Abstract
Although sometimes difficult to measure at large scales, spatial pattern is important in natural biological spaces as a determinant of key ecological properties such as species diversity, stability, resiliency and others1, 2, 3, 4, 5, 6. Here we demonstrate, at a large spatial scale, that a common species of tropical arboreal ant forms clusters of nests through a combination of local satellite colony formation and density-dependent control by natural enemies, mainly a parasitic fly. Cluster sizes fall off as a power law consistent with a so-called robust critical state7. This endogenous cluster formation at a critical state is a unique example of an insect population forming a non-random pattern at a large spatial scale. Furthermore, because the species is a keystone of a larger network that contributes to the ecosystem function of pest control, this is an example of how spatial dynamics at a large scale can affect ecosystem service at a local level.
It has been common to assume, sometimes only implicitly, that the patchiness of an ecosystem reflects some underlying habitat factor (for example, marshweed occurs in marshes) even though that factor may not be evident8, 9. However, it is well known that various intrinsic biological dynamics are capable of producing pattern even in a landscape that is homogeneous for the organism involved10, 11. This raises the question for any non-random spatial pattern about whether it is caused by factors that are exogenous (broadly, underlying habitat patchiness) or endogenous (broadly, biological aspects of the organism independent of the habitat patchiness)12, 13.
In our study site in southern Mexico the underlying habitat for a species of tropical arboreal ant, Azteca instabilis, is essentially uniform. It is the collection of shade trees planted in a coffee plantation, where the original intention of the farmer was to plant the trees uniformly. The ant species is common in the Mesoamerican tropics, where it is frequently encountered on casual walks in the forest. However, discerning any spatial pattern of its colonies is inevitably obstructed by the heterogeneity of the habitat it normally occupies. However, the species also inhabits shade trees in traditional shaded coffee farms, a uniform habitat both by intention and as measured. Ant nest formation is exclusively in the shade trees; consequently a non-random pattern in the spatial distribution of ant colonies must be a result of endogenous factors, because the underlying habitat is uniform. We find that the colonies indeed are non-random, even though the shade trees themselves are uniform (Fig. 1).
Figure 1: Distribution of nests of Azteca instabilis over a 45-ha plot (the three missing hectares are on inaccessible terrain).
The distributions of colonies found in all censuses are notably clumped (the first and last censuses are shown here) with an average of 328 trees occupied. The nests appear to drift around, as is evident from a comparison of the two panels. Note the dynamic nature of the system over time: the two small rectangles illustrate both the complete disappearance of a cluster and the appearance of another cluster where only a single nest had been before.
High resolution image and legend (105K)The basic biology of the ant is not unusual. After a queen establishes a colony in a tree, the colony may grow to the point that satellite nests are established in neighbouring trees, presumably one part of the mechanism whereby patchiness is generated. Although the details of satellite formation are not completely known (see Supplementary Information), it is evident from our data that ants within a particular nest establish other nests in nearby trees. Unabated satellite formation would obviously result in a continuous expansion of nests throughout all shade trees in the habitat, which means that some force must limit this expansion. On this farm the ant has a series of natural enemies, any one of which, or any combination thereof, could form the basis for the control that must occur. A parasitoid phorid fly is known to reduce ant foraging activity14, and has a density-dependent response to clusters of ant nests (Fig. 2), in addition to a qualitative behavioural response to the ants (see Supplementary Information).
Figure 2: Attack rates of phorid fly parasites as a function of nest-cluster density.
Density of nests based on a 20 m circle surrounding the point at which phorid attack trials were done. Error bars, s.e.m. The attacks were highly variable, but the relation with the density of the local clusters of ant nests is statistically significant (P = 0.042; see also Supplementary Information).
High resolution image and legend (24K)Based on this natural history, we propose a three part dynamic. First, nuptial flights produce founding queens that disperse as propagule rain over a large area. Second, successful colonies occupy neighbouring trees with satellite colonies. Third, phorid parasitoids concentrate on clusters of ant nests, causing a dramatic behavioural response and possibly direct mortality, thus dramatically reducing ant survivorship in dense clusters of nests. The cellular automata model developed here (see Methods and Supplementary Information) is based on these three features, where a central cell becomes occupied or dies depending on the Moore neighbourhood, N, with the probability of satellite expansion being a linear function of N (ps = s0 + s1N), as is the probability of mortality (pm = m0 + m1N).
The range of parameter values to instantiate the cellular automata model (see Methods and Supplementary Information) obtained from the field censuses were: for satellite expansion, s0 = 0.0–0.8, s1 = 0.0133–0.035; and for mortality, m0 = 0–0.45, m1 = 0.031–0.097. A systematic search of this range of parameter space produced the following parameters: s0 = 0.0035, s1 = 0.035, m0 = 0.116, m1 = 0.036, as those producing the best approximation to both the population densities of nests over time and the cluster size distribution (as measured by the mean/variance ratio). Output from the model and observed data from the field are shown in Fig. 3.
Figure 3: Time (in six month intervals) series for population density (top) and mean variance ratios (bottom) for the parameters s0 = 0.0035, s1 = 0.035, m0 = 0.116 and m1 = 0.036.
In both cases two separate runs are pictured: one in black, the other in grey (hardly noticeable in the bottom panel because the two runs are so similar). Horizontal lines are the values of the six field samples (two samples are so close as to appear the same).
High resolution image and legend (135K)The overall population densities in the simulations are concentrated between 200 and 500, and the mean variance ratios between 0.4 and 0.5, both close to the range of our observations in nature (represented as horizontal lines in Fig. 3). The model output reflects the erratic nature of cellular automata models, with the same parameters generating a dramatic variability both of population densities and mean variance ratios. However, because the possible range could be from 0 to 10,800 for population density and from 0 to +infinity for mean variance ratios, the ability of the model, with parameter values within our empirical envelope, to generate population densities and patterns so close to those we observed in the field suggests that the basic interpretation of the spatial dynamics is probably correct.
Although our modelling approach is distinct, the underlying biological interactions are similar to those studied by Pascual and colleagues, suggesting that we should expect a power law relation between cluster size and frequency. Indeed, as expected, the distribution of cluster sizes in our plot does follow a power function (Fig. 4a). Furthermore, calculating the frequency of cluster sizes, as generated by the model, produces a similar power relation (Fig. 4b) as would be suggested if the system is near criticality15. Further studies of the model show that there is a broad region of parameter space in which the power law holds, suggesting that this may be a case of robust criticality16.
Figure 4: Log of cumulative frequency of log cluster sizes.
a, From field samples, based on a minimum distance of 20 m between nests that are judged to be in the same cluster. b, From field-parameterized cellular automata stochastic model, based on a 90 
120 lattice, where each lattice point is intended to model a single shade tree. Clusters are defined based on individual lattice points in contact with any other lattice point in the Moore neighbourhood.
The importance of these results lies in the fact that strong spatial pattern is formed in the face of habitat homogeneity, connecting with the well-known consequences of spatial pattern on topics such as species diversity, ecosystem stability or resiliency and others. Furthermore, it is likely that this pattern formation also is related to biological control of several important coffee pests such as the coffee berry borer (Hypthenemus hampei)17, the green coffee scale (Coccus viridis)18 and coffee rust (Hemileia vastatrix)19. All of these controls are effected through the spatial patterning of this system, as discussed in detail elsewhere20.
Methods Summary
All trees in a 45-ha plot in a shaded coffee plantation were located and the presence of ant colonies therein noted, a process repeated at 6-month intervals for 2 years. Non-randomness of nests was established through quadrat-based computation of mean and variance of number of nests per quadrat. Attack rates of phorid flies were determined in locations that varied in the local number of ant nests, by placing a small amount of ant-nest carton with a few ants in a container and counting the number of phorid attacks over a 20 min period. The stochastic cellular automata was constructed based on the natural history observations of the ants forming satellite nests on nearby trees plus the phorid flies encountering nests in proportion to their local density. The model was parameterized with field data and compared with actual distributions in the field. Both the distribution of nests in the field and the distribution generated by the cellular automata were examined for the distribution of cluster sizes.
Full methods accompany this paper.
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