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.2019 Mar 27;286(1899):20190365.
doi: 10.1098/rspb.2019.0365.

Digging the optimum pit: antlions, spirals and spontaneous stratification

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Digging the optimum pit: antlions, spirals and spontaneous stratification

Nigel R Franks et al. Proc Biol Sci..

Abstract

Most animal traps are constructed from self-secreted silk, so antlions are rare among trap builders because they use only materials found in the environment. We show how antlions exploit the properties of the substrate to produce very effective structures in the minimum amount of time. Our modelling demonstrates how antlions: (i) exploit self-stratification in granular media differentially to expose deleterious large grains at the bottom of the construction trench where they can be ejected preferentially, and (ii) minimize completion time by spiral rather than central digging. Both phenomena are confirmed by our experiments. Spiral digging saves time because it enables the antlion to eject material initially from the periphery of the pit where it is less likely to topple back into the centre. As a result, antlions can produce their pits-lined almost exclusively with small slippery grains to maximize powerful avalanches and hence prey capture-much more quickly than if they simply dig at the pit's centre. Our demonstration, for the first time to our knowledge, of an animal using self-stratification in granular media exemplifies the sophistication of extended phenotypes even if they are only formed from material found in the animal's environment.

Keywords: animal traps; extended phenotype; granular materials; optimized construction; self-organization; spontaneous stratification.

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Conflict of interest statement

We have no competing interests.

Figures

Figure 1.
Figure 1.
Antlion pits and spontaneous stratification. (a) AnEuroleon nostras pit at the bottom of a hedge row in southwest Guernsey; coin diameter: 24 mm. (b) A cartoon of grain ejection and the segregation of ejected grains of two different sizes during pit construction: the larger (blue) grains are thrown on average further than the smaller (silver) grains in the same scoop of ejecta because their ratio of momentum to drag is higher. (c) A two-dimensional representation of the helical pit-construction trench; the irregular features are reversals of direction. (d) Close shot of an experimental ‘quasi-two-dimensional’, Hele-Shaw, cell as in [17]; a mixture of two grain types in equal volumes is poured from the top left corner and self-stratifies into successive layers of grains of each type [17]; the red rough sugar cubes are larger than the white round sand grains and have a greater angle of repose. (e) Simulated grains are poured as in a Hele-Shaw cell using the rules in our model; red: large grains; blue: small grains.
Figure 2.
Figure 2.
Experimental results. (a) Relationship between the observed number of ejected large grains and their expected number based on the substrate mixture and unbiased ejection; blue (black): 1–2 mm (1.5–3 mm) in diameter; dashed black line: line of equality; they-difference between the regression line and the line of equality represents the number of observed large grains in excess of expected number. (b) Relationship between the ratio of the observed to the expected number of large grains (blue and black) in the pit wall and pit volume; circle (square): 20% (30%) volume fraction of large grains; solid red line: regression line, dashed red lines: 95% confidence interval for the regression line. Three and two of the 16 antlions were not included in (a) and (b), respectively, because they performed little or no pit building. (c–d) Experimental pot with a paper annulus over a mixture of silver sand and large black (blue) grains; the pit is in the middle of the hole in the paper annulus; small paper labels ‘J’ and ‘K’: pot IDs.
Figure 3.
Figure 3.
Image of the pit att = 700 from the spiral-digging model with initial radiusr = 25; an average result over 50 pits (see the electronic supplementary material, video S2 for an animation of the dynamics); red: excess of large grains, blue: excess of small grains, white: large and small grains mixed according to initial distribution (25% large grains by volume); solid vertical red (blue) lines: the maximum throwing distance of large (small) grains from the initial dig position at a spiral radius ofr = 25 cells from the pit centre; dashed vertical red (blue) lines: the equivalent for large (small) grains thrown from the pit centre at pit completion.
Figure 4.
Figure 4.
Model results. (a) The fraction of the removal window volume occupied by large grains and (b) the average avalanche size, 〈st〉, over time for the spiral-digging and the null models with redistribution; solid lines: averages over 50 pit realizations; dashed line: expected volume fraction of large grains in the removal window based on large grains occupying 25% by volume in the original mixture; dotted line: 4% volume occupied by large grains in the removal window used to define a ‘completed pit’ (electronic supplementary material). (c) The ratio of the volume fraction of large grains ejected and large grains in the mixture, and (d) the time to pit completion against initial spiral radius,r, for spiral digging; red circles: averages over 50 pit realizations; solid red line: smoothed form of the relationship; dashed red lines: 95% CI envelope; dashed black line: final pit radius of 30 cells in the model (the average of 18 mm in the experimental pits, electronic supplementary material, table S1), at which the pit has a perfect small-grain lining; solid black lines: the spectrum of initial spiral radii,r, 10–42 (6–25 mm), where spiral digging offers substantial time savings over central digging. (Online version in colour.)
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References

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