I've seen papers report source/received levels of animal vocalisation using three measures: rms, peak and peak-to-peak. Even within a field there doesn't always seem to be a single convention, and papers will report different measures for the same sound type (e.g. bat calls report with rms in one paper, and peak in another).
Can I convert between the measures, and how valid are these conversions?
Comparing dB values in inappropriate ways is likely to be the largest source of error in bioacoustics. Your question can be broken up in several subquestions:
A) What are the differences between the different metrics? Two references are useful, both for underwater acoustics, but applicable also to air: the ISO 18405 standard for underwater acoustics terminology, which is comprehensive, but not easy to read, and Madsen (2015), which is specifically about short pulses/transients. Peak-pressure ($\ p_{pk}$) or zero-to peak pressure ($\ p_{0-pk}$) is the maximum positive pressure of the signal and peak-to-peak pressure ($\ p_{pk-pk}$) is the difference between the maximum positive pressure and the minimum negative pressure. Many signals are symmetrical, in which case $\ p_{pk-pk}=2\times p_{0-pk}$, but this is not always the case. Root-mean-squared pressure ($\ p_{rms}$) is a time-averaged value, measured/calculated over some duration T (equal to the duration of the signal for short signals) and given as $\ p_{rms}=\sqrt {\frac {p^2 (t)} T}$
B) Can one convert from one to the others? The general rule is no. For pure sine wave signals only, $\ p_{pk-pk} = 2\sqrt 2\times p_{rms} $, or in dB notation $\ L_{pk-pk}=L_{rms}+9 dB $. For all other signals, one generally cannot convert in a simple way between the two measures. For noisy signals, the peak and peak-peak measures are poorly defined and not recommended.
C) How can different source levels be compared? Source level is the sound pressure level in front of an animal, normalized to some reference distance. For bats, this distance is 10 cm, for most other animals it ius 1 m, unless specified otherwise. This means that source levels not referenced to the same distance cannot be compared directly, but must be adjusted for the difference in reference distance, equal to a factor of $\ 20log_{10}(\frac {r_1} {r_2})$. To convert source levels measured at 10 cm to 1 m, 20 dB should be subtracted. Note also that because of the difference in reference pressure ($\ p_0$) between air and water ($\ 20\mu Pa$, vs. $\ 1\mu Pa$, respectively), source levels cannot be compared directly between air and water.
References
ISO 18405 Underwater acoustics - terminology.
Madsen, P. T. 2005. Marine mammals and noise: Problems with root mean square sound pressure levels for transients. The Journal of the Acoustical Society of America 117:3952-3957.
While with additional information, the three measurement can be related, there are three typical situations for these measures
rms: long signal that are best characterized by their energy or intensity (example: ambient noise)
p2p: short transients, where waveforms are asymmetric and no further processing is done (example: explosions)
peak: short transients, where processing is done to obtain the signal amplitude (example: amplitude function of cetacean echolocation clicks)
The three measurements are typically inter-convertible, though strictly speaking the inter-convertibility holds for sinusoidal sounds only (not always applicable to real-data). If we have a waveform X then
rms(X) = peak(X)/sqrt(2)
# 'rms' is the root-mean-square of all samples in X.
# 'peak' is the absolute maximum sample value of X.
and
peak-to-peak(X) = 2 x peak(X)
# peak-to-peak is the difference between the highest and lowest samples.
However, the actual choice of measurement to report depends on both the properties of the sound, and the field convention. For very short sounds that occupy that span only a few samples, it may not make sense to report an rms reading for example - where a peak measurement may be more representative. On the other hand, if you have longer sounds with occasional blips due to unavoidable background noise, an rms reading may provide a more stable readout of sound level.
Even if there is no broad convention, it may make sense to report the measurement/s of the papers that you'd like to compare your results with.
