Supplementary material for “Predicting leadership using nutrient requirements and dominance rank of group members”by Cédric Sueur, Andrew J. J. MacIntosh, Armand T. Jacobs, Kunio Watanabe and Odile Petit
Details about semi-free ranging conditions of Tonkean and rhesus macaques
The two groups had complete access to approximately0.32 ha (maximal length = 80m; maximal width = 60m) of wooded parkland as well as indoor housing within the enclosure. The indoor housing (20 m²) was made of cement and tiling, and animals were able to climb on it. The enclosure consisted of various slopes and uneven ground. The distribution of vegetation was also heterogeneous, with three layers (grass, trees and bushes) being unevenly distributed throughout the enclosure. Within the park, animals moved cohesively (as a group or in sub-groups) (Sueur and Petit 2008; Sueur, Briard, et al. 2011). They used the park in a heterogeneous way according to ecological conditions (topology and vegetation; (Sueur et al. 2011). Despite the ad libitum provision of commercial primate pellets and water within the indoor housing, animals were observedto spend 36.3% of their time foraging and searching for food outside the indoor enclosure (see (Sueur, Salze, et al. 2011) for details). Fresh fruit and vegetables were provided at the same location once a week, one hour after the end of the observation session. Thus, the behaviour of the animals was unlikely to have been affected strongly by this event. Animals were habituatedto human presence within their enclosures.
Table S1: characteristics for each member of the Tonkean macaque group(Sueur et al. 2009; Sueur, Briard, et al. 2011)
Id / Body mass (kg) / Status* / Protein requirement (g.day-1) / Energy requirement (Kcal.day-1) / Water requirement (ml.day-1) / Dominance rank / Di (relative rank)Ga / 14.8 / Male / 37.57 / 1171.34 / 1171.34 / 1 / 0.18
Je / 12.7 / Female / 32.22 / 1004.66 / 1004.66 / 2 / 0.16
La / 9.6 / Female / 24.33 / 758.61 / 758.61 / 3 / 0.15
Ne / 9.4 / Pregnant female / 47.64 / 928.41 / 1485.46 / 4 / 0.13
Ol / 9.0 / Lactating female / 40.80 / 710.98 / 1421.96 / 5 / 0.11
Pa / 8.2 / Oestrus and then pregnant female / 41.53 / 809.36 / 1294.97 / 6 / 0.09
Sh / 7.0 / Subadult male / 17.71 / 552.24 / 552.24 / 7 / 0.07
Ta / 6.5 / Juvenile male / 16.44 / 512.56 / 512.56 / 8 / 0.05
Ul / 6.1 / Juvenile male / 15.42 / 480.81 / 480.81 / 9 / 0.04
Uj / 4.5 / Juvenile female / 11.35 / 353.81 / 353.81 / 10 / 0.02
*If unspecified, individuals are adults
Table S2: characteristics for each member of the rhesus macaque group(Sueur and Petit 2008; Sueur 2010)
Id / Body mass (kg) / Status* / Protein requirement (g.day-1) / Energy requirement (Kcal.day-1) / Water requirement (ml.day-1) / Dominance rank / Di (relative rank)Ro / 10.9 / Male / 27.64 / 861.79 / 861.79 / 1 / 0.125
Po / 10.3 / Male / 26.11 / 814.17 / 814.17 / 2 / 0.117
Pa / 7.9 / Lactating female / 40.00 / 1247.35 / 1247.35 / 3 / 0.108
Ve / 1.9 / Subadult female / 4.73 / 147.45 / 294.90 / 4 / 0.100
Ka / 8.5 / Female / 21.53 / 671.30 / 671.30 / 5 / 0.092
Ji / 7.6 / Pregnant female / 38.48 / 1199.73 / 1199.73 / 6 / 0.083
Ki / 10 / Female / 25.35 / 790.35 / 790.35 / 7 / 0.075
Co / 8 / Female / 20.26 / 631.61 / 631.61 / 8 / 0.067
Ma / 9.3 / Female / 23.57 / 734.79 / 734.79 / 9 / 0.058
Ba / 7.9 / Lactating female / 40.00 / 1247.35 / 1247.35 / 10 / 0.050
Or / 8.6 / Pregnant female / 43.57 / 1358.47 / 1358.47 / 11 / 0.042
Cl / 8 / Lactating female / 40.51 / 1263.23 / 1263.23 / 12 / 0.033
Ca / 3.5 / Female / 8.80 / 274.44 / 274.44 / 13 / 0.025
Li / 7.1 / Lactating female / 35.93 / 1120.36 / 560.18 / 14 / 0.017
Vo / 1.8 / Subadult female / 4.47 / 139.51 / 139.51 / 15 / 0.008
*If unspecified, individuals are adults
Table S3: characteristics for each member of the Japanese macaque group(MacIntosh et al. 2011; Jacobs et al. 2011).
Id / Body mass (kg, estimated) / Status* / Protein requirement (g.day-1) / Energy requirement (Kcal.day-1) / Water requirement (ml.day-1) / Dominance rank** / Di (relative rank)Um / 12.0 / Male / 30.44 / 949.10 / 949.10 / 1 / 0.057
Pi / 11.0 / Male / 27.89 / 869.73 / 869.73 / 2 / 0.054
Pu / 12.0 / Male / 30.44 / 949.10 / 949.10 / 3 / 0.051
Ya / 10.0 / Male / 25.35 / 790.35 / 790.35 / 4 / 0.048
Re / 9.0 / Lactating female / 34.20 / 1066.48 / 1066.48 / 1 / 0.057
Ci / 7.0 / Lactating female / 26.57 / 828.36 / 828.36 / 2 / 0.054
Le / 6.0 / Lactating female / 22.75 / 709.31 / 709.31 / 3 / 0.051
ReSA / 3.0 / Subadult female / 7.53 / 234.76 / 234.76 / 1.5 / 0.056
CiSA / 3.0 / Subadult female / 7.53 / 234.76 / 234.76 / 2.5 / 0.053
Pa / 8.0 / Pregnant female / 40.51 / 1263.23 / 1263.23 / 4 / 0.048
Ge / 6.0 / Lactating female / 22.75 / 709.31 / 709.31 / 5 / 0.045
Te / 7.0 / Lactating female / 26.57 / 828.36 / 828.36 / 6 / 0.042
PaSA / 3.0 / Subadult female / 7.53 / 234.76 / 234.76 / 4.5 / 0.047
Pe / 7.5 / Lactating female / 28.48 / 887.89 / 887.89 / 7 / 0.039
Ro / 7.0 / Female / 17.71 / 552.24 / 552.24 / 8 / 0.036
S04 / 3.0 / Subadult female / 7.53 / 234.76 / 234.76 / 8.5 / 0.035
Not / 8.0 / Lactating female / 40.51 / 1263.23 / 1263.23 / 9 / 0.033
Pg / 7.0 / Female / 17.71 / 552.24 / 552.24 / 10 / 0.030
TT / 5.0 / Female / 12.62 / 393.50 / 393.50 / 11 / 0.027
NotSA / 3.0 / Subadult female / 7.5289 / 234.7575 / 234.7575 / 11.5 / 0.026
Nom / 7.5 / Lactating female / 28.48 / 887.89 / 887.89 / 12 / 0.024
Sad / 7.5 / Lactating female / 28.48 / 887.89 / 887.89 / 13 / 0.021
Wh / 8 / Pregnant female / 40.51 / 1263.23 / 1263.23 / 14 / 0.018
Ch / 7.5 / Lactating female / 37.97 / 1183.85 / 1183.85 / 15 / 0.015
Mi / 7 / Female / 17.71 / 552.24 / 552.24 / 16 / 0.012
St / 7.5 / Lactating female / 28.48 / 887.89 / 887.89 / 17 / 0.009
Do / 6 / Lactating female / 22.75 / 709.31 / 709.31 / 18 / 0.006
StSA / 3.0 / Subadult female / 7.5289 / 234.7575 / 234.7575 / 19 / 0.003
Gi / 3.0 / Subadult female / 7.5289 / 234.7575 / 234.7575 / 19 / 0.003
*If unspecified, individuals are adults; ** For this group, the dominance hierarchy was calculated separately for males and females
Description of the model according to the ODD Protocol
This section describes the model according to ODD Protocol (i.e. Overview, Design concepts and Details) (Grimm et al. 2006, 2010). The model was developed in Netlogo 3.15 (Bryson et al. 2007; Sueur, Petit, et al. 2010). One time step in the simulation represents one minute.
1. Purpose
The purpose of the model is to assess how the interaction between dominance rank and nutrient requirements of group members results in a viable or unviable decision making system, and whetheror not leadership is biased toward one or several specific individuals. A decision making system is considered as viable in this study when all members can satisfy all of their needs and therefore survive indefinitely. We built a general model where individuals have to move between different areas of their environment to satisfy three different needs: water, protein and energy. Animals belong to different categories influencing their nutrient expenditures (table 1) or intakes (table 2).
2. Entities, state variables ans scales
The group environment is a two-dimensional environment of 96x96 connected cells. Each cell represents one meter. Each cell has four immediate neighbours and the sides of the arena are joined to form a torus. The environment is composed of four areas: one area for foraging for proteins, one area for foraging for energy, one water source, and one resting site (to which individuals return at night to sleep). The positions of the different areas were fixed within the model, but this does not affect results since variability among needs, i.e. which needs are the greatest and the smallest, is much greater between individuals and groups than between areas. To simplify the model and better understand the influence of the two main parameters on the emergence of leadership, there is no intra-group competition in this model,i.e. all individuals could occupy the same area, andthere is no depletion of requirementsat each foraging area.
According to the distribution of areas inside the torus, groups have a travel distance between two areas ranging from 25 to 75 metres. This range fits with travel distances in primate species of similar body mass and similar group size to those used as models in this study(Garber 1989; Isbell et al. 1999; Chapman and Chapman 2000; Noser and Byrne 2007; Sellers et al. 2007). Individuals have a walking speed of 0.4m.s-1.The time step is one minute.
Each individual in the mode has three needs. Each need (water, protein and energy) is linked to an internal reserve and depends on the body mass of individuals. Each of the three considered reserves is limited by a maximum level above which each group member cannot gain further reserves, and a minimum level at which each group member will die. We defined the need Nias . In this way, the need evolves between 1 (highest need, weakest reserve) and 0 (weakest need, highest reserve). Then we uniformed this parameter to fit with the range of dominance values (see 7.1.). According to data from macaques (Nakagawa 1989, 2009; National Research Council (U.S.). Committee on Animal Nutrition 2003; Sueur, Deneubourg, et al. 2010), the daily protein requirement is estimated at 2.54 g.day-1.kg-1, the daily energy requirement at 351.7 Kcal.day-1.kg-1, and the daily water requirement at 0.24 ml. KJ-1 (i.e., 20 ml.day-1.kg-1). Individual expenditure per need and activity is described in Table 1. Details of individual intake rate per need are shown in Table 2.
A relative dominance rank was implemented in the model. When individuals differ in dominance rank, the relative dominance rank of an individual was equal to its absolute rank divided by the sum of ranks.
As our main aim was to test the interaction between dominance rank and nutrient requirements of group members on the decision-making system, the only two individual characteristics in the model are the dominance rank and the body mass of individuals (influencing directly the three nutrient requirements). We also took into account for observed data (see Testing conditions in the main document) whether females were pregnant or lactating and therefore must adapt their needs to their respective reproductive state. The three needs are ranked in order of importance for animals: water, protein, energy (i.e., if the needs for water and protein are equal, drinking water is given priority, whatever the animal category).
Two assumptions are made: firstly, if there is an advantage to living in a social group, then group members should synchronize their activities in order to stay cohesive. Secondly, individuals do not know the requirements of their conspecifics (previous studies (Rands et al. 2008; Conradt et al. 2009; Sueur, Deneubourg, et al. 2010) showed that such an ability may not be necessary for effective group coordination).
3. Process overview and scheduling
We used a state-dependent dynamic model (Rands et al. 2004) to determine how the interaction between dominance rank and nutrient requirements affect the viability of a decision making system and the distribution of initiations (from distributed to personal leadership) in a group (Simpson et al. 2004; Raubenheimer et al. 2009).
At each time-step, each reserve of every individual decreases (i.e. expenditure, table 1) depending on the individual category and the current activity. In order to complete this reserve, the individual has to carry out the corresponding activity (i.e. intake, table 2). This gain may be accomplished by initiating a movement towards one specific area or by joining a movement to one specific area. Optimal foraging decisions were implemented in the model: when an individual decides to forage, it will therefore forage until its personal reserves have been replenished. If two reserves are almost similar, this implementation allows the individuals to not make to some round-trips between the two corresponding areas and expend reserves instead of fulfil them.
When individuals need water, protein or energy, they have to move toward the respective area. When the group is taking part in one of the three specific activities (eating protein, eating a source of energy, or drinking water), each individual gains a certain amount of the requirement. Reserves are also depleted during the night (from step 720 to step 1440). A simulation stops when any one reserve in one individual reaches 0, or after 90 days. A previous study showed that 90 days is largely enough to assess whether a decision-making system is viable or not (i.e. the maximum number of days we observed in previous studies for the non viability of decision-making system was about 10 days;(Sueur, Deneubourg, et al. 2010; Sueur 2012).
The probability to initiate a movement at time t for individual i will depend on both its dominance rank and its greatestof the 3 needs.
Pi = WD* Di + WN * Ni + WR*R
where Pi is the probability that the individual will initiate a movement, WD and WN are the respective weights of dominance and need in the probability to initiate. WR is a weight for randomness R (and R =1). 0 < WD,WN, WR < 1 and WD + WN +WR= 1. These weights are set by the modeller. Niis the highest need (between water, protein and energy) for individual i at time t and 0 < Ni < 1. Diis the relative dominance rank of individual isuch that where S is the group size. The model is stochastic so thatat each time step in the model, a number between 0 and 1 is randomly attributed to each agent.When this number is lower than the theoretical probability Pi, the individual decides for the entire group to changethe group’s activity by initiating a movement to satisfy its respective requirement (and then all the group moves and follows this individual to keep cohesion). Where this number is higher than the theoretical probability, on the other hand, the agent does not decide for the entire group. The higher the dominance rank and the needs of an individual, the more it will initiate movements and emerge as a leader. In the next step, when the need of the previous initiator is satisfied, a new initiator will emerge and make a decision for the whole group.
4. Design concepts
Emergence: The first output of the model is the viability of a decision-making system, i.e. whether it results in the survival of all individuals in the group (over a period of 90 days, considered as viable) or to the death of an individual (the system is not viable). Then, we observed the emergence of leadership and assessed whether the leadership was biased (personal leadership) or not (distributed leadership) according to the dominance hierarchy and the nutrient requirements of group members.
Adaptation: We measure whetherindividual differences in dominance rank and nutrient requirements, as well as their interaction (no correlation, negatively, or positively correlated), result in the survival of all individuals within the group or not, and how these factors affect the distribution of initiations.
Sensing: Each individual has three needs to satisfy. Each need level ranges from 0 to 1, and one individual decides which need level is high enough to motivate its decision to move and carry out an activity. When a reserve is at its maximum, the equivalent need level equals 0. When a reserve is close to its minimum, the equivalent need level is close to 1. Each reserve changes according to the expenditure and intake of each group member.
Interaction: Group members have to decide collectively about their activities and in which areas to carry out these activities. These consensus decisions and the identity of the individualsthat initiate movements (and will thus at the end of the simulation be the leader) depend on dominance rank, the needs of each group member, and the interaction between these two variables.
Stochasticity: Intake and expenditure of each requirement have a certain stochasticity expressed by the standard deviation (±SD) in tables 1 and 2. At each time step, the value of intake and expenditure are randomly chosen following a normal distribution. The process of choosing a leader is also stochastic.
Collectives: Collectives are represented as social groups of primates. Collectives occur as phenomena emerging from the individual characteristics (i.e. the dominance rank and the body mass) and behaviour (i.e. decisions) of individuals.
Observation: We observed the outcome of the decision-making system (i.e. the survival of all individuals or the death of one of them) for each tested combination. We then calculated the distribution of initiations between group members. For Observed data (see testing conditions in the main document), the simulated distribution of initiations was compared to the observed distribution for each studied group.
5. Initialisation
At the start of a simulation, individuals are situated at the same distance from each area (i.e. middle of the torus). According to the different conditions (nature of the interaction between dominance hierarchy, body mass, and weight of influence of each variable), individuals make a consensus decision to carry out a specific activity according to their requirements and then move to the area in which they can carry out this activity and hence satisfy their needs.
6. Input
The model uses the file “attributes.txt” including Id, bodymass and nutrient requirements of individuals and the file “links.txt” including links between individuals (i.e., social network, not used for this study).
References
Bryson JJ, Ando Y, Lehmann H (2007) Agent-based modelling as scientific method: a case study analysing primate social behaviour. Philosophical Transactions of the Royal Society B: Biological Sciences 362:1685 –1699
Chapman CA, Chapman LJ (2000) Interdemic Variation in Mixed-Species Association Patterns: Common Diurnal Primates of Kibale National Park, Uganda. Behavioral Ecology and Sociobiology 47:129–139
Conradt L, Krause J, Couzin ID, Roper TJ (2009) “Leading according to need” in self-organizing groups. Am. Nat 173:304–312
Garber PA (1989) Role of spatial memory in primate foraging patterns: Saguinus mystax and Saguinus fuscicollis. American Journal of Primatology 19:203–216
Grimm V, Berger U, Bastiansen F, Eliassen S, Ginot V, Giske J, Goss-Custard J, Grand T, Heinz SK, Huse G, Huth A, Jepsen JU, Jørgensen C, Mooij WM, Müller B, Pe’er G, Piou C, Railsback SF, Robbins AM, Robbins MM, Rossmanith E, Rüger N, Strand E, Souissi S, Stillman RA, Vabø R, Visser U, DeAngelis DL (2006) A standard protocol for describing individual-based and agent-based models. Ecological Modelling 198:115–126
Grimm V, Berger U, DeAngelis DL, Polhill JG, Giske J, Railsback SF (2010) The ODD protocol: A review and first update. Ecological Modelling 221:2760–2768
Isbell LA, Pruetz JD, Nzuma BM, Young TP (1999) Comparing measures of travel distances in primates: Methodological considerations and socioecological implications. American Journal of Primatology 48:87–98
Jacobs A, Watanabe K, Petit O (2011) Social Structure Affects Initiations of Group Movements but Not Recruitment Success in Japanese Macaques (Macaca fuscata). International Journal of Primatology 32:1311–1324
MacIntosh AJJ, Alados CL, Huffman MA (2011) Fractal analysis of behaviour in a wild primate: behavioural complexity in health and disease. Journal of The Royal Society Interface
Nakagawa N (1989) Bioenergetics of Japanese monkeys (Macaca fuscata) on Kinkazan Island during winter. Primates 30:441–460
Nakagawa N (2009) Feeding rate as valuable information in primate feeding ecology. Primates 50:131–141
National Research Council (U.S.). Committee on Animal Nutrition (2003) Nutrient requirements of nonhuman primates. National Academies Press.
Noser R, Byrne RW (2007) Travel routes and planning of visits to out-of-sight resources in wild chacma baboons, Papio ursinus. Animal Behaviour 73:257–266
Rands S, Cowlishaw G, Pettifor R, Rowcliffe JM, Johnstone R (2008) The emergence of leaders and followers in foraging pairs when the qualities of individuals differ. BMC Evolutionary Biology 8:51
Rands SA, Pettifor RA, Rowcliffe JM, Cowlishaw G (2004) State–dependent foraging rules for social animals in selfish herds. Proceedings of the Royal Society of London. Series B: Biological Sciences 271:2613–2620
Raubenheimer D, Simpson SJ, Mayntz D (2009) Nutrition, ecology and nutritional ecology: toward an integrated framework. Functional Ecology 23:4–16
Sellers W., Hill R., Logan B. (2007) An agent-based model of group decision making in baboons. Philos Trans R Soc Lond B Biol Sci 362:1699–1710
Simpson SJ, Sibly RM, Lee KP, Behmer ST, Raubenheimer D (2004) Optimal foraging when regulating intake of multiple nutrients. Animal Behaviour 68:1299–1311
Sueur C (2010) Influence Des Relations Sociales Sur Les Prises de Dcisions. Editions.
Sueur C (2012) Viability of decision-making systems in human and animal groups. Journal of Theoretical Biology 306:93–103
Sueur C, Briard L, Petit O (2011) Individual Analyses of Lévy Walk in Semi-Free Ranging Tonkean Macaques (Macaca tonkeana). PLoS ONE 6:e26788
Sueur C, Deneubourg J-L, Petit O, Couzin ID (2010) Differences in Nutrient Requirements Imply a Non-Linear Emergence of Leaders in Animal Groups. PLoS Comput Biol 6:e1000917
Sueur C, Petit O (2008) Shared or unshared consensus decision in macaques? Behavioral Processes 78:84–92
Sueur C, Petit O, Deneubourg J (2009) Selective mimetism at departure in collective movements of Macaca tonkeana: an experimental and theoretical approach. Animal Behaviour 78:1087–1095
Sueur C, Petit O, Deneubourg J (2010) Short-term group fission processes in macaques: a social networking approach. J Exp Biol 213:1338–1346
Sueur C, Salze P, Weber C, Petit O (2011) Land use in semi-free ranging Tonkean macaques Macaca tonkeana depends on environmental conditions: A geo-graphical information system approach. Current Zoology 57:8–17