We survey a variety of experimental paradigms for studying animal abilities to count, to understand numerical information and to perform simple arithmetic operations. There is a huge body of evidence that different forms and elements of quantitative judgement and numerical competence are spread across a wide range of species, both vertebrate and invertebrate. Here we pay particular attention to the display of numerical competence in ants. The reason is that most of the existing experimental schemes for studying numerical processing in animals, although often elegant, are restricted by studying subjects at the individual level, or by the use of artificial communicative systems. In contrast, the information-theoretic approach that was elaborated for studying number-related skills in ants employs their own communicative means and, thus, does not require the subjects to solve any artificial learning problems, such as learning intermediary languages, or even learning to solve multiple choice problems. Using this approach, it was discovered that members of highly social ant species possessed numerical competence. They were shown to be able to pass information about numbers and to perform simple arithmetic operations with small numbers. We suggest that applying ideas of information theory and using the natural communication systems of highly social animals can open new horizons in studying numerical cognition.

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We simulated the situation of risky hunting in the striped field mouse Apodemus agrarius in order to examine whether these animals are able to make a choice between small and large quantities of live prey (ants). In the first (preliminary) experiment we investigated to what extent mice were interested in ants as a live prey and how their hunting activity depended on the quantity of these edible but rather aggressive insects. We placed mice one by one into arenas together with ant groups of different quantities, from 10 to 60. Surprisingly, animals, both wild-caught and laboratory-reared, displayed rather skilled predatory attacks: mice killed and ate from 0.37 ± 003 to 4 ± 0.5 ants per minute. However, there was a threshold number of ants in the arenas when rodents expressed signs of discomfort and started to panic, likely because ants bit them. This threshold corresponds to the dynamic density (about 400 individuals per m2 per min) in the vicinity of anthills and ants' routes in natural environment. In the second experiment mice had to choose between different quantities of ants placed in two transparent tunnels. Ants here served both as food items and as a source of danger. As far as we know, this is the first experimental paradigm based on evaluation of quantity judgments in the context of risk/reward decision making where the animals face a trade-off between the hedonistic value of the prey and the danger it presents. We found that when mice have to choose between 5 vs. 15, 5 vs. 30, and 10 vs. 30 ants, they always tend to prefer the smaller quantity, thus displaying the capacity for distinguishing more from less in order to ensure comfortable hunting. The results of this study are ecologically relevant as they reflect situations and challenges faced by free-living small rodents.

1. Red wood ants are among the most numerous generalist predators and strongly affect the composition of arthropod communities in forest ecosystems. However, their trophic position remains poorly understood. Stable isotope analysis was applied to study the trophic position of Formica aquilonia and reveal seasonal changes in its trophic links with both myrmecophilous aphids and other invertebrates in a mixed forest of western Siberia.2. The δ15N values of F. aquilonia exceeded those of herbivores and aphids by approximately 3.5‰. Despite obligate trophobiotic relationships with aphids, F. aquilonia occupied the trophic position of first‐order predator. The higher content of 13C in the worker ants, compared with members of grazing food chains, was explained by their consumption of 13C‐enriched aphid honeydew.3. Myrmecophilous tree‐dwelling aphids were enriched in 13C and 15N relative to grass‐inhabiting species, and the honeydew of tree‐dwelling aphids had higher δ13C values than those of the honeydew of grass‐inhabiting aphids.4. The decrease in δ13C values of the worker ants from spring and summer to autumn apparently reflected the transition from the collection of tree sap and feeding on the aphid honeydew from trees with high 13C content in the spring and early summer to a more diverse liquid diet in late summer, which included 13C‐depleted honeydew of aphids from herbs.5. The prevalence of the 15N‐depleted aphid honeydew in the ants' diet in the second half of the summer is discussed as one possible explanation for the seasonal decline in δ15N values of the worker ants.

Kolmogorov complexity furnishes many useful tools for studying different natural processes that can be expressed using sequences of symbols from a finite alphabet (texts), such as genetic texts, literary and music texts, animal communications, etc. Although Kolmogorov complexity is not algorithmically computable, in a certain sense it can be estimated by means of data compressors. Here we suggest a method of analysis of sequences based on ideas of Kolmogorov complexity and mathematical statistics, and apply this method to biological (ethological) "texts." A distinction of the suggested method from other approaches to the analysis of sequential data by means of Kolmogorov complexity is that it belongs to the framework of mathematical statistics, more specifically, that of hypothesis testing. This makes it a promising candidate for being included in the toolbox of standard biological methods of analysis of different natural texts, from DNA sequences to animal behavioural patterns (ethological "texts"). Two examples of analysis of ethological texts are considered in this paper. Theses examples show that the proposed method is a useful tool for

In this review we integrate results of long term experimental study on ant "language" and intelligence which were fully based on fundamental ideas of Information Theory, such as the Shannon entropy, the Kolmogorov complexity, and the Shannon's equation connecting the length of a message (l) and its frequency (p), i.e., l = − log p for rational communication systems. This approach enabled us to obtain the following important results on ants' communication and intelligence: (i) to reveal "distant homing" in ants, that is, their ability to transfer information about remote events; (ii) to estimate the rate of information transmission; (iii) to reveal that ants are able to grasp regularities and to use them for "compression" of information; (iv) to reveal that ants are able to transfer to each other the information about the number of objects; (v) to discover that ants can add and subtract small numbers. The obtained results show that information theory is not only excellent mathematical theory, but many of its results may be considered as Nature laws.

Abstract-Behavioral mechanisms regulating the competitive relations between the red wood ant Formica aquilonia and the ground beetles Carabus regalis, Pterostichus melanarius, P. magus, P. oblongopunctatus, Harpalus smaragdinus, and Amara nitida were studied by artificially initiated collisions between living insects as well as with the use of imitation models. Members of different functional groups within an ant family (aphid-milkers, hunters, and guards) behaved differently towards beetles. Active ants were shown to respond selectively to different features of the possible competitors, such as coloration, the presence of "appendages" (legs, antennae), body symmetry, rate of movement, and scent. Field and laboratory experiments demonstrated the ability of beetles to avoid collisions with active ants. The scent of anthill material attracted ground beetles, which consumed dead ants. The gained individual experience may allow the beetles to use supplementary forage resources in the territories controlled by ants. The flexible tactical patterns facilitate spatial segregation of ground beetles and ants in the same territory and result in a more complete utilization of food resources.

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