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Testing the level of ant activity associated with quorum sensing: an empirical approach leading to the establishment and test of a null-model. (English) Zbl 1407.92152

Summary: On the basis of experimental observations, this paper develops two well-defined mathematical models for the level of activity of Pharaoh’s ants (Monomorium pharaonis) within their nesting area, with the aim of providing a more general understanding of animal activity. Under specific conditions, we observe that the activity of ants within their nesting area appears to show no dependence on their density. Making the assumption that all ants move independently of one another, this behaviour can be mathematically modelled as a random process based on the binomial distribution. Developing the model on this basis allows an exponential distribution to be exposed that underlies the time-intervals between ants leaving the nesting area. Such a distribution is present, irrespective of whether the ant population in the nesting area remains constant or steadily depletes, and suggests that ant-ant interactions do not play any significant role in determining ant activity under the experimental conditions adopted. The mathematical framework presented plays the role of a null model that will have a wide range of applications for detecting other determinants of activity-level (not addressed in this study) including environmental and social factors such as food availability, temperature, humidity, presence of pheromone trails, along with intraspecific and interspecific interactions outside the nest and, indeed, more generally. The null model should have applications to a range of organisms. Lastly, we discuss our data in relation to a recent study of ants leaving their nest [T. O. Richardson et al., “Record dynamics in ants”, PLOS ONE 5, No. 3, Article ID e9621 (2010; doi:10.1371/journal.pone.0009621)] in which the null model was rejected in favour of record dynamics, where ant-ant interactions were conjectured to play a role.

MSC:

92D50 Animal behavior
62P10 Applications of statistics to biology and medical sciences; meta analysis

Software:

Matlab
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References:

[1] Adler, F. R.; Gordon, D. M., Information collection and spread by networks of patrolling ants, American Naturalist, 40, 373-400 (1992)
[2] Ame, J. M.; Rivault, C.; Deneubourg, J. L., Cockroach aggregation based on strain odour recognition, Animal Behaviour, 68, 793-801 (2004)
[3] Anderson, T. W.; Darling, D. A., Asymptotic theory of certain goodness of fit criteria based on stochastic processes, Annals of Mathematical Statistics, 23, 193-212 (1952) · Zbl 0048.11301
[4] Broom, M.; Nouvellet, P.; Bacon, J. P.; Waxman, D., Parameter-free testing of the shape of a probability distribution, Biosystems, 90, 509-515 (2007)
[5] Dornhaus, A.; Chittka, L., Information flow and regulation of foraging activity in bumble bees (Bombus spp.), Apidologie, 35, 183-192 (2004)
[6] Fourcassie, V.; Deneubourg, J. L., The dynamics of collective exploration and trail-formation in Monomorium pharaonis: experiments and model, Physiological Entomology, 19, 291-300 (1994)
[7] Fuqua, W. C.; Winans, S. C.; Greenberg, E. P., Quorum sensing in bacteria: the LuxR/LuxI family of cell density-responsive transcriptional regulators, Journal of Bacteriology, 176, 269-275 (1994)
[8] Gordon, D. M., The development of an ant colony’s foraging range, Animal Behaviour, 49, 649-659 (1995)
[9] Haigh, J., Probability Models (2002), Springer: Springer London · Zbl 1041.60002
[10] Hölldobler, B.; Wilson, E. O., The ants (1990), Harvard University Press: Harvard University Press Cambridge, MA
[11] Hogg, R. V.; Tanis, E. A., Probability and Statistical Inference (2006), Prentice: Prentice N.J
[12] Jackson, D. E.; Holcombe, M.; Ratnieks, F. L.W., Trail geometry gives polarity to ant foraging networks, Nature, 432, 907-909 (2004)
[13] Jeanson, R.; Rivault, C.; Deneubourg, J.-L.; Blanco, S.; Fournier, R.; Jost, C.; Theraulaz, G., Self-organized aggregation in cockroaches, Animal Behaviour, 69, 169-180 (2005)
[14] Kvam, P. H.; Vidakovic, B., Nonparametric Statistics with Applications to Science and Engineering (2007), Wiley: Wiley Hoboken, New Jersey · Zbl 1183.62207
[15] Lauzon-Guay, J. S.; Scheibling, R. E.; Barbeau, M. A., Formation and propagation of feeding fronts in benthic marine invertebrates: a modeling approach, Ecology, 89, 3150-3162 (2008)
[16] Lilliefors, H. W., On Kolmogorov-Smirnov test for exponential distribution with mean unknown, Journal of the American Statistical Association, 64, 387-389 (1969)
[17] Miller, M. B.; Bassler, B. L., Quorum sensing in bacteria, Annual Review of Microbiology, 55, 165-199 (2001)
[18] Nouvellet, P.; Bacon, J. P.; Waxman, D., Fundamental insights into the random movement of animals from a single distance-related statistic, American Naturalist, 174, 506-514 (2009)
[19] Parrish, J. K.; Edelstein-Keshet, L., Complexity, pattern, and evolutionary trade-offs in animal aggregation, Science, 284, 99-101 (1999)
[20] Pratt, S. C.; Mallon, E. B.; Sumpter, D. J.T.; Franks, N. R., Quorum sensing, recruitment, and collective decision-making during colony emigration by the ant Leptothorax albipennis, Behavioral Ecology and Sociobiology, 52, 117-127 (2002)
[21] Renshaw, E., Modelling Biological Populations in Space and Time (1993), CUP: CUP New York · Zbl 0779.92016
[22] Robinson, E. J.H.; Richardson, T. O.; Sendova-Franks, A. B.; Feinerman, O.; Franks, N. R., Radio tagging reveals the roles of corpulence, experience and social information in ant decision making, Behavioral Ecology and Sociobiology, 63, 627-636 (2009)
[23] Richardson, T. O.; Robinson, E. J.H.; Christensen, K.; Jensen, H. J.; Franks, N. R., Record dynamics in ants, PLoS ONE, 5, 3, e9621 (2010)
[24] Sibani, P.; Dall, J., Log-Poisson statistics and full aging in glassy systems, Europhysics Letters, 64, 8-14 (2003)
[25] Sudd, J. H., The foraging method of Pharaoh’s ant, Monomorium pharaonis (L.), Animal Behaviour, 8, 67-75 (1960)
[26] Seeley, T. D., The wisdom of the hive: The social physiology of honey bee colonies (1995), Harvard University Press: Harvard University Press Cambridge, MA
[27] Seeley, T. D.; Visscher, P. K.; Passino, K. M., Group decision making in honey bee swarms, American Scientist, 94, 220-229 (2006)
[28] The MathWorks Inc., 3 Apple Hill Dr., Natick, MA 01760. MATLAB R2009.; The MathWorks Inc., 3 Apple Hill Dr., Natick, MA 01760. MATLAB R2009.
[29] Visscher, P. K.; Seeley, T. D., Coordinating a group departure: who produces the piping signals on honeybee swarms?, Behavioral Ecology and Sociobiology, 61, 1615-1621 (2007)
[30] Wilson, E. O., Chemical communication among workers of the fire ant Solenopsis saevissima (Fr. Smith) 1. The organization of mass-foraging, Animal Behaviour, 10, 134-147 (1962)
[31] Wilson, E. O., The relation between caste ratios and division of labor in the ant genus Pheidole (Hymenoptera: Formicidae), Behavioral Ecology and Sociobiology, 16, 89-98 (1984)
[32] Whitlock, M. C., Combining probability from independent tests: the weighted Zmethod is superior to Fisher’s approach, Journal of Evolutionary Biology, 18, 1368-1373 (2005)
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