We estimated detection distances with a standardized set of three prey types: a small insect (mealworm head on), as well as a small and a large moth with target strengths of −40 dB, −20 dB, and −5 dB, respectively [25], [26]
http://plosone.org/article/info:doi/10.1371/journal.pone.0002036#article1.body1.sec2.sec4.p1

Introduction.
In their brief explanation of the method used to calculate the detection distances of differently-sized insect prey, the authors of this paper have made a conceptual error which has led to incorrectly calculated results. This in turn, may have a bearing on the interpretation of the results and the conclusions drawn from them in the paper’s discussion.

Critique.
The authors evidently intended to calculate the detection distances of three size categories of insect prey for bats echolocating at different call intensities and different echolocation frequencies. However, rather than defining the three categories of insects using their size in terms of maximum planar cross-sectional area (CSA), the authors have chosen to categorize them in terms of target strength (TS). This is conceptually wrong as the TS of prey is affected by Rayleigh scattering in addition to prey CSA and is therefore, dependent on the frequency of ensonification. This is clearly seen in Fig. 1, which is a theoretical equivalent of the empirical data provided in Fig. 2a by Surlykke et al. (1999), (authors’ ref [25]). The empirical data in the latter reference evidently contains some degree of offset and experimental error.

Please view Figure 1 and Tables 1a, b, and c here: http://www.plosone.org/attachments/pone.0002036.kerry.pdf

From Fig. 1, it is clearly seen that if a constant TS line is drawn horizontally from the -20dB point on the y-axis, the equivalent CSA on the x-axis is different for each of the three frequency curves depicted. From this, we can conclude that the prey within each of the three TS categories proposed by the authors for calculating prey detection distances, are non-identical at each frequency (and for each bat). This is contrary to the intention of the authors as they specifically name one of the prey as being the ‘front-on’ cross-sectional-area of a mealworm, specifically indicating that the CSA of this insect (and by inference, that of the other two insects) was meant to be identical for each bat (and frequency) in the detection distance calculations. Fig. 1 clearly indicates that the sizes of prey are not consistent when identical TS’s are used for each frequency in the detection distance calculations.

In table 1b, I have calculated the effective CSA of the three prey TS’s (-40, -20 and -5dB) at each ensonification frequency, summarized in Table 1a, as specified by the author. Not only does Table 1b show the different effective CSA’s (and sizes) of the ‘same’ insect at different echolocation frequencies due to the effects of Rayleigh scattering, it also shows that the CSA of a mealworm only approaches a realistic ‘front-on’ CSA for this insect at higher ensonification frequencies. Although not specified by the authors, I additionally calculated the CSA of the mealworm at 100 kHz, which turned out to be 8.6 mm2. Assuming the ‘end-on’ CSA of the mealworm to be approximately circular in form, this equates to a mealworm diameter of 3.3mm, which approximates the diameter of mealworms with which I am familiar! For this reason, I have assumed for the calculations in Table 1c that the three TS categories used by the authors were obtained from three sizes (CSA) of prey at 100 kHz (although it is possible at a pinch that the authors used the TS values calculated at their highest reporting frequency of 70 kHz).

Detection Distance Modelling.
Table 1c presents the results of detection distance calculations based on the CSA of three sizes of insect prey, namely a mealworm with CSA of 8.6 mm2, a small moth of 105 mm2 and a large moth of 3162 mm2. The TS of each of these insects is different at each frequency due to their individual CSA’s and the frequency-dependent effects of Rayleigh scattering on target echoes. This is particularly evident in the detection distances calculated for the mealworm prey. Note that several of the detection distances calculated for the small mealworm CSA are very small, which may make them effectively invisible to some echolocating bats due to pulse-echo overlap. On the other hand, the Ts of the largest prey is similar for at all specified frequencies due to the reduced effects of Rayleigh scattering on large CSA prey.

The model used for calculating the detection distances in Table 1c differs from that typically used by others in that it does not treat planar targets as if they were spherical, which typically leads to over-estimation of distance for small and short-range targets. The model also accounts for the aperture of bat pinnae, which avoids additional over-estimation of distances for small and short-range targets. A conservatively sized pinna aperture (or CSA) of 113 mm2 was assumed for all species of bats addressed by this paper.

Conclusion.
The concept of using fixed values of TS instead of fixed values of CSA for any insect prey at different frequencies is erroneous as it ignores the effects of Rayleigh scattering and is equivalent to changing the size (CSA) of the ‘same’ insect for each bat echolocating at a different frequency. Consequently, the methodology employed by the authors for calculating detection distances of prey in this paper requires significant revision.

Some of the re-calculated detection distances using fixed values of CSA for the three categories of prey (and particularly for the mealworm), differ significantly from those calculated by the authors using fixed TS. Consequently, some of the statements made and conclusions drawn by the authors in their discussion may require revision.