanston, IL 60208
Keywords: Adaptive demography, division of labor, nest construction, polymorphism, social
insects, spatial network.
Corresponding author:
Nick Gravish
ngravish@gatech.edu
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Image capture
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Two digital cameras were used over the course of the experiments; a 12 megapixel DSLR
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camera (Canon Rebel XS) and an 8 megapixel point and shoot camera (Canon Powershot A470).
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LabVIEW and the free software development kit (SDK) available from Canon were used to
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automate image capture and download from the DSLR camera. The free Canon Hack
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Development Kit (CHDK; http://chdk.wikia.com) software and LabVIEW were used for
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automated image capture with the Powershot camera.
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Image analysis
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Image masks generated in Photoshop were imported into Matlab as a matrix Axy where x
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and y were the horizontal and vertical position of the pixel and a value of Axy equal to 1
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corresponded to a tunnel and 0 to no tunnel. The projected tunnel area, A, was measured as the
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total number of non-zero elements in the matrix multiplied by the areal dimension of an
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individual pixel determined through calibration points in the image.
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We used image morphology functions in Matlab to extract information about tunnel
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morphology. Image matrices were first reduced to their base image skeleton in which all tunnels
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in the matrix were shrunk to a thickness of a single pixel which traced along the center of the
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tunnels (See Fig. 2c). We defined the degree of a pixel () as the number of 1 valued pixels
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surrounding it in an 8-connected neighborhood,
.
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We use the concept of a network in which tunnels are described as planar graphs
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consisting of a set of vertices defined as start-points, branches, or end-points of tunnels
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connected together by edges that represent the interconnecting tunnels (Barthélemy, 2011; Buhl
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et al., 2002; Buhl et al., 2004). The tunnel network was extracted by computing  at all non-zero
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pixels in the image skeleton. Pixels where  are start or endpoint vertices while  are
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branching vertices. Tunnels between vertices are connected by paths of  pixels. Because of
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the thinning process, vertices in the tunnel network that connect more than three tunnels are often
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represented in the thinned mask as two or more degree three pixels. To account for this, we
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merged all vertices that were within a distance of approximately two tunnel diameters. We
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validated this algorithm through manual selection of the edge and vertices connections for all the
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final images.
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The path length, l, of each tunnel (Fig. 2c) was determined by summing the distance
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between adjacent pixels in the image skeleton, with vertical or horizontal steps representing 1
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pixel length and steps along the diagonal directions representing
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of tunnels, L, was estimated as the sum of the lengths of the individual tunnels. The local tunnel
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width, w, was defined as twice the distance to the nearest tunnel wall (computed using the
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images distance transform; Fig. 2c). The average tunnel width, W, was computed as the ratio of
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A/L.
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Nonlinear regression
pixel length. The total length
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We assessed the statistical significance of fit parameters in nonlinear regressions among
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the three treatments using the methods described in Motulsky (Motulsky and Ransnas). We test
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the statistical significance of pooling data among treatments (all data described by one set of
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parameters) compared to the goodness of individual fits with separate fit parameters using an F-
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test. The significance of the fit was determined from the value,
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where SS is the sum of squares error for the pooled and separate data, and df is the corresponding
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degrees of freedom. The F ratio is evaluated with a numerator of
and
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denominator
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more powerful than the combined fit.
and a significance value of p < 0.05 indicates that separate fits are statistically
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References
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Barthélemy, M. (2011). Spatial networks. Physics Reports 499, 1-101.
Buhl, J., Deneubourg, J.-l. and Theraulaz, G. (2002). Self-Organized Networks of Galleries in the
Ant Messor Sancta. Growth (Lakeland), 163-175.
Buhl, J., Gautrais, J., Sole, R. V., Kuntz, P., Valverde, S., Deneubourg, J. L. and Theraulaz, G.
(2004). Efficiency and robustness in ant networks of galleries. European Physical Journal B 42, 123129.
Motulsky, H. J. and Ransnas, L. A. (1987). Fitting Curves to Data Using Nonlinear-Regression - a
Practical and Nonmathematical Review. Faseb Journal 1, 365-374.
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