The study was conducted in and near the Calakmul Biosphere Reserve (CBR), located in the south-central Yucatan Peninsula of Mexico (18°07′21″N, 89°47′00″W). Elevations in the CBR range from 260 to 385 m. The climate is tropical with mean annual temperatures fluctuating between 22 and 26 °C. Annual rainfall is highly variable, but generally ranges between 900 and 2000 mm. Each year includes two distinct seasons: the wet season (June–November) and the dry season (December–May). The vegetation is composed of low and medium semievergreen forest, low and medium semideciduous forest, and high evergreen forest (Vester et al. 2007).
Three troops of black howler monkeys were selected; two troops were located at the Calakmul archaeological site, within the southern section of the CBR (18°07′21″N, 89°47′00″W), while one troop was on the Conhuas communal forest area, at the northern edge of the southern section (18°32′06″N, 89°53′40″W). Study troops were composed of 4–9 individuals, with at least one adult male and one adult female (N = 20). Monkeys were individually identified using sex, size and specific traits, such as fur characteristics and scars. Troop habituation to the presence of observers was not required for the troops at the archaeological site because of their regular contacts with the CBR staff, tourists and other researchers. However, 3 days of habituation were required for the Conhuas troop before monkeys stopped fleeing from observers or howling in their presence.
Since black howler monkeys are strictly arboreal and move relatively slowly compared to other arboreal primates, we were able to follow closely their daily movements and make direct observations on their behaviour. We monitored the troops from September to December 2009 and from February to April 2010, covering a wet and the following dry season. Each troop was followed for a maximum of 7 hours per day and 4 days each month, for an average total of 105·7 hours per troop. We assumed that movements of an individual represented the movements of the whole troop because black howlers form cohesive groups and do not separate while moving (Byrne 2000). Therefore, we followed only one individual at a time, preferentially the individual that was leading the troop's movements (N = 16 focal individuals). If this individual went out of sight for more than four trees in a row, another individual was randomly chosen among those remaining visible.
We recorded 54 trajectories, which we divided into 112 subtrajectories. A subtrajectory was defined as the continuous movement record for a given focal individual; a new subtrajectory started when another focal individual had to be followed or when trajectories were interrupted by movements that were not related to foraging. Trees in subtrajectories were located with a global positioning system (GPS, <10 m precision), with their distances and azimuths from the GPS-positioned tree recorded to maintain precision. We identified the species, measured the diameter at breast height (DBH, cm at 1·3 m) and evaluated the phenological state (proportion of young and mature leaves, presence of buds, flowers and ripe or unripe fruits) for all trees that were visited, even those upon which monkeys did not feed. Positions of all trees for which the crowns were directly connected to those of visited trees were also registered to evaluate all possible movement options for howlers.
Continuous focal observations of behaviours were simultaneously conducted to locate feeding activities both spatially and temporally, and to distinguish foraging movements from other movements. Observed behaviours were classified into four categories: feeding, moving, resting and other (Appendix S1). When feeding behaviours were recorded, items that were consumed were identified. All movements not related to foraging, that is, those associated to the category other (e.g. confrontation between troops or fleeing) were removed from the analysis.
To explore phenological tracking of resources by black howlers, we monitored fruiting peaks for each species that was known to be consumed and tested if monkeys preferentially moved to certain trees belonging to these species during their fruiting periods. Every week during the study, we monitored the phenological state of 400 trees that were located within the troops' home ranges. We used the number of trees bearing fruits as a function of time since the beginning of the study as a proxy for general phenological variation throughout the study period (further details are provided in The Model section).
Attraction to Trees, Food Items and Feeding Patches
To quantify the feeding preferences of black howlers for tree species and food items, we constructed two indices of attraction. The attraction index for tree species (referred to as the rank index) was based on a selectivity index that had been previously calculated for black howlers in the CBR (Rivera & Calmé 2006). The selectivity index used by Rivera & Calmé (2006) was calculated with the Chesson's index (εi, Chesson 1983), which considers the proportion of a species in the diet, weighted by its proportion in the environment, and the sums of these proportions for all species evaluated. This index ranges from -1 (negatively selected species) to 1 (positively selected species). From the Rivera & Calmé (2006) selectivity index, we attributed an attraction value ranging from 0 to 4 to all species that were recorded to having been eaten during our study, with four being the most preferred species. We modified the Rivera & Calmé (2006) index because several species used in their calculations did not appear to be consumed during our study. Since Chesson εi is affected by the total number of species included in the analysis, we converted the original selection values into more simple ones that were still representative of the order of selection.
We also calculated an attraction index for the food items that were recorded as being eaten during the study (referred to as the food item index), based on preferences outlined in previous studies on howlers (Silver et al. 1998; Pavelka & Knopff 2004; Rivera & Calmé 2006). This index was calculated by dividing the rank of the food item by the total number of items that were known to be consumed for a given species in our study. It ranged from 0 to 1, with 1 corresponding to the most preferred. Tree species and food items that were consumed during the study, and their associated attractiveness ranks are presented in Appendix S2.
We also expected that large trees belonging to preferred species, and the trees surrounding them, were more likely to be visited than other trees. Thus, we delineated areas, named hereafter as patches, which consisted of trees belonging to the three most preferred species (Ficus sp., Manilkara zapota and Brosimum alicastrum) with a DBH > 50 cm (discriminating 77% of all the trees visited during observations). The patches also included all trees that were located within a radius of 40 m, a distance that generally included all immediate trees surrounding the main tree.
We modified a recently developed movement model, which incorporates resource selection functions into a Markov chain framework (Colchero et al. 2011). We modelled movements that were recorded in subtrajectories as a series of discrete steps, t. Each step was divided into two distinct stages: (i) the movement from one tree to the next (destination tree); and (ii) the time spent on the destination tree. We constructed the model so that at each step, we could determine whether the tree of destination reduced the distance to the nearest high-quality patch. Although the original model proposed by Colchero et al. (2011) used a Bayesian framework to better account for missing data and measurement error, our data set did not have any of these data limitations and, therefore, it was sufficient to draw inferences on both processes from a maximum-likelihood approach (Geyer 1992; Brooks et al. 2011).
Let xi represent the location of tree i and Xg,t be a random variable for the location of troop g at step t. The first stage of the model evaluates the multinomial probability that troop g moves from a tree of origin i to a tree of destination j within a time interval Δt and within an observation window wi, centred on tree i. We defined the observation window wi as all trees for which the crowns were connected to the crown of the tree of origin, not including the tree of origin such that i ∉ wi. We deemed it sufficient to only include close neighbouring trees since howler monkeys usually move between trees by walking along connecting branches. We considered that the time required to leave a tree and enter the next is negligible. Thus, we assumed that Δt is constant. The multinomial probability of movement from the origin tree to the destination tree is
where m(zj,t, b, c) is a link function that relates the vector of covariates, zj,t associated with tree j with the probability of moving from the tree of origin to the tree of destination. Vectors b and c represent parameters linking these covariates to the movement process. This link function is calculated as
where Rj is the attraction to the species of the destination tree j (Rank), Dj is the distance between the trees of origin and destination (Dist), Pj is the Euclidean distance between the tree of destination and the closest patch of highly attractive trees (Patch; set to 0 when monkeys were using a patch), Ej,t is the distance between the tree of destination and the closest tree where monkeys had previously eaten during the whole study period (Eaten), Ht represents the time since the start of the study in days, Ij is an indicator that assigns 1 if the tree belongs to species s and 0 otherwise and S is the total number of species recorded in the study. These last variables were used to estimate the effect of phenology on the attractiveness of the trees of destination, measured by the species-specific parameters cs. Alternatively, to account for nonlinear (i.e. quadratic) phenological changes, we tested the following link function
where parameter c1,s measures the strength of attractiveness of the species s of tree j as a function of time, and parameter c2,s measures the time when this attractiveness reaches its maximum. Due to the poor performance of this alternative model (all parameters c2,s were larger than the duration of the study), we only report results from Eqn. 2a.
The second section of the model considers the time that troop g spends in the tree of destination j at step t, which we label as yg,j,t. We assumed that the time spent in the destination tree declined exponentially as a function of the covariates, for which we used an exponential generalized linear model (GLM; Nelder & Wedderburn 1972) of the form yg,j,t ~ exp(λj,t), where λj,t is the rate parameter for which the inverse represents mean time spent in each tree. We modified the canonical link to accommodate negative parameter values, such that
where q(vj,t, a) is a link function with parameter vector a that relates the vector of covariates vj,t to the time spent on tree j. This link function was calculated as
where Rj corresponds to the species attractiveness rank as explained above, Fj,t is the attractiveness rank of the most preferred food item that was available in the destination tree during the recording day (Part), and Kg,t is a proxy for satiation state. This proxy for the satiation state was calculated as the amount of time spent eating earlier in the day, weighted by the time spent foraging actively, which included eating and searching for food in a tree (Eaten2). If we assume that the time spent eating is a function of the amount of food ingested, this ratio represents the return on the food ingested earlier in the day, and thus approximates the satiation state of the animal. Since howlers eat regularly and have slow gut-passage times compared to other species (Milton 1981), we included in the analysis all previous feeding events in the same day, not only the last one. Definitions and expected effects of covariates are presented in Table 1.
Table 1. Descriptions and expected effects of covariates on the probability of moving to a destination tree or to leave the destination tree
|Probability of moving to a destination tree||Dist||Distance in metres between tree of origin i and tree of destination j.||Negative|
|Rank||Attractiveness rank of tree of destination j, based on an independent electivity index of tree species consumed by Alouatta pigra in Calakmul Biosphere Reserve (Rivera & Calmé 2006). Ranks range from 0 to 4, with 4 being the most strongly selected species.||Positive|
|Patch||Distance in metres between destination tree j and nearest patch border. Patches were defined as discrete areas of attraction, centred on trees of species with rank of 4 and DBH > 50 cm, and covering a 40 m radius around attraction centres.||Negative|
|Eaten||Distance between destination tree j and nearest tree where monkeys were seen eating earlier during the study period.||Negative|
|Phenol||Linear model of phenology as a function of time since the beginning of the study (15 September 2009). Since it was impossible to assess phenological states for all trees for all dates, time since the beginning of the study was used as a proxy for general phenological variation throughout the study period.||Species- dependent|
|Probability of leaving a destination tree||Rank2||Attractiveness rank of the destination tree (see Rank).||Positive|
|Part||Attractiveness rank of the most preferred food item available in the actual tree, ranging from 0 to 1, with 1 being the most preferred part. This attractiveness rank is species-specific and only applies to tree parts known to be consumed by Alouatta pigra.||Positive|
|Eaten2||Satiation state, which is the amount of time spent eating earlier in the recording day, weighted by the amount of time spent foraging actively (which included eating and searching for food items in the same tree).||Negative|
As mentioned above, the data structure allowed us to draw inference for movement processes from a maximum-likelihood approach. Thus, we constructed the likelihood function as
where G corresponds to the total number of groups (i.e. 3), Tg is the total number of steps per group, a, b and c are parameter vectors to be estimated, x is the vector of all destination trees, y is the vector of times spent on each destination tree, W is a matrix of observation windows, and Z and V are design matrices of covariates for processes of movement to, and time spent within, the destination trees. Maximum likelihood estimates (MLEs) for all parameters were obtained using a Metropolis algorithm within a Markov chain Monte Carlo method (Geyer 1992; Beerli & Felsenstein 2001; Clark 2007; Brooks et al. 2011) with 50 000 iterations and a burn-in of 5 000 iterations. We tested 10 different combinations of the seven covariates that have been described above (Table 2). For model selection, we used Akaike Information Criterion (AIC, Akaike 1974). We performed all statistical analyses in R.2.12.2 (R Development Core Team 2011) and required the libraries mvtnorm and msm (Genz, Bretz & Hothorn 2006; Jackson 2011).
Table 2. Tested covariate combinations for movement and time spent on a tree, and their associated AIC and ΔAIC values that were obtained by likelihood maximization. Suffixes prm and prl represent the probability of moving to a destination tree and leaving a destination tree, respectively. The S value in the number of parameters column refers to the number of tree species recorded during the study
|1||prm(Dist, Rank, Patch, Eaten), prl(Rank2, Part, Eaten2)||7||23451||0||0·53|
|2||prm(Dist, Rank, Eaten), prl(Rank2, Part, Eaten2)||6||23452||0·5||0·42|
|3||prm(Dist, Rank, Patch), prl(Rank2, Part, Eaten2)||6||23456||5·2||0·04|
|4||prm(Dist, Rank), prl(Rank2, Part, Eaten2)||5||23458||6·4||0·02|
|5||prm(Dist, Rank, Patch, Eaten, Phenol), prl(Rank2, Part)||6 + S||23554||103·0||0·00|
|6||prm(Dist, Rank, Patch, Eaten, Phenol), prl(Part, Eaten2)||7 + S||23613||161·9||0·00|
|7||prm(Dist, Rank, Patch, Eaten, Phenol), prl(Part)||6 + S||23774||322·6||0·00|
|8||prm(Dist, Rank, Patch, Eaten, Phenol), prl(Rank2, Eaten2)||7 + S||25049||1597·6||0·00|
|9||prm(Dist, Rank, Patch, Eaten, Phenol), prl(Rank2)||6 + S||35297||11845·4||0·00|