Feropods will not help: research and mathematical modeling of ant lion larvae pits

The explorer, fascinated by the greatness and beauty of the world outside of his city, by the will of fate finds himself in places where he has never been before. Wounded and exhausted, he looks for a way home, meeting on his way soulless and indifferent passers-by who are ready to watch with reverence the death of another. Not ready to put up with such social injustice, he intervenes and rescues an unknown creature from the voracious jaws of a terrible monster. This creature is small, but with a big heart, offers it its assistance in response to salvation. And the voracious monster becomes, by a twist of fate, the prey of an even larger creature, in front of whom everyone trembles without exception.

It sounds like the plot of some Hollywood adventure film, but in fact it is “The Ant's Journey” (1983) - a beautiful cartoon that has long been disassembled into quotes. An ant saves a kozyavka (“I hear it from a kozyavka!”) From a trap made by one very entertaining creature - the ant lion. And today we’ll talk about them, or rather, about how biologists in collaboration with physicists conducted a study of the structure of antlion traps. Why such traps can not be called simple pits, as the larvae of antlions make them and what are the exact parameters of these deadly buildings? To these and other questions we will find the most interesting answers in the scientists' report. Go.
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Tools, architecture and pits of death

Scientists who have decided to conduct this study argue that the use of tools by animals is painfully overrated. And this statement can not be called unfounded. For example, chimpanzees use tools for food in just 1% of cases. Much more attention should be paid to the buildings that various creatures use on an ongoing basis, including nests and traps for catching prey.


Making traps out of the web is difficult, but familiar, but silk bridges across rivers is a completely different level of skill.

Building traps is not the most popular skill among the inhabitants of our planet. Among vertebrates, only humans have this skill. And among invertebrates, spiders and their networks, the complexity, diversity and mathematical accuracy of which are amazing, come to mind first. Of course, our octopus friends are not the only ones who use silk produced by their own bodies as a building material. In addition to 10,000 species of spiders, the larvae of 2,000 species of caddisflies also use silk, as well as the larvae of 4 species of Arachnocampa from the genus of mushroom mosquitoes.

But the construction of traps without the use of silk is common only among several hundred species of ant and a small number of species of worms. One of these builders is the ant lion larva.


An adult ant lion playing peeking with a photographer.

The ant-lion is not a mythical chimera or the brainchild of a science fiction writer, it is a family of insects that very much resemble dragonflies. But they got their non-standard name for the appearance and habits of the larvae.


"Cute" muzzle of the ant lion larva.

Ant lion larvae are of two species, depending on the behavior. Some live in the sand and chase their prey, so to speak they hunt in the classical way. Others, who have patience and architectural skills, build pits up to 5 cm deep and about 8 cm in diameter in the sand. The larva itself digs in the center of its trap, leaving only its massive and very strong mandibles on the surface. The victim, as a rule, an ant, having the imprudence to step on the edge of the fossa, begins to slide down to its inevitable death. Grabbing the prey, the ant lion larvae injects digestive enzymes into its body and literally drinks the victim, throwing its exhausted chitinous exoskeleton outside the trap.


Larva ant lion.

If the prey was painfully quick and energetic and trying to get out of the trap, the larva begins to throw at her head grains of sand, which can knock the victim down. In the same way, literally working with their heads, antlion larvae build their traps. And it was precisely the construction process that interested scientists. The sand is very heterogeneous and consists of sand grains (grains) of different sizes and, accordingly, weight (like snowflakes, for example). The ant-lion larvae are building in a spiral, sorting the grains of sand in a specific order. How and why - these are questions that scientists have decided to find answers to.

The basis of the study

Scientists decided to conduct observations under controlled conditions using sand grains of three specific sizes and a paper ring, necessary for determining the size of the ejected grains, the diameter of the trap, and other measurements.


Image number 1: a - the appearance of the ant lion larvae trap (photo taken on the island of Guernsey); b - image of the radius of emission of grains depending on their size and weight; - two-dimensional image of the spiral trajectory of the construction of the pit-trap: d - a snapshot of the edge of the pit-trap from the experiment (we can see a clear separation / sorting of the granules); e is a pit-trap model that takes into account the Hele-Show rule.

16 larvae of antlions of the species Euroleon nostras, which were taken from the wild nature (southeast of the island of Guernsey), were made as experimental. Scientists note a surprising observation: the pits of these larvae were located under the hedges, i.e. in shrubs, not in open sandy spaces, as is usually the case. This is probably an attempt to use shrubs as protection from rain. In addition, scientists have noticed that the larvae built traps only in places where there was a minimum of debris (fallen leaves, branches, etc.). These observations alone are enough to make a preliminary conclusion about the non-random choice of the location of the pit-trap construction.

The researchers prepared a test sand mixture of natural dry silver sand from the beaches of Guernsey, grains of black silica (1-2 mm, average of 0.0078 g) and grains of blue silica (1.5-3 mm, average of 0.028 g). Flower pots with a height of 14 cm and a depth of 12 cm were used as building sites. Each of the building components was placed in a pot in a specific order: at the base was a 7 cm layer of natural sand, then one layer to the middle of the pot (2.5 cm from the top) from 4 mixtures of 20-30% of large particles (black or blue silica) and 80-70% of natural sand. From above, everything was covered with a paper ring, necessary for measurements, with a diameter of 12.6 cm (hole - 4 cm).

All the larvae were placed in the center of the flower pots. Most of the larvae began construction during the first hour of observation. And after about two days, each of the larvae built a trap hole with a diameter of 12 to 23 mm. Scientists collected all the particles that the larvae threw away during construction (they turned out to be on a paper ring) and sifted for sorting. The location of the discarded colored grains on the paper ring was manually marked with photos. Scientists did not want to use automated methods in order to get more accurate results.

Observation results

Image number 2: the results of laboratory observations.

As can be seen from schedule 2a, the larvae preferably got rid of larger nuggets. Blue and black particles of silica were thrown 1.3 times more than they were in the mixture. Scientists also noticed that as the size of the pit increased, the number of large particles in its walls decreased ( 2c and 2d ). This observation may be due to the fact that small pits cannot contribute to sufficient stratification. That is, the convergence of granules (like an avalanche) when the victim falls into the pit is much more likely with a larger volume of the pit itself. In addition to this, a concomitant factor is precisely the smaller grains, since their angle of repose is smaller, therefore slippage is more likely.

Simply put, small grains are important for ant lion larvae, because at their expense, the prey will most likely roll to hungry mandibles, and will not get out with the words “phew, carried through”. It turns out that the larvae build pits not mindlessly, but consciously sorting out building materials, ensuring maximum efficiency of the future construction.

Observations by observations, but for a complete understanding of the architecture of ant-lion traps, the scientists decided to see what the computational model of this building would look like.

Spiral Digging Simulation

First of all, scientists note that the ant lion larvae do not build their traps in the same way as other “diggers” do. The process of digging occurs in a spiral, rather than vertically. And mathematical modeling can reveal the secrets of this process.

In the creation of the model used previous work on self-organization in granular media. Scientists considered a mixture of small and large granules (grains) as a one-dimensional lattice with nodes i = 1,2, ..., L, representing a cross section of a real experimental well. Small particles in volume and height are 1, and large - 2. Thus, the height at node i, hi is calculated from the sum of small and large particles at the node, where the local slopes on each side are z _i ^Left = h _i - h _{i -1} and z _i ^Right = h _i - h _{i + 1} .

A landslide will occur only if the arithmetic average over the granules of the local gradient exceeds the critical level. It is also obvious that the large particles will be more stable with a steeper slope than small ones. In turn, small grains located on large ones are more stable than large ones on small ones. This condition is necessary to account for stratification in the mathematical model.

A grain can roll left / right if the local slope in the appropriate direction exceeds the critical point, z _i ^c . If z _i ^Left and z _i ^Right exceed the critical figure, then the granule will roll in the direction of the steepest slope or in a random direction, if z _i ^Left = z _i ^Right ﹥ z _i ^c .

Determination of the power (size) of a landslide is the total number of falls of granules in the pit over a certain time interval ( t ). As for weight, it is determined by the size of the granules themselves: the large ones contribute 2 to the general indicator, and the small ones - 1. Thus, all the granules that participate in the landslide are taken into account: the initial ones and those that were captured by the flow in the process of movement.


Image No. 3: the result of the spiral model at t = 700 and the initial radius r = 25. Small blue particles are small, red - large, and white - a mixture of both, taking into account the fact that large ones are not more than 25%.

In the initial state, the grain models are added in size randomly until h _i = H or H + 1, taking into account the condition that 25% of the total number of grains are large. The dimensions of the “removal / ejection window” were set as 5x5 (width to depth) in accordance with the fact that the ant lions emit at each step of the process of digging a hole. This "window" was centered in a certain lattice site, which can be shifted in accordance with the spiral digging path. The program can throw out grains any number until the stable state of the walls of the simulated trap pit is reached.

Scientists, using Stokes approximation and Newton's second law, derived the trajectory formula for the ejected grains:



v _x and v _y - horizontal and vertical components of the velocity of the grain;
g is the gravitational acceleration;
⍺ = g / v _T is the form drag coefficient, where v _T is the final velocity of the particles: 150 cm / s for small particles and 1000 cm / s for large ones.

The initial rate at which the grains are ejected is as follows: v ₀ = (70 + δv) cm / s. And the throw direction: θ ₀ = (50 + δθ) °.

The initial radius of the well ( r ) is 25. The model carries out the process of digging on each node 4 times, which ensures the helicity of removing most of the grains. The spiral reaches the center after 8r steps, and the completion of the well occurs when the number of large grains in the “removal window” falls below the critical point.

To understand the effectiveness of the spiral method of pits-trap formation, scientists compared the above model with three models with centralized digging: a model without redistribution of grains (they are simply removed in the process), a model without resistance of grains (the trajectories of small and large grains are the same) considering resistance.

Simulation results

Image number 4: simulation results.

The first indicator, which should be compared in models and real observations, is the number of large particles removed. In the spiral model of large particles, at the end of the digging, it became 1.4 times smaller than it was in the initial mixture. It should be noted that centralized models with / without resistance showed a decrease of only 1.05 times. Accordingly, the results of the spiral model are correlated with real observations, which confirms the calculations of the proportionality of large and small grains in the construction of trap holes.

The radius of the modeled pit was 30 units, which, when taking into account the scaling, is almost identical to the larvae observed in a laboratory experiment - 18 mm. It is worth noting the observed average radii at which the removal of large particles is greatly accelerated to achieve a larger radius of the well (jump on chart 4c ).

Upon completion of the construction of the wall of the pit-traps, the larvae are almost completely covered with small grains. Similar was observed in all models; however, only in the spiral process was this process carried out faster.


Table comparing the performance of various models described above. As we see, it is the spiral versions of the models that turned out to be the most effective.

The ratio between the initial radius (r ≈18), for which the completion time is minimized (strong decline on graph 4d ), and the final well radius predicted by the model, is 0.60.

If we talk about the cost of time, then here the spiral method of digging is better than others. With an initial radius of 25, the spiral model took half the time to complete the pit than other models. Comparison of data showed that the spiral model reduces the time for completion of the pits by 60% with a final diameter in the range of 10 ... 42 units, i.e. 6-25 mm in reality, which was confirmed by the results of observations in a laboratory experiment.

For more detailed acquaintance with the nuances of the study I strongly recommend to look into the report of the research group .

Epilogue

Sometimes, watching the insect, you think about what is on the mind of this little creature. Does it understand how the world works, is it aware of the physical processes that surround it, does it use them? This study may or may not answer the question “is it aware?”, But more than yes it answers the question “does it use?”.

Digging a hole is easy, at least at first glance. However, the pit trap must be as efficient as possible, because the life of the one who built it depends on its success. If the ant lion larvae didn’t use the spiral model of digging, didn’t sort grains of sand, they wouldn’t get the food so easily.

Although the larvae of the antlions are terrible predators with large mandibles, they prefer to use their intellect as the main and most effective weapon in the struggle for life in the harsh conditions of wildlife. However, without the huge mandibles and dissolving the insides of the victim of poison they would be more difficult.




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