## 2 Methods
second order derivative) of the frequency-time course of each call (RoC, expressed at kHz/ms\({}^{2}\)). The frequency-time course was calculated by measuring the frequency with peak amplitude from successive power spectra taken throughout the call. Each power spectrum was calculated from a zero-padded 1024-point FFT of successive 128 \(\upmu\)s portions of the call. Each successive power spectra overlapped the previous one by 80% (102.4 \(\upmu\)s) giving a resolution in the frequency-domain of 1.6 kHz. The frequency with maximum amplitude of each power spectrum was used to mark out the frequency-time course of the call. The seventh parameter was a standardised bandwidth measurement, taken from a normalised version of the power spectrum calculated to measure frequency with maximum energy of the call. Standardised bandwidth was defined and measured as the bandwidth of the call at 80% of the maximum amplitude. A high bandwidth measurement denotes a relatively broad spread of energy across the echolocation call while a low value energy focused into a narrow range of frequencies. The next four parameters measured the distribution of energy across an echolocation call. Each call was subjected to a Hilbert transform [35] and multiplied by its conjugate; the output was normalised between zero and one. The resulting signal was separated into four quartiles, and the sum of each quartile's amplitude was divided by the sum of the signal's total amplitude. This gave the energy each quartile contained expressed as a proportion of the call's total energy. The final parameter was a discrete variable that categorised calls into one of three previously described types [36] and one devised by us: constant frequency (CF), frequency modulated (FM), quasi-constant frequency (QCF), and kinked (K). Kinked calls were characterised by having a sudden decrease in frequency in the final quarter of the call. This degree of frequency modulation was calculated by comparing the initial peak frequency, and the final peak frequency of the quarter. If the degree of modulation was above a threshold of 6 kHz, and the first quarter of the call did not contain a positive frequency modulation (indicative of a call from _Rhinolophus_ sp. ), then the echolocation call was classed as kinked. If a kink in the last part of the call was not present, the call was checked for constant frequencies. This was done by checking if the start and end frequency of the call were both less than the centre frequency of the call (indicative of a call from _Rhinolophus_ sp.). If this category was rejected, the call was then tested for frequency modulation. FM calls were defined as having a relatively constant rate of change in frequency. Rate of change was calculated as the mean second-order derivative of a 1\({}^{\text{st}}\) order polynomial fitted to the start, centre, and end frequencies of the call. Calls whose rate of change was less than 0.2 were classified as FM. Calls not fitting any of the above categories were classified as being QCF. The extracted parameters were tested for normality in SPSS (SPSS Inc., Chicago IL) using a Shapiro-Wilk's W test and were not normally distributed. Therefore all extracted parameters are expressed as medians \(\pm\) interquartile ranges. For the purpose of comparison with other studies, the five base parameters were also summarised as mean \(\pm\) one standard error (SE). Call parameters were classified to genus and species using three classification algorithms: DFA (quadratic with cross-validation), SVM, and ENN. DFA is relatively robust to deviations from normality, which are likely to reduce performance slightly [37]. Examination of the covariance matrices showed that they were heterogeneous and transformation of the data did not reduce heterogeneity, nor did it reduce deviation of the data from normality. Therefore, quadratic discriminant functions were calculated in all analyses [37], using untransformed data.