Strong positive allometry of bite force in leaf-cutter ants increases the range of cuttable plant tissues

ABSTRACT Atta leaf-cutter ants are the prime herbivore in the Neotropics: differently sized foragers harvest plant material to grow a fungus as a crop. Efficient foraging involves complex interactions between worker size, task preferences and plant–fungus suitability; it is, however, ultimately constrained by the ability of differently sized workers to generate forces large enough to cut vegetation. In order to quantify this ability, we measured bite forces of Atta vollenweideri leaf-cutter ants spanning more than one order of magnitude in body mass. Maximum bite force scaled almost in direct proportion to mass; the largest workers generated peak bite forces 2.5 times higher than expected from isometry. This remarkable positive allometry can be explained via a biomechanical model that links bite forces with substantial size-specific changes in the morphology of the musculoskeletal bite apparatus. In addition to these morphological changes, we show that bite forces of smaller ants peak at larger mandibular opening angles, suggesting a size-dependent physiological adaptation, probably reflecting the need to cut leaves with a thickness that corresponds to a larger fraction of the maximum possible gape. Via direct comparison of maximum bite forces with leaf mechanical properties, we demonstrate (i) that bite forces in leaf-cutter ants need to be exceptionally large compared with body mass to enable them to cut leaves; and (ii), that the positive allometry enables colonies to forage on a wider range of plant species without the need for extreme investment in even larger workers. Our results thus provide strong quantitative arguments for the adaptive value of a positively allometric bite force.


Projection of the mandibular joint rotational axis Filament length
The length of the filaments L f il connecting muscle fibres and apodeme determines the relationship between muscle fibre length and mandibular opening angle (see below). We estimated L f il as the difference between the internal radius and apodeme radius, L f il = r i − r apo . The internal radius represents the effective radius of attachment; the apodeme radius was defined as the equivalent radius of the apodeme cross-sectional area, assuming a circular shape, [see 2, for an exact definition].

Variation of morphological force determinants with opening angle
In order to correct the bite force measurements in this study for sizedependent differences in opening angle, we predicted the variation of bite force across the entire worker size range, based on a previously derived biomechanical model [3]. To this end, we extracted reference measurements from tomographic scans, and used the following equations, as derived in Püffel et al. [3], in combination with Eq. 3 in the main text: The effective inlever length, |L i,e f f (θ )|, varies with opening angle, θ , as: where L i is the mandible inlever, R is the mandible joint axis of rotation, and Â is the apodeme main axis, which is approxi mately aligned with the orientation of the net muscle force vector (see Fig. 1E). γ 0 is the angle between the muscle line of action and the effective inlever, measured at a reference opening angle, θ 0 . The apodeme displaces as: The fibre pennation angle varies with θ as: where L t,0 is the average total length of the muscle fibres (sum of fibre length and filament length) at θ 0 . Filament-attached fibres vary in length as: where L f ,0 is the average length of filament-attached fibres. Fibre length changes, in turn, affect muscle stress and thus bite force (see Fig. 1G and main text). For more details on parameter definitions and the geometrical basis of these equations, see Püffel et al. [3].

References
[1] Kang V, Püffel F, Labonte D. Kinematics of leaf-cutter ant mandibles challenge the hinge joint paradigm in winged biting insects. Manuscript submitted for publication.
[2] Püffel F, Pouget A, Liu X, Zuber M, van de Kamp T, Roces F, Labonte D. 2021 Morphological determinants of bite force capacity in insects: a biomechanical analysis of polymorphic leaf-cutter ants. Journal of the Royal Society Interface 18: 20210424.
[3] Püffel F, Johnston R, Labonte D. 2023 A biomechanical model for the relation between bite force and mandibular opening angle in arthropods. Royal Society Open Science 10: 221066.   F b,m , is proportional to m 0.79 ; this scaling coefficient is sub-stantially lower than that obtained for fully-corrected data (0.90, see main text). (G) In order to correct the force data for size-dependent differences in mandibular opening angle, we used physiological parameters of the mandible closer muscle extracted for closely-related A. cephalotes ants [3], and fitted the opening angle at which muscle stress peaks, θ opt , for each of the 13 different size classes (see Eq. 3 in the main text). Maximum muscle stress, σ and shape Table S1. Results of reduced major axis regressions describing the relationship of bite force with body mass and head volume (labelled with *), respectively, on log -transformed data. 'Fully-corrected' implies that all four correction steps were done (see main text), 'angle-uncorrected' means that corrections (i-iii) were performed, and 'raw' refers to uncorrected data. 95 % confidence intervals are provided in parentheses.  Table S2. Results of reduced major axis regressions describing the relationship of mandibular opening angle in degrees, (i) at which muscle fibre length is optimum, θ , and (ii) at which bite forces are maximum, θ , with body mass in mg on log10-transformed data. 95 % confidence intervals are provided in parentheses.  Table S3