A.B. Sendova-Franks

Anderson

E.J.H. Robinson

H.J. Jensen

J.H. Jensen

Jackson

K. Christensen

Kleinbaum

N.R Franks

Nouvellet

Richardson

Sendova-Franks

Sibani

T.O. Richardson

Whitlock

Richardson, T. O.

Christensen, K.

Jensen, Henrik J.

Franks, Nigel R.

Sendova-Franks, Ana B.

Robinson, E. J.H.

UWE Bristol Research Repository

Comment on P. Nouvellet, J.P. Bacon, D. Waxman, "Testing the level of ant activity associated with quorum sensing: An empirical approach leading to the establishment and test of a null-model"

Richardson, Thomas O.

Robinson, Elva Joan Hilda

Christensen, Kim

White Rose Research Online

This is a repository copy of Comment on P. Nouvellet, J.P. Bacon, D. Waxman, "Testing the level of ant activity associated with quorum sensing: An empirical approach leading to the establishment and test of a null-model.”.White Rose Research Online URL for this paper:https://eprints.whiterose.ac.uk/46219/Version: Published VersionArticle:Richardson, Thomas O., Robinson, Elva Joan Hilda orcid.org/0000-0003-4914-9327, Christensen, Kim et al. (3 more authors) (2011) Comment on P. Nouvellet, J.P. Bacon, D. Waxman, "Testing the level of ant activity associated with quorum sensing: An empirical approach leading to the establishment and test of a null-model.”. Journal of Theoretical Biology. pp. 356-358. ISSN 1943-5193 https://doi.org/10.1016/j.jtbi.2010.11.004eprints@whiterose.ac.ukhttps://eprints.whiterose.ac.uk/Reuse Items deposited in White Rose Research Online are protected by copyright, with all rights reserved unless indicated otherwise. They may be downloaded and/or printed for private study, or other acts as permitted by national copyright laws. The publisher or other rights holders may allow further reproduction and re-use of the full text version. This is indicated by the licence information on the White Rose Research Online record for the item. Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. Letter to EditorComment on P. Nouvellet, J.P. Bacon, D. Waxman, ‘‘Testing thelevel of ant activity associated with quorum sensing: Anempirical approach leading to the establishment and test of anull-model’’Nouvellet et al. (2010) report the results from two experimentswith the Pharaoh’s ant, Monomorium pharaonis and test a nullmodel. Their experimental set-up consists of a nest in an arenawitha G-shaped object (like a hangman’s scaffold) placed close to thenest. The distal end of the G-object is vertical and slippery so thatants that reach it fall off. In the first experiment, ‘with replacement’,ants fall directly back into the arena. In the second experiment,‘without replacement’, a container is placed under the far end of theG-object so that ants that have fallen from it are unable to go backto the arena. Each of the two experiments was repeated with4 different ant colonies and the data reported covers about 1.5 h.Their null model has two versions corresponding to the twoexperiments. Both versions assume that ants move independently(i.e. do not interact) anddrop randomly from the scaffold. However,the second model takes into account the diminishing number ofants that have the opportunity to climb theG-object. There is closeagreement between the results from each of the two experimentsand the respective version of the null model. For the experiment‘with replacement’, the accumulated number of ants that havedropped increases linearly with time and the time intervalsbetween drops are exponentially distributed. This is compatiblewith amodel of independent Poissonian agents. For the experiment‘without replacement’, the increase in the accumulated number ofants that have dropped slows down with time, the time intervalsbetweendrops increasewith time and their distribution is differentfrom exponential. However, when the time intervals betweendrops are scaled by their expected values, they are well fitted byan exponential distribution. This is compatible with a model ofindependent Poissonian agents where their diminishing number(finite-size effect) is taken into account.Nouvellet et al. (2010) compare and contrast their results withthose in Richardson et al. (2010a).We reported the results fromoneexperimental and one control treatment on colonies of the antTemnothorax albipennis aswell as a nullmodel very similar to theirs(Richardson et al., 2010a). In the experimental treatment, weremoved every ant as it exited the nest in 13 colonies over periodsranging from 2 to 200 h. In the control treatment, we recorded thetimespreviously unseen, ‘newants’ leave thenest in 7 colonies overa period of 60 h. We found that in both cases the event ratesdecreased rapidly over time. This rapid decay was compatibleneither with classical exponential decay (homogeneous Poissonprocess) nor with a heterogeneous Poisson process. The latter nullmodel was based on experimental results of individual antheterogeneity and also included the effect of a declining numberof ants remaining in the nest, i.e. a finite-size effect (Richardsonet al., 2010a). We tested the hypothesis that such exits followrecorddynamics (Sibani and Littlewood, 1993). In recorddynamics,events are triggered when a fluctuating, record, signal exceeds ahistorical ‘high water mark’. While exponential decay is charac-terised by Poisson statistics in linear time, record dynamics arecharacterised by Poisson statistics in logarithmic time (Sibani andLittlewood, 1993; Anderson et al., 2004). Our results demonstratethat under both experimental conditions the process of ants exitingtheir nests is compatible with a record dynamics process(Richardson et al., 2010a). Systems exhibiting record dynamicsare charactrerised by strong interactions, non-stationarity andnon-exponential deceleration over time.Now we will comment specifically on that part of the paperby Nouvellet et al. (2010) where they compare and contrasttheir result that ants do not interact with our result that ants dointeract.(1) Nouvellet et al. (2010) state that their experiments arecomparable to our experiments, see e.g. section 8, 1st paragraph.We strongly disagree. We measure the exit times of all antsleaving the nest. Nouvellet et al. (2010) measure the time ants fallfrom the tip of the scaffold placed in an arena. Hence, the latterstudy concerns the activity of ants that have already left their nestand subsequently happen to reach the particular point in the arenawith the G-shaped object, choose to climb it, reach its tip and fallfrom it. The ants in our experiments and the ants in the experi-ments by Nouvellet et al. (2010) make their decisions in twodifferent environments: inside and outside the nest, respectively.These two environments differ according to both direct andindirect ant–ant interactions. For example, the colony inside thenest has a resilient social and spatial structure (Sendova-Franks andFranks, 1994). This affects direct interactions. The nest interior isassociated with particular diffusion patterns of airborne phero-mones and gases (Cox and Blanchard, 2000). This affects indirectinteractions. For these reasons alone our experiments are notcomparable. Furthermore, the set-up in the experiments byNouvellet et al. (2010) is artificial because they have not takeninto account indirect interactions outside the nest. Likemany otherant species, Pharaoh’s ants rely heavily on indirect interactions viapheromone trails outside the nest and lay these trails duringexploration (Jackson et al., 2006). Hence ants could also be usingthe density of pheromone trails to assess local density. These trailslast for several days, so over the course of the experimentsContents lists available at ScienceDirectjournal homepage: www.elsevier.com/locate/yjtbiJournal of Theoretical Biology0022-5193/$ - see front matter & 2010 Elsevier Ltd. All rights reserved.doi:10.1016/j.jtbi.2010.11.004Journal of Theoretical Biology 269 (2011) 356–358described (approximately 100 min) the density information fromthis source would not be expected to change. Therefore, one mightpredict that the two treatments would not differ according toindirect interactions.(2) Nouvellet et al. (2010) attempt to discredit our conclusion oflog-Poisson statistics for exit time in our experiments, see e.g.section 9, 4th paragraph and Appendix C. They argue that they arenot convinced by our conclusions because:(2a) Nouvellet et al. (2010) show that the data from their first,‘without replancement’ experiment do not follow a log-Poissionprocess by noting that the number of ’’ants leaving their nest’’(falling from the G-shaped object) is not what is expected from alog-Poisson process (Fig. 10).We agree that the data from the experiments by Nouvellet et al.(2010) are not compatiblewith a log-Poisson process. However, westrongly disagree with their assumption that our experiments arecomparable with their experiments. Hence their argument thatbecause they do not find compatibility with a log-Poisson process,we should not find it either, is invalid.(2b) Nouvellet et al. (2010) compare our Fig. 3 (Richardson et al.,2010a) with their Fig. 11a (Survivorship versus ln(Tk/Tk1)) andour Fig. 4 (Richardson et al., 2010a) with their Fig. 11b (No. antsleaving versus ln(t)). Their argument is that by visual inspectionthe compared figures seem similar. Hence, they are arguingthat even for data they have shown to follow a Poissonprocess, just by applying our plots, they could get a visualimpression of a log-Poisson process, indicating this has happenedin our case.We strongly disagree. First, Fig. 11a was not plotted correctly inthe online version of the paper. The y-axis had to be logged and thex-axis inverted. Even after these corrections were made in thepublished version of the paper, the survivorship plot is far from astraight line (as it must be for a log-Poisson process) and based ononly a third of the scale for ln(Tk/Tk1) in our Fig. 3 (Richardsonet al., 2010a). Second, Fig. 11b uses ln (natural logarithm) ratherthan logarithm base 10 as we do in Fig. 4 (Richardson et al., 2010a).This makes the region with a supposedly straight line in Fig. 11bappear larger. A close inspection, however, reveals that it is only0.2–0.4 of an order of magnitude compared to the 3 orders ofmagnitude in our Fig. 4 (Richardson et al., 2010a). Neither of theplots in Fig. 11 provides evidence for a log-Poisson process. Hence,the argument by Nouvellet et al. (2010) that their data, whichfollows a Poisson process, looks similar to our data when plotted assurvivorship versus ln(Tk/Tk1) and number of ants leaving versusln(t) is invalid.(2c) Nouvellet et al. (2010) examine our results in Table S1(Richardson et al., 2010a) and conclude that 5 of the 13 colonieswhich underwent the treatment condition (38%) and 3 of the 7colonies that underwent the control condition (42%) showevidenceto reject the log-Poisson process (Appendix C).We strongly disagree. The Anderson–Darling test we used doesnot compare our data for the survivorship of the log times in Fig. 3and Table S1 (Richardson et al., 2010a) with an exponentialdistribution. Instead it tests whether the residuals from the linearregression models fitted to the data in Fig. 3 are compatible with anormal distribution. Not onlywere any deviations very small in themajority of cases but it is well known that linear regression isrobust to small deviations from normality (Kleinbaum et al., 2008,p. 48). Such deviationswould disappear hadwe used themuch lesssensitive Kolmogorov–Smirnov test applied several times byNouvellet et al. (2010) in their study. Hence their argument thatour statistical results reported in Table S1 show evidence to rejectthe log-Poisson process is invalid.(2d) Nouvellet et al. (2010) also carry out a meta-analysis of allp-values from the Anderson–Darling tests for the 13 treatment andthe 7 control colonies separately, using the weighted Z-method(Whitlock, 2005). They conclude that the overall p-value associatedwith the null hypothesis that the distribution of exit times is log-Poisson process is po0.001 in both cases (Appendix C).We strongly disagree. First, as pointed out above, these p-valuesrelate to the compatibility of residuals from linear regressionmodels with the normal distribution. Second, the meta-analysistests the null hypothesis that all p-values should be uniformlydistributed between 0 and 1 rather than give an overall p-value(Whitlock, 2005). To illustrate this point we carried out meta-analysis tests on data from Nouvellet et al. (2010). This is not tointimate that we doubt their claim that the results from their ownstudy are compatible with a Poisson process. Rather we wish todemonstrate that themeta-analysis is a heterogeneity test becausethe null hypothesis could be rejected even when the p-values ofindividual tests are greater than 0.05 as in Nouvellet et al. (2010).When the weighted Z-method for meta-analysis (Whitlock, 2005)is applied to the p-values for the 4 Anderson–Darling tests for theirfirst experiment, ‘with replacement’ (Tables 1 and 2), the p-value isless than 0.05. We used the p-value for the first colony p¼0.113weighted by the number of observations, N¼585 (section 3, thirdparagraph, Nouvellet et al., 2010) and the p-values 0.1, 0.08 and 0.4weighted by the respective estimated number of the ants in thenesting area, Ne, namely 500, 300 and 100 (Table 2, Nouvellet et al.,2010). The result for such a weighted Z-method is Zw¼2.16,p¼0.015, one-tailed (Whitlock, 2005). We also applied Stouffer’smethod: Zs¼2.08, p¼0.019, one-tailed and Fisher’s combinedprobability test: w2F¼15.85, df¼8, po0.05 (Whitlock, 2005). Inother words, if we take the p-value in each of these three methodsto represent an overall p-value,wewould reject the null hypothesisthat the data for the first ‘with replacement’ experiment inNouvellet et al. (2010) is compatible with a Poisson process. Thiswould not make sense because none of the individual p-values isless than 0.05. However, if we correctly interpret themeta-analysisas a test of heterogeneity, the results are not surprising because thep-values for the Anderson–Darling test for the first experiment,‘with replacement’ in Nouvellet et al. (2010) are heterogeneous.The meta-analysis is sensitive to this heterogeneity even though itinvolves only 4 colonies compared to our sample sizes of 13 and 7colonies. For this reason, their meta-analysis of our data ismisplaced and their argument that our statistical results reportedin Table S1 show evidence to reject the log-Poisson process isinvalid.Finally, we note that data from new experiments and analysesbased on per-capita statistics, which thus control for finite-sizeeffects (Richardson et al., 2010b) are also consistent with recorddynamics, that is, log-Poisson statistics. However, for colonieswitha manipulated demographic structure, and hence by proxy alsomanipulated interaction structure, the data are consistent withPoisson, rather than log-Poisson, statistics (Richardson et al.,2010b). This is further evidence that our conclusion of recordstatistics originating from ant–ant interactions is sound.In summary, the claim by Nouvellet et al. (2010) that theirresults are comparable to those obtained by Richardson et al.(2010a) is invalid because the experiments in the two studieswere carried out in two different environments, outside and insidethe nest, respectively. Ant–ant interactions in these two environ-ments differ but also the experimental design in Nouvellet et al.(2010) does not take into account indirect ant–ant interactions.Furthermore, the plot of their data in the format of our data, evenafter correction, shows no evidence of log-Poisson statistics. Theirmeta-analysis of the p-values in our study is misguided andincorrectly applied. Our null model (Richardson et al., 2010a),which includes the finite-size effect of the declining colony size andis therefore a numerical version of the analytical null model ofNouvellet et al (2010), shows that log-Poisson statistics cannot beobtained from a heterogeneous Poisson process with a finiteLetter to Editor / Journal of Theoretical Biology 269 (2011) 356–358 357number of components. For all these reasons, each and everyargumentNouvellet et al. (2010)make against our results is invalid.In our experiments ant exits are compatible with a log-Poissonprocess.Nouvellet et al. (2010) have set up an experiment using ahangman’s scaffold thatminimises the ants’ ability to interact withone another. They then conclude that in this regime ants do notinteract. This is analogous to an ichthyologist who uses dynamitefor fishing and then concludes that fish do not swim. BenjaminFranklin once said (in the Continental Congress just before signingthe Declaration of Independence, 1776) ‘‘Wemust, indeed, all hangtogether, or most assuredly, we shall all hang separately.’’ In theexperiments of Nouvellet et al. (2010) the ants may indeed hangseparately but their criticisms of our work simply do not hangtogether.ReferencesAnderson, P.E., Jensen, H.J., Oliveira, L.P., Sibani, P., 2004. Evolution in complexsystems. Complexity 10, 49–56.Cox, M.D., Blanchard, G.B., 2000. Gaseous templates in ant nests. J. Theor. Biol. 204,223–238.Jackson, D.E., Martin, S.J., Holcombe, M., Ratnieks, F.L.W., 2006. Longevity anddetection of persistent foraging trails in Pharaoh’s ants,Monomorium pharaonis.Anim. Behav. 71, 351–359.Kleinbaum, D.G., Kupper, L.L., Muller, K.E., 2008. Applied Regression Analysis andOther Multivariable Methods 4th edition Thomson Brooks/Cole, Belmont, CA,USA.Nouvellet, P., Bacon, J.P., Waxman, D., 2010. Testing the level of ant activityassociated with quorum sensing: an empirical approach leading to the estab-lishment and test of a null-model. J. Theor. Biol. 266, 573–583.Richardson, T.O., Robinson, E.J.H., Christensen, K., Jensen, J.H, Franks, N.R., Sendova-Franks, A.B., 2010a. Record dynamics in ants. PLoS One 5, e9621.Richardson, T.O.,Christensen, K., Franks, N.R., Jensen, H.J., Sendova-Franks, A.B.2010b Group dynamics and record signals in the ant Temnothorax albipennis.(available online) J. Roy. Soc. Interface (doi: 10.1098/rsif.2010.0286).Sendova-Franks, A.B., Franks, N.R., 1994. Social resilience in individual workerants and its role in the division of labour. Proc. R. Soc. London B 256,305–309.Sibani, P., Littlewood, P.B., 1993. Slow dynamics from noise adaptation. Phys. Rev.Lett. 71, 1482–1485.Whitlock, M.C., 2005. Combining probability from independent tests: theweighted Z-method is superior to Fisher’s approach. J. Evol. Biol. 18,1368–1373.T.O. RichardsonDepartment of Engineering Design and Mathematics, University of theWest of England, Coldharbour Lane, Bristol BS16 1QY, UKSchool of Biological Sciences, University of Bristol, Woodland Road,Bristol BS8 1UG, UKE.J.H. RobinsonDepartment of Biology and York Centre for Complex Systems Analysis,University of York, Heslington,York YO10 5DD, UKK. Christensen, J.H. JensenInstitute for Mathematical Sciences, Imperial College London, 53Prince’s Gate, Exhibition Road, South Kensington Campus,London SW7 2PG, UKK. ChristensenDepartment of Physics, Blackett Laboratory, Imperial College London,Prince Consort Road, London SW7 2AZ, UKH.J. JensenDepartment of Mathematics, Imperial College London,South Kensington Campus, London SW7 2AZ, UKN.R FranksSchool of Biological Sciences, University of Bristol, Woodland Road,Bristol, BS8 1UG, UKA.B. Sendova-Franks nDepartment of Engineering Design and Mathematics, University of theWest of England, Coldharbour Lane, Bristol BS16 1QY, UKE-mail address: ana.sendova-franks@uwe.ac.ukReceived 30 August 20102 November 20102 November 2010n Corresponding author.Letter to Editor / Journal of Theoretical Biology 269 (2011) 356–358358

Comment on P. Nouvellet, J.P. Bacon, D. Waxman, "Testing the level of ant activity associated with quorum sensing: An empirical approach leading to the establishment and test of a null-model.”

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Comment on P. Nouvellet, J.P. Bacon, D. Waxman, “Testing the level of ant activity associated with quorum sensing: An empirical approach leading to the establishment and test of a null-model”

Comment on P. Nouvellet, J.P. Bacon, D. Waxman, "Testing the level of ant activity associated with quorum sensing: An empirical approach leading to the establishment and test of a null-model.”

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