Volume 13, Issue 9 p. 1938-1948
PRACTICAL TOOLS
Open Access

forceX and forceR: A mobile setup and r package to measure and analyse a wide range of animal closing forces

Peter T. Rühr

Corresponding Author

Peter T. Rühr

Institute of Evolutionary Biology and Animal Ecology, University of Bonn, Bonn, Germany

Correspondence

Peter T. Rühr

Email: [email protected]

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Alexander Blanke

Alexander Blanke

Institute of Evolutionary Biology and Animal Ecology, University of Bonn, Bonn, Germany

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First published: 29 May 2022
Citations: 1
Handling Editor Thomas White

Abstract

  1. Animal closing forces such as bite and pinch forces may determine access to food and mates and are therefore important performance metrics related to fitness. Previous measurement setups to obtain in vivo closing force data were often custom-made for each study, hampering comparisons among different studies. Additionally, most setups were limited in the size range of taxa they can measure, especially towards smaller species.
  2. We introduce forceX, a closing force measurement setup that allows the measurement of a large range of taxa with a great size variety, and forceR, an accompanying software package to analyse the data. forceX is mostly based on off-the-shelf components and 3D-printed or metal-turned parts. Gape distance can be modified during measurements, and replaceable tip elements of varying thickness allow a minimal gape distance of ~0.3 mm. Thus, forceX allows closing force measurements of smaller species, while still being able to measure medium-sized animals as well. Animals are not harmed during the measurements, and the whole setup can be assembled within minutes, is battery-powered, light-weight and transportable.
  3. The forceX system is able to accurately (linear regression of measured forces vs. control forces: p < 0.001; R2 > 0.999; n = 1,609) and reproducibly (mean of absolute relative errors = 0.93%; SD = 1.42%; n = 1,609) measure forces across three orders of magnitude (0.01–10 N). Importantly, whole force curves, instead of just maximum force values are stored, and forceR allows extracting individual peak shapes from these curves to facilitate the statistical analysis of both maximum force values and peak curve shapes.
  4. forceX and forceR facilitate rapid and minimally invasive in vivo measurements and analyses of closing forces in animals across a wider range of taxa than previously possible, including, for example, many small species of the megadiverse insects. The system allows studying the characteristics, predictors, and evolution of both maximum closing forces and force curve shapes.

1 INTRODUCTION

Closing forces, such as bite and pinching forces, are important performance metrics for many animals. They can relate to dietary spectra (e.g. Aguirre et al., 2002; Meyers et al., 2018; Shi et al., 2020), influence the outcome of conflicts (e.g. Claussen et al., 2007; Husak et al., 2006; Lailvaux et al., 2004) and impact reproductive success (e.g. Husak et al., 2009; Lappin & Husak, 2005). The dependencies of closing forces on size, ecology, age or phylogeny have been studied in vivo in a wide range of vertebrate groups, including cartilaginous and bony fishes (Grubich et al., 2012; Huber et al., 2005), crocodilians (e.g. Erickson et al., 2012), birds (e.g. Herrel et al., 2005), turtles (e.g. Herrel et al., 2002), squamates (e.g. Herrel et al., 2001; Jones et al., 2020), frogs (Lappin et al., 2017) and mammals (e.g. Becerra et al., 2011; Dessem & Druzinsky, 1992; Freeman & Lemen, 2008; Sakamoto et al., 2010; Santana & Dumont, 2009). However, just a few studies investigated closing forces in invertebrates so far. We could find published closing force data on seven species of scorpions (van der Meijden et al., 2010), one camel spider (van der Meijden et al., 2012), 19 crustaceans (Block & Rebach, 1998; Blundon, 1988; Bywater et al., 2008; Claussen et al., 2007; Elner & Campbell, 1981; Govind & Blundon, 1985; Lailvaux et al., 2009; Levinton & Judge, 1993; Malavé et al., 2018; McLain et al., 2015; Miranda et al., 2016; Oka et al., 2016; Smith & Palmer, 1994; South et al., 2020; Taylor, 2000; Taylor et al., 2000; Wilson et al., 2007; Yamada & Boulding, 1998), and 33 insects (David et al., 2016a, 2016b; Hao et al., 2018; Huang, 2012; Paul & Gronenberg, 2002; Spagna et al., 2008; Weihmann et al., 2015; Wheater & Evans, 1989). The investigated species represent only a small fraction of the vast taxonomic and anatomical diversity of the megadiverse invertebrates. Given their immense importance to ecosystems (Prather et al., 2013) and their potential for understanding the evolution of performance traits, the paucity of closing force data in these taxa is a knowledge gap that warrants attention.

1.1 Previous closing force measurement methods

Many closing force experiments have relied on custom-made strain gauge-based measurement setups (Claussen et al., 2007; DeChow & Carlson, 1983; Dessem & Druzinsky, 1992; Erickson et al., 2003; Grubich et al., 2012; Hylander, 1979; Paul & Gronenberg, 2002; Weihmann et al., 2015; Williams et al., 2009). The minimum gape distances of these setups are limited by the minimal thickness of the tip elements at which forces are measured, and the distance between the tip elements after their elastic deformation at maximum closing force. Other closing force studies used custom implementations of a setup developed by Herrel et al. (1999) for bite force measurements in lizards. The setup is based on a piezoelectric force transducer, which, in contrast to strain gauge-based transducers, effectively does not deform under the application of forces. This isometric sensor behaviour has the advantage that the tip elements of the setup do not move towards each other, allowing for gape distances that are force-independent and only limited by the thickness of the tip elements and their distance from each other. The setup was used to measure closing forces in a wide range of animals, for example, a camel spider (van der Meijden et al., 2012), scorpions (van der Meijden et al., 2010), stag beetles (Goyens et al., 2014), lizards (e.g. Lappin et al., 2006), turtles (e.g. Herrel et al., 2018), frogs (Lappin et al., 2017), birds (e.g. Herrel et al., 2005) and bats (e.g. Aguirre et al., 2002).

Animal closing forces were shown to be gape-angle dependent in cockroaches and bats (Dumont & Herrel, 2003; Ross & Iriarte-Diaz, 2014; Santana, 2016; Weihmann et al., 2015; Williams et al., 2009), so the size of and distance between the tip elements of a measurement setup may limit the taxa suited for physiologically meaningful force measurements. While the distance between the tip elements in the Herrel et al. (1999) setup is adjustable, allowing closing force measurements with different gape angles and specimen sizes, the replaceable tip elements of the setup have a minimum thickness of ~2 mm each, resulting in a theoretical minimum gape distance of 4 mm. To our knowledge, so far the smallest species measured with this setup was Anolis humilis Peters, 1863 (Squamata: Dactyloidae) with a snout-vent length of 32.7 mm (Wittorski et al., 2016). This is more than three times larger than, for example, the peak of the size-frequency distribution of the megadiverse insects, which lies at ~10 mm (Finlay et al., 2006). The relatively large cockroach Periplaneta americana (L. 1758; Hexapoda: Blattodea), which is the only insect species where the gape angle-dependency of bite force was studied, exhibited the strongest bite forces at a mandible gape distance of only 0.5 mm (Weihmann et al. (2015) and Figure S1a). A gape distance of 4 mm, as in the Herrel et al. (1999) setup, would therefore not allow bite force measurements for the majority of insects (Figure S1b). Although the system by Weihmann et al. (2015) allows measuring bite forces at very small gape distances, the operator has to sedate and fix the test animals to the setup with dental cement.

To overcome the size limitations of previous setups, we propose the forceX (force eXperiment) measurement setup, a battery-powered, portable system that allows rapid closing force measurements in a wide range of animals, particularly of small invertebrates. forceX measurements do not harm the test animals, allowing repeated measurements and a subsequent release, facilitating population level or multi-generation studies. While many previous studies focused only on maximum closing forces (but see Boulding, 1984; Huber et al., 2005; Goyens et al., 2014; Weihmann et al., 2015; David et al., 2016a, 2016b; Gomes et al., 2020), forceX is complemented with the new forceR package to run in-depth analyses on how the force is applied over time, that is, the shape of force curves. Variation in the force curve shapes between individuals and species could be the result of differences in biomechanics, physiology and/or behaviour. These differences may in turn be related to function, ecology and phylogeny. For example, some animals may require a rapid peak of force to critically damage or kill whereas others may require a stable force to hold prey securely for extended periods of time.

2 MATERIALS AND METHODS

2.1 Description and implementation of forceX

The core of forceX is a lightweight (2.5 g) piezo-electric force transducer (model 9215A; Kistler), which is designed to convert forces (≥1 mN) into an electric signal. The transducer shows a linear relationship between force and charge across its entire range and at a wide range of temperatures (Kistler Group, 2020). The transducer is fixed on a central ‘main body’ (Figure 1) and a ‘lever’ is attached to its upper side via a threaded rod. At the opposite end of the lever, it houses one of two exchangeable stainless steel ‘tip elements’ on its bottom surface. The second tip element is fixed to the main body so that it sits directly below the upper tip element. The fixed rotation of the lever on its fulcrum can be adjusted so that the distance of the tip elements from each other suit the test subject's gape angle. Although the 9215A force transducer can measure compressive forces of up to 200 N, it is mounted into the forceX so that it measures tensile forces and should therefore not be loaded with more than 20 N (Kistler Group, 2020). With the custom charge amplifier (see below), forces of no more than 12 N can be measured, but by changing the amplifier circuitry, this value could be increased.

Details are in the caption following the image
(a) CAD model of the forceX setup. (b) Assembly of the forceX sensor unit including tip elements, lever and main body. For detailed assembly instructions, see Data and Code Availability section. (c) Orthographic views of the sensor unit.

The general design of this setup is an advancement of the setup described in Herrel et al. (1999), with the major advantage of having the possibility to use 40 times thinner tip elements. These tip elements can vary in thickness and thus accommodate a wide taxonomic range: large animals with high closing forces require tip elements with high resistance to bending, whereas small animals require minute gape distances with thin tip elements that do not show high bending resistance. forceX provides a calibrated system that can either be produced with a standard fused deposition modelling (FDM) 3D printer or metal-turned. We have printed our 3D-printed forceX version with an MK3S+ (Prusa Research) and PLA filament (extrudr). The metal version was produced by the Central Workshops of the Department of Biology, University of Cologne. For detailed assembly instructions, including a complete parts list, CAD models, and schematics of the electronics, see the Data and Code Availability section.

2.1.1 Microscope

A stereo microscope allows to visually monitor the animal behaviour in more detail and aids when measuring small animals and the position of their body parts on the tip elements. We used a Junior Stereo 3D microscope (Bresser GmbH) with a single built-in LED powered by two AA batteries.

2.1.2 Camera

A module that houses a camera connected to a Raspberry Pi (model 3 B+ or higher; www.raspberrypi.org) can be added to the setup. The camera can help with the investigation of gape-angle dependencies of closing forces and in identifying non-distal bites and pinches after the measurement has been conducted. While there is a wide range of cameras available, we used an affordable 5-megapixel RPi Camera (B) rev. 2.0 with adjustable focus (Waveshare International Limited; Figure 1; Figure S2).

2.1.3 Tip elements

Tip elements with different edge shapes and thicknesses of down to 0.1 mm were laser cut from SAE 316 L grade stainless steel plates to fit gape distances as low as ~0.3 mm. Three holes were punched into each plate so they can be screwed onto the main body and the lever via three M1 bolts with countersunk heads. Closing forces should only be measured at the edges of the tip elements near the main body and the lever (Figure 2b). At this edge, the lever ratio of forceX is 10.5 mm/19.5 mm ≈0.538 mm. The protruding edges of the tip elements should only be used to insert the plates between the force-exerting animal parts in case the tip elements are not voluntarily grasped by the animal.

Details are in the caption following the image
(a) The forceX setup (excluding the camera module) with a computer running LJStreamUD (LabJack Corporation). (b) Bite force measurement of a stag beetle (Lucanidae sp.) with the metal-turned forceX version. The distal tips of the mandibles are close to the lever and the main body to ensure a constant lever ratio both in the forceX setup and in the mandibles (bi). (c) Graph of a bite force measurement before (grey) and after (green) amplifier drift correction. The red line indicates the zero-voltage line.

2.1.4 Charge amplifier and power source

The 9215A force transducer creates minuscule charges in response to force-induced mechanical stress. A custom, small and light-weight analogue amplifier was designed to amplify these charges. Due to the nature of the resistor-capacitor circuit (R = 20 GOhm; C = 470 pF) within the amplifier, it responds to input charges with a time constant of
τau = R × C = 9,400 ms . (1)

The charge amplifier possesses a 3-way toggle switch to amplify the charge signal to 20 V/N, 2 V/N, or 0.5 V/N so that the signal can be spread over the full range of the digital data acquisition device (see below) depending on the maximum closing force of the currently measured animal. The charge amplifier should be powered by ±15 to ±20 V DC. The custom-made power supply provides a maximum voltage of ±18 V from four 9-volt batteries. With the current version of the amplifier, forces of up to 10 N can be measured. By varying the properties of the RC unit components, this could be increased to a maximum of 20 N, which is the maximum tensile force to which the force transducer should be loaded. For questions and inquiries about how to manufacture the custom charge amplifier, please contact M. Dübbert (see Acknowledgements). Alternatively, but not tested by us, an ICAM Type 5073A charge amplifier (Kistler) could be used in combination with further proprietary Kistler products.

2.1.5 Force recordings

To measure in vivo closing forces, specimens are held between two fingers to allow voluntary closing movements on the tip elements (Figure 2b). Visual inspection of the process enables the operator to check the position of the force-exerting animal parts on the tip elements during the experiment to prevent recordings of subdistal bites or pinches. With such subdistal interactions, that is when not the distal tips, but more proximal parts of the force-exerting organs touch the tip elements, the transmission of muscle forces is more effective due to more advantageous mandibular lever mechanics, resulting in higher recorded closing forces that are difficult to compare within and among specimens (Figure S3; Lappin & Jones, 2014). If voluntary closing movements do not occur, touching head or body parts of the test animals with a fine brush may increase their aggressiveness (Weihmann et al., 2015; own observations). Stinging insects can be put into a conical lab tube, which has had its tip cut off so that the specimen head fits through the hole while the thorax does not (Figure S4a–c). Paper tissue prevents the insect from crawling backwards. Small animals can be held with a device built from a rubber eraser and fishing line (Figure S4d–e). Appropriate protection should be used when handling poisonous or otherwise harmful animals.

When the upper tip element is pressed downwards, the lever pivots around its fulcrum, while the lower tip element remains stationary. Thus, the ‘M2 threaded rod’, which is secured onto the lever via the M2 hex nut, is pulled upwards, resulting in a tensile force at the force transducer. This generates a proportional charge, which is passed via an insulated coaxial cable (1651C1, Kistler, Winterthur, Switzerland) to the charge amplifier. The 9215A is an isometric force transducer with a low displacement of the piezo element so that there is no notable rotation of the lever. The distance between the two tip elements thus remains effectively constant even during strong forces. The tip elements can be adjusted according to the specimen's gape angle by changing the fixed rotation of the lever on its fulcrum via the M2 hex nut on the threaded rod, and by using bite plates of different thicknesses. The continuous, amplified voltage signal is converted into a digital signal by a 12-bit USB data acquisition device (U3-HV, LabJack Corporation) and passed to the LJStreamUD v1.19 measurement software (LabJack) on a computer via a USB cable (Figure 2a).

Details are in the caption following the image
Analyses of bite curve shapes and setup validation. (a, b) Normalized graphs of the five strongest individual bites (I-V) of T. surinama (Orthoptera) (a) and D. bucephalus (Coleoptera) (b). (c, d) Comparison of polynomial model fits with varying numbers of coefficients to describe the normalized bite curves (black lines) of T. surinama (c) and D. bucephalus (d). In the left panels of b and c, graphs for models with one to 20 coefficients are shown. Coloured graphs represent the first four model fits that show an AIC change of <5% compared to a fit with one more coefficient, as evaluated in the right panels. Grey graphs show models that do not meet this criterium. (e) PCA of polynomial models with 6 coefficients describing the bite curve shapes of T. surinama (cyan) and D. bucephalus (red). Bite V of D. bucephalus resembles the bites of T. surinama most (a) and is also closer to those of T. surinama in the PCA plot. (f) Box plots of repeated forceX measurements against known forces with linear regression (dashed line). The red line indicates a theoretical 1:1 correspondence between measured and known forces. Both axes are log10-scaled. For more details, see Table S1.

3 R PACKAGE forceR

forceR was written for the R programming environment (R Core Team, 2022) to prepare force data measured with the forceX setup for further signal processing and statistical analyses (Rühr, 2022). The package is, however, applicable to any kind of continuous time-series measurements. Functionalities of forceR include cropping and plotting of time series data, correction of RC-unit charge amplifier drifts, automatic or manual correction of potential baseline drifts, reduction of sampling frequency, extraction of maximum forces, automatic identification of single peaks (=bites or pinches), rescaling (normalization) of individual peak curves in x and y, identification of best polynomial fits to describe all curves and the export of peak curve models for subsequent analyses of curve shape differences (Figure S5). Below, we describe the theory behind the main functions of forceR. The package can be installed from the Comprehensive R Archive Network (CRAN). For more information and examples, please refer to the package vignette at https://CRAN.R-project.org/package=forceR.

3.1 Amplifier drift correction

To correct for the systemic voltage drift of the amplifier RC unit (Figure 2c), a sampling rate-dependent correction value (cv) is calculated for each time series as
cv = e 1 f / τau , (2)
with f = sampling frequency [Hz] and τau = time constant [ms].
At each time step t, a voltage value is predicted for t that would result from the amplifier drift without external stimulation (i.e. without a force acting on the transducer), and the difference of the measured value and the prediction is added to the corrected value of the previous time step:
V . corr t = V . corr t 1 + V . raw t V . raw t 1 * cv , (3)
where V.corr is the corrected voltage value, V.raw is the raw voltage value passed from the amplifier, and cv is the correction value from Equation 2.
For the first time step (t = 1), the corrected voltage is assumed to be equal to the raw voltage:
V . corr 1 = V . raw 1 . (4)
The function ‘amp_drift_corr()’ carries out the above corrections.

3.2 Baseline drift correction

The piezoelectric crystal of the force transducer creates minuscule charges so that factors such as temperature and static electricity changes produce fluctuations in the baseline (zero-line) of the voltage signal. This is most apparent in the highest amplification setting (20 V/N) and is usually negligible at the lowest amplification (0.5 V/N). An unstable baseline can be continually adjusted throughout the measurement with the function ‘baseline_corr()’ in an automatic or an interactive mode.

3.2.1 Automatic mode

The automatic baseline adjustment of ‘baseline_corr()’ (‘corr.type’ = “auto”) invokes a sliding window approach (window size = ‘window.size.mins’), during which the voltage ‘minimum’ within each window is stored as a vector. Here, a ‘minimum’ is defined using the parameter ‘quantile.size’. If ‘quantile.size’ is set to 0.05, the value below which 5% of the measurement data within the current window lies is treated as the current window's ‘minimum’. Not taking the actual minimum within each window prevents the treatment of short undershoots (e.g. artefacts created during the measurement) as minima. In a second iteration that runs through the whole time series, another sliding window (window of size = ‘window.size.means’) calculates the average of the ‘minima’ within each window and stores it for each time step. The resulting ‘minimal’ values of the second interaction are subtracted from the original time series. This approach works well for time series with relatively short peaks. For longer peaks, the ‘window.size.mins’ should be increased. However, the greater ‘window.size.mins’ becomes, the less reliable the baseline-correcting effect of the function becomes.

3.2.2 Interactive mode

If the automatic approach of ‘baseline_corr()’ does not yield acceptable results, an interactive approach to correct the baseline can be performed instead (corr.type = “manual”). This approach works better for measurements with long, plateau-like peaks. Here, the user is prompted to interactively mark as many points on a plot of the whole measurement as they see fit to define the actual baseline. A spline is then interpolated between these points and the values of this spline are subtracted from the original time series.

All parameters passed to the function in automatic mode are stored in a log file. In manual mode, the function stores all user-defined baseline points in the log file instead. In addition, the results of the procedure can be saved as PDF files.

3.2.3 Individual peak identification

The function ‘find_strongest_bites()’ identifies the highest peaks including their ascending and descending slopes in each time series, that is force curve shapes of individual bites or pinches. We chose to select the strongest bites because maximum performance values are best comparable between individuals and maximal performance is expected to be under natural selection (Hertz et al., 1988; Losos et al., 2002). In a first iteration, the function identifies all potential slope starts and ends via the ‘initial.threshold’ that is by default set to 0.05 (=5%) of the maximum force value of the respective time series. In a second iteration, the function optimizes the slope starts and ends found in the first iteration. Starting from each slope start, a sliding window of size ‘slope.length.start’ moves backwards in time and calculates the slope within the current window. The parameter ‘slope.thresh.start’ defines below which slope the sliding window process is stopped. The time point at which the threshold is reached is treated as the actual start of that bite. The same is done in forward direction starting from each slope end. Here, ‘slope.length.end’ defines the sliding window size, and ‘slope.thresh.end’ defines the slope threshold. All settings of the function have default values that are suitable for the curve progressions of most insect bites. The peak optimization is performed only for the strongest n bites, where n is defined by the ‘no.of.bites’ parameter. The resulting peak force curves can be plotted and checked with the ‘plot_bites()’ function, and individual peak starts and ends can be interactively adjusted using the ‘correct_bite()’ function if necessary.

3.3 Polynomial model fitting

After rescaling all individual peaks with the functions ‘rescale_curves()’, ‘red_bites_100()’, and ‘avg_curves()’, the function ‘find_best_fits()’ can be used to find the best polynomial degree fitting all normalized force curves. This function fits polynomial models with 1 to 20 coefficients (Figure 3c,d, left panels) and uses the Akaike information criterion (AIC) to evaluate the goodness of the fits (Figure 3c,d, right panels). A model is considered a good fit when the percentage of AIC change from one model to the next (e.g. a model with 6 coefficients to a model with 7 coefficients) is <5%. The first four coefficients per curve that fulfil the criterion are stored. A histogram of how often models with which number of coefficients were good fits is evaluated and the function returns the numerical value of the coefficient that fulfilled the criterion of a good fit most often. This value can be used to convert all individual force curves into polynomial functions with the ‘curve_to_poly()’ function of forceR for further analyses.

3.4 Validation

3.4.1 forceX setup

The 9215A force transducer is pre-calibrated and ready to use. We did, however, test the accuracy of the measurements performed with the whole forceX setup with its lever mechanics, power source and charge amplifier after correction for amplifier and baseline drift with the forceR functions ‘amp_drift_corr()’ and ‘baseline_corr()’ to ensure that the measured and processed values correspond to the actual forces acting on the tip elements. To achieve standardized force measurements, we tied weights ranging from 1 to 972 g to the upper tip element with a thin thread and repeatedly recorded the output voltage signal with different amplification settings. The weights, including the threads that were used to tie them to the tip element, were measured with laboratory balances (1–200 g: Analytical Balance XS205DU (Mettler Toledo, Greifensee, Switzerland); > 200 g: AX2202 (Sartorius AG)). The voltage signal was converted to a force signal with the ‘y_to_force()’ function of forceR. For each of the 1,609 repetitions, force values were extracted and a log10-log10 linear model was fitted to all data points. Relative errors between the input forces and the measured forces and their standard deviations were calculated, grouped by weight and amplification setting (Table S1). All data acquired during validation are deposited at Zenodo (Rühr & Blanke, 2022).

3.4.2 Maximum force values

We used the forceR workflow example (Supporting Information) to simulate bite series and automatically extract the five strongest bites per species, as well as maximum bite force per bite, specimen and species. We then ran a linear regression of log10-transformed maximum bite force per specimen over log10-transformed body mass and calculated relative errors between known input forces and extracted forces.

3.4.3 Force curve shapes

To test the ability of the package to differentiate between different peak shapes, we measured in vivo bite forces of the spur-throat toothpick grasshopper Tetrataenia surinama (L., 1764; Orthoptera: Acrididae) and the stag beetle Dorcus bucephalus (Coleoptera: Lucanidae) and calculated polynomial model fits describing the five strongest bites of each species as described above. We then quantified differences of these models with a principal component analysis (PCA) of the model coefficients. Additionally, a similar curve shape analysis of simulated data was run using the forceR workflow example (Supporting Information).

4 ASSESSMENT

4.1 Validation

4.1.1 forceX setup

forceX measurements that were drift-corrected and converted to force values through the forceR package reliably reflect the actual forces of the control weights (mean of absolute relative errors = 0.93%; SD = 1.42%; n = 1,609) across four orders of magnitude (Figure 3f). Depending on the input force and amplification settings, mean relative errors ranged from 0.021% to 2.24% with standard deviations between 0.19% and 3.15% (Supplementary Table 1). The log–log linear regression model had a statistically significant fit with a high explanatory value (p < 0.001; R2 > 0.999).

4.1.2 Maximum force values

Relative differences between known input forces and extracted forces of the force series simulations range between 0% and 0.00074%, resulting in virtually identical regressions of force over body mass (Figure S6).

4.1.3 Force curve shapes

The comparison of the five strongest bites of T. surinama (Orthoptera) and D. bucephalus (Coleoptera) show that T. surinama bites possess gently ascending and descending slopes and a short peak (Figure 3a), whereas D. bucephalus bites show more steep slopes and prolonged, plateau-like peaks (Figure 3b). As described above, we fitted polynomial models with six coefficients to the bite curves (Figure 3c,d). The PCA of these model fits revealed a tight cluster of the bites of T. surinama, separated by PC1 from the bites of D. bucephalus (Figure 3e). Bites I–IV of the latter form a cluster as well, while bite V of D. bucephalus lies in-between the clusters of the two species, and this bite indeed resembles the bites of T. surinama more than the others (cf. Figure 3a,b). The reflection of bite-specific curve shape differences in the PCA results implies that the model fits are sufficient descriptors and may be used for further statistical analyses of bite curve shapes. The PCA of the polynomial models of the extracted bite curves from the simulations corroborates this finding. Here, PC1 mainly codes for the position of the peak within the force curve (early vs. late peaks) and PC2 for plateau-like peaks vs. sinusoidal peaks (Figure S8).

5 DISCUSSION

In vivo closing force measurements with forceX are fast, accurate and reproducible, and do not harm the animal, allowing a subsequent release or repeated measurements of the same specimen. Custom parts of the standardized forceX setup can be readily 3D-printed or metal-turned, while the remaining parts are almost exclusively off-the-shelf components. The distance of the tip elements from each other can be altered by hand during the measurements to accommodate differently sized animals or to vary the gape angle. Additionally, tip elements of different thicknesses can be used to further increase the range of measurable taxa. This allows closing force measurements of a larger taxonomic range than previous setups. The whole assembly, including the microscope, power source and charge amplifier can be assembled within minutes, is independent of mains power, only weighs 1.4 kg/2.28 kg (3D-printed/metal-turned) and fits into a small, waterproof portable case (Figure S9).

The forceR package readily corrects time series for charge amplifier and baseline drifts, extracts maximum force values, identifies individual peaks and prepares the measurement data for further analyses by grouping information specimen- and species-wise. Our validation experiments showed that forces from 0.01–10 N can be reliably measured and drift-corrected, yielding not only information on the maximum bite forces but also providing digital peak curve shapes. Differences in these curve shapes can be quantified and statistically analysed. forceR accepts not only forceX measurements but continuous time series of all kinds.

We think that forceX in combination with forceR greatly improves the ability to measure closing force performance in a repeatable way. Additionally, its ease of use, reproducible components and fast assembly make its use widely accessible and appropriate for use in the field. We anticipate that it will help shed light on the micro- and macroevolution of performance in a wide range of taxa, particularly in the huge diversity of small insects and other arthropods.

AUTHORS' CONTRIBUTIONS

P.T.R. and A.B. conceived the setup and designed the metal-turned forceX version with the help of L. Leson and C. Kremer (see Acknowledgements); P.T.R. designed the 3D-printable forceX version, wrote the forceR package, collected and analysed the data, created instructions, figures and videos and led the writing of the manuscript. P.T.R. and A.B. contributed critically to the drafts and gave final approval for publication.

ACKNOWLEDGEMENTS

Leo Leson, Carlo Kremer (Central Workshops of the Department of Biology, University of Cologne), Michael Dübbert and Mehrdad Ghanbari (Group of Proffessor Büschges, University of Cologne) helped with the design and realization of both the electronics and mechanical parts of the setup. Zimai Li (Max Planck Institute for Chemical Ecology, Jena, Germany) is thanked for letting us introduce his technique to hold small specimens. PTR and AB were supported by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreement No. 754290, ‘Mech-Evo-Insect’) awarded to AB. AB was supported by the Feutsche Forschungsgemeinschaft (DFG) under the Individual Research Grants program (grant agreement no. BL 1355/4-1). We are grateful for helpful comments by Anthony Herrel on an earlier version of this manuscript. We thank Marc Jones and one anonymous reviewer for their constructive comments, which improved the quality of this manuscript.

    CONFLICT OF INTEREST

    The authors declare no competing interests.

    PEER REVIEW

    The peer review history for this article is available at https://publons.com/publon/10.1111/2041-210X.13909.

    DATA AVAILABILITY STATEMENT

    forceX CAD files for 3D printing and metal-turning and schematics of custom electronics, and assembly instructions are available at Thingiverse: https://www.thingiverse.com/peter_tr/designs/. The source code, documentation and vignette of forceR is available released on CRAN (Rühr, 2022). All data mentioned above, plus a bundled version of the forceR package at the time of publication, and all data and code to run validation tests and produce related figures, are available on Zenodo (Rühr & Blanke, 2022).