Auditory processing at two time scales by the cricket Gryllus bimaculatus

Robust object recognition is a primary goal of sensory processing (Barlow, 1961). The evaluation of multiple cues not only removes ambiguities, but also provides enhanced certainty about the identity and quality of a given object. A potential benefit of using multiple cues is that highly selective responses can arise despite broad tuning of single filters in a processing cascade (Schüch and Barth, 1990). In acoustic communication systems where signals serve mate attraction, the cues encoded in syllables and phrases are typically distributed over several time scales, as, for instance, in the songs of birds or in human speech. The acoustic signals of many insects [grasshoppers, bushcrickets, crickets and cicadas (Gerhardt and Huber, 2002)] also provide cues on several time scales by grouping pulses into chirps. Acoustic signalling by crickets provides one of the simplest perceivable cases of all, as many species produce series of largely identical events (pulses) that are broadcast in pulse trains [chirps (Huber et al., 1989)]. By separation of time scales, cricket songs emit short-scale cues, such as the pulse periodicity, and large-scale features, such as the duration or period of chirps (Pollack, 2000). For the perception of both time scales, filter functions are known (Schildberger, 1984; Doherty, 1985a; Hedwig and Poulet, 2004; Hennig et al., 2004; Hennig, 2009). Activation of both filters and thus both time scales is important in crickets, although activation of a single filter may in some cases suffice to elicit positive responses by females (Tschuch, 1977; Hennig, 2009). To understand how information from both time scales is fused, the response properties of both filters as well as the integration process have to be known. Past research has focused on the pulse filter on the short time scale (Schildberger, 1984; Poulet and Hedwig, 2005; Hennig, 2009; Doherty, 1985a), and the response profile of the chirp filter on the long time scale is only partly known (Doherty, 1985a; Doherty, 1985b). In particular, information about the crucial cues for the detection of a chirp pattern from the available temporal parameters, chirp duration, pause, period or duty cycle, is not sufficient. Knowledge about the combination rules for fusing information from two different time scales towards song recognition is also required to better understand the decision process underlying phonotactic orientation.

Here we performed phonotactic experiments with female crickets in order to determine the response profile of the chirp filter. By combination of different pulse and chirp patterns in a single stimulus we examined the effectiveness of single time scales and possible interactions between the short and the long time scale. By using sinusoidal stimuli composed from two modulation frequencies, we determined the robustness of the detection process against masking levels, and by introduction of phase changes we investigated whether processing on the long time scale of the chirp filter takes place in the time or frequency domain (Schmidt et al., 2007; Hennig, 2009).

Gryllus bimaculatus De Geer 1773 were taken from a laboratory stock or obtained as nymphs from a commercial supplier (Das Futterhaus, Berlin, Germany) and females were raised to adulthood in isolation from males. Males and virgin females were tested from one week after their final moult. The experiments performed comply with the regulations of the National Institutes of Health (publication no. 86-23), and with the current laws of Germany.

Song models were generated digitally by multiplication of a given signal envelope with a sine wave (4.5 kHz) using LabView Software (National Instruments, Austin, TX, USA). Envelopes of rectangular stimuli were generated from a series of pulses and pauses with rise and fall times of 1 ms. Envelopes of sinusoidal stimuli were constructed by addition of sine waves. The resulting waveform was normalized to the maximum such that the signal envelope varied between zero and 1. When introducing phase changes, the envelope for some stimuli was shifted in time to ensure zero levels at the beginning (Hennig, 2009). Further patterns resulted from the addition of two sine waves at different frequencies. Note that typical beat patterns did not become apparent in these experiments, as the frequencies used were very different (Yost, 2000). A waveform similar – but not identical – to a beat pattern was generated when the amplitude of a given frequency (center frequency: f_c=25 Hz) was amplitude modulated with a modulation frequency (f_m) of 3 Hz (Yost, 2000). The spectrum of such a stimulus consists of three frequencies: f_c and two side frequencies at half the amplitude of f_c (f_c+f_m and f_c–f_m). If the phase for all three frequencies is kept at zero, the stimulus is amplitude modulated. A shift of the phase of f_c produces a frequency-modulated pattern at almost constant amplitude.

Behavioural tests were performed on a locomotion compensator (Kramer treadmill) (for details, see Weber et al., 1981; Hennig, 2009) in an anechoic chamber at 25±2°C. Experiments were conducted in the dark except for the infrared light used to monitor the movements of the cricket. Crickets were placed on top of a sphere, and were free to walk but were kept in place by compensatory sphere rotations while song models were presented from loudspeakers in their horizontal plane. The rotations of the sphere were monitored by displacement transducers. After sampling their output signal by an AD board (PCI-6221, National Instruments), the walking velocity and virtual track of the insect were calculated.

During a test session, the digital song signals were converted to an analogue signal (16 bit, 100 kHz, PCI-6251, National Instruments), adjusted to a chosen intensity via a digitally controlled attenuator (PA5, Tucker Davis Technologies, Alachua, FL, USA), amplified (Tucker Davis) and broadcast via one of two loudspeakers (Piezo horn tweeter PH8, Conrad Electronics SE, Hirschau, Germany) separated by an angle of 90 deg. Signal amplitude was calibrated with a condenser microphone (Brüel & Kjær Type 4133, Nærum, Denmark) and a measuring amplifier (Brüel & Kjær Type 2231). Sound measurements were obtained 0.5 cm above the sphere, with the microphone directed towards the loudspeaker. Sound intensities were 80±2 dB SPL (re. 2×10^–5 Pa r.m.s., fast reading).

Females were tested with acoustic stimuli presented for 100 s from each loudspeaker consecutively. A control stimulus, similar to the calling song of males, was presented at the beginning and also the end of each session to control for a change of motivation (positive control). Female crickets were tested with four to seven test stimuli in each session (25 to 40 min). Further controls included the presentation both of continuous unmodulated tones at 4.5 kHz as well as silent intervals for 100 s, in order to obtain measures for baseline activity of individual females [negative control (see Hennig, 2009)]. For each walking track, the walking distance (d), vector length (L) and angle towards the loudspeaker (γ; after correction for the respective loudspeaker position) was calculated and referenced to the measures of the walking track obtained for the initial control stimulus according to the following formula (for details, see Schul, 1998): relative phonotaxis_test=(d_test/d_control)×L_test×cos|γ_test–γ_control|.

The value of relative phonotaxis for the first presentation of the positive control was therefore the value of the vector length; crickets typically achieved scores of 0.8 (Schul, 1998; Hennig, 2009). Test sessions in which the response to the final control was more than 20% below that of the first control or in which the responses to continuous tones or silent intervals serving as negative controls was higher than 0.2 were excluded from the data set. Data from 20 to 90 females per test program are given as means ± s.d.

Statistical analysis was performed with the values of relative phonotaxis obtained for individual females for a particular test or control stimulus. In most but not all cases, the scores of relative phonotaxis were normally distributed. Therefore, a non-parametric test was chosen – the Friedman test (a non-parametric repeated-measures ANOVA) with a Dunn’s post test – considering multiple tests of individual females in different test series, and performed using GraphPad InStat 3 (GraphPad Software, La Jolla, CA, USA). For all test series, the relative phonotactic scores for the positive control (first and last control pattern in a test series) were not significantly different from one another. Equally, there was no significant difference between the two negative controls (the silent and continuous tone control). Three classes of attractiveness emerged for all test patterns: (1) female responses were not significantly different from the positive control, (2) female responses were not significantly different from the negative control or (3) female responses were different from both positive and negative control types, indicating intermediate attractiveness. In Figs 1, 2, 3, these three classes are indicated by shaded boxes and were usually separated at phonotactic scores of 0.3 and 0.6.

Males were placed in a setup equipped with 16 microphones (Conrad TCM141, Vivanco MA222 preamplifier, Conrad Electronics SE), each of which recorded the song of an individual male. Males were kept in glass jars and separated acoustically by boxes (0.2×0.2×0.2 m) lined with sound-absorbing foam. During one recording session (8–12 h), singing males were detected using LabView 7.0 (National Instruments) and the microphone signal of singing males was automatically sampled to the hard disk of a computer at 100 kHz (PCI 6221, National Instruments) for a duration of 20 s. For each singing male, five such song sequences were recorded during one session at a temperature of 25±2°C.

For analysis of the song pattern, the envelope of the recorded signal was calculated as the root mean square (r.m.s.) over a time window of 4 ms, equivalent to the observed lower limit of temporal resolution of female crickets (Schneider and Hennig, 2012), and the resulting envelope of a song sequence was normalized to its peak value. Further analysis was performed with a supervised program that detected pulses automatically by means of an adjustable threshold. Pulse and pause durations of all recordings were computed for a threshold set at 35±5% of the maximal value. The relatively high threshold was chosen to avoid distortion of measured pulse and pause durations by gaps and masking pulses. However, this procedure affected the measures of the chirp parameters, but by less than 5%. Recordings were taken from 46 males and for each male between 90 and 200 chirp sequences were analyzed.

The goal of the first series of experiments was to determine which relevant cues females extract from the long time scale of the chirp pattern. Which range of the parameter space is acceptable for female crickets and are there invariant responses in the temporal domain? Stimuli were constructed from trains of pulses with a fixed pulse period of 40 ms presented at a constant duty cycle of 0.5. Two features describe the periodical chirp pattern completely: chirp duration and chirp pause (Fig. 1A, inset). The chirp duration of a pattern was changed by variation of pulse train duration. Chirp period and chirp duty cycle emerged as further temporal cues from these two parameters. Chirp period was defined as the time from the beginning of a chirp to the beginning of the next chirp (Fig. 1A, inset). Chirp duty cycle was defined as chirp duration divided by chirp period (Fig. 1B, inset) and served as a measure for sound energy over time. By variation of the chirp period, a consistent preference of females and a good match with the chirp period of male songs was obtained (Fig. 1A). For chirp duty cycles between 0.3 and 0.7, a single optimal range of chirp periods in the range between 200 and 500 ms was observed (Fig. 1A). This range overlapped with the distribution of chirp periods in male songs (mean ± s.d.=363.4±86.1 ms, N=46). Interestingly, this response optimum was still recognizable for stimuli without any pulsed structure at all (Fig. 1A, filled circles). Variation of the chirp duty cycle at different chirp periods also revealed a single optimal range between 0.3 and 0.7, provided the chirp period was between 200 and 500 ms (Fig. 1B). However, the energy of male songs as indicated by their chirp duty cycles (mean ± s.d.=0.30±0.06, N=46) was between 0.2 and 0.4 and thus at the lower edge of the preference function of females (Fig. 1B).

In a further step, we determined the minimal values for chirp duration and chirp pause that were required for the detection of a chirp pattern. In one test series, the number of pulses in a train was increased from one to three pulses for different chirp periods and led to an increase of chirp duration from 20 ms (one pulse) to 100 ms (three pulses). The response of females was lowest for patterns with a single pulse (Fig. 1C, triangles), either because the activation of the pulse filter was insufficient or because the mimicked chirp duration was too short. For patterns with two or three pulses, the response scores increased (Fig. 1C). In this test series, the response of females depended on the duty cycle of the test patterns, as the response scores for these stimuli overlapped with the previously determined functions for variation of the duty cycle (grey lines in Fig. 1C were redrawn from 1B for comparison). In a second test series, the minimal pause required for the detection of the chirp pattern was determined. The response of females increased for pause durations of 40 to 80 ms (Fig. 1D). Chirp pauses below 40 ms were in the range of a single pulse period and were not effective. As for short pulse trains, the response depended on the duty cycle of the pattern, because the scores of females again coincided with the data obtained previously (Fig. 1B,D). In conclusion, female crickets evaluated the chirp period and the chirp duty cycle of a pattern as the most consistent cue over a wide range of chirp durations and chirp pauses (Fig. 1). The limits for detection of a chirp pattern (minimal chirp duration and minimal chirp pause) were not of a fixed minimal value, but depended on the duty cycle.

The filter functions for detection of the correct pulse and chirp patterns operate on different time scales. Conceptually, these filters may be viewed as independent entities and the combination of their outputs would determine the attractiveness of the overall pattern as measured by phonotactic scores. To explore whether the tuning of the chirp filter depends on the value of the pulse period with which the chirp duration was filled, females were tested with similar stimuli as above, but with different pulse periods. At pulse periods of 20 or 66 ms, both presented with a pulse duty cycle of 0.5, crickets exhibited mostly low response scores (Fig. 2). Intermediate response scores were only obtained for a chirp period of 333 ms and a chirp duty cycle of 0.5 at a pulse period of 20 ms, which corresponded to the preferred chirp parameters (Fig. 1A,B).

The extensive data sets obtained for variation of chirp parameters allowed the construction of the response profiles of the chirp filter for the different pulse periods tested (Fig. 3). For a pulse period of 40 ms, the best responses were observed for chirp and pause durations between 0.1 and 0.4 s at duty cycles between 0.3 and 0.7 (Fig. 3A). At longer pause durations, the response scores of female crickets were reduced, but at longer chirp durations the responses still remained at an increased intermediate level. At unattractive pulse periods, the responses dropped to low levels (Fig. 3B,C). For a pulse period of 20 ms (Fig. 3B), a small increase of responses was observed in the same range as for a pulse period of 40 ms (Fig. 3A). For a pulse period of 66 ms, the responses remained low for all tested combinations of chirp and pause durations (Fig. 3C).

The goal of the second series of experiments was to evaluate the relative importance of the temporal parameters on different time scales. For these tests, stimuli were designed in which the chirp rate was kept at a particular value between 1 chirp s^–1 (equivalent to a chirp period of 1000 ms) and 7 chirps s^–1 (143 ms). For each chirp rate, the pulse rate of the pattern was systematically varied between 15 and 50 pulses s^–1 (equivalent to pulse periods of 66 and 20 ms, respectively). The duty cycle of those patterns was kept at 0.5 for both the pulse and the chirp pattern. Stimuli without a chirp structure (0 chirps s^–1) and without a pulse pattern (0 pulses s^–1) were also tested (Fig. 4A,B,F).

The pulse filter was tuned to 25 to 30 pulses s^–1 if the chirp rate was kept at 3 chirps s^–1 (Fig. 4A). Notably, the response of female crickets to a chirp pattern of 3 chirps s^–1 without pulse trains (0 pulses s^–1; arrow in Fig. 4A) was higher than to a pattern with the same chirp rate but an unattractive pulse rate of 16 pulses s^–1 (see level of dashed line in Fig. 4A). This finding indicated a suppression of the response of females to an attractive chirp rate by the unattractive pulse rate. The same phenomenon was observed for variation of the chirp rate (Fig. 4B). For the attractive pulse rate of 25 Hz, the response function encompassed a wide range of accepted chirp rates. However, the response to continuous pulse train without chirp structure (0 chirps s^–1) was higher than the response to an unattractive chirp rate of 7 chirps s^–1 (see arrow and level of dashed line in Fig. 4B). This finding suggested that unattractive chirp rates also inhibited the response to otherwise attractive pulse rates.

The previous section indicated an inhibitory interaction of the two filters for the pulse and the chirp pattern. How then are the responses of the pulse and chirp filters integrated and weighted over the short and long time scales? In a basic scheme of serial processing, incoming pattern information would be processed first by one filter (pulse) and then by the second (chirp; see Fig. 4C). In this case, the output of the pulse filter would provide the input pattern for the chirp filter. The reversed scenario appears unlikely, because the chirp filter would then remove information about the short time scale on which the following pulse filter operates. In a parallel processing scheme, the respective outputs of pulse and chirp filter can be integrated by a neuronal detector equipped with a particular threshold for activation (Fig. 4D). Present evidence suggests that the pulse and chirp filter can exert an inhibitory influence on either the output of the opposite filter or the hypothetical detector neuron (Fig. 4A,B).

In the case of parallel processing, there are two possible scenarios of output integration on different time scales: a logical AND operation will require the output of both filters, whereas in the case of an OR operation only one of the filters would suffice. To examine these two possibilities, the data were plotted in a response profile for the different rates of pulses and chirps per second (Fig. 4F). Fig. 4E indicates the predictions of the response profile if an AND or an OR operation is performed by the integration of time scales. The shape of the profile does not support an OR operation for the fusion of time scales in the auditory pathway of crickets, because high level responses at low pulse or chirp rates were not apparent (Fig. 4F). A strictly binary AND operation was also not visible, as females responded with intermediate levels if either of the two filters was activated (raised responses at zero levels of pulse and chirp rates; Fig. 4F).

To test whether individual females can be categorized into different types of integration or weightings of filter input, females were tested with a basic set of stimuli: pulse pattern with best pulse period, 40 ms (equivalent to 25 pulses s^–1); chirp pattern with best chirp period, 333 ms (equivalent to 3 chirps s^–1); and combined best pulse and chirp period (see Fig. 5A) on different days repeatedly. Fig. 5A shows the mean responses of all females to the respective stimuli and confirms the results shown in Fig. 4. In Fig. 5B, the mean response of individual females that were tested repeatedly was plotted with their response to the sole pulse and chirp patterns. Individual females were tested between three and six times on different days. If females fell into different groups according to their type of integration, response clusters at the lower left (AND – operation) or upper right (OR – operation) were expected in Fig. 5B. However, mean responses of females were distributed over the whole range of score values (Fig. 5B). Responses of females also exhibited considerable variability between different days of testing, as standard deviations varied between 0.1 and 0.3 for responses to the pulse as well as the chirp pattern. Best responses by female crickets were only obtained if both filters and thus both time scales were activated (Fig. 5A), although singular activation may in some cases suffice to elicit high scores (Fig. 5B). A regression analysis over the mean of all females should reveal a slope near 1, if the responses of females were separable according to their operation types (AND, OR). However, the upward sloped regression was not significant (P>0.11; Fig. 5B). Clearly no clusters of responses and thus also no separable types of females were observed.

In the previous sections, the response profile of the chirp filter (Fig. 1) and its interaction with the pulse filter (Figs 2, 3, 4, 5) were described. Although both filters cover different time scales, it is also possible that the tuning and the phenotypic properties of the chirp filter originate from properties of the pulse filter, for example by a long time constant of the pulse filter. Alternatively, if processing on long time scales is in part rooted in the frequency domain, the profile of the chirp filter may arise as an emergent property of processing on short time scales. For instance, the addition of similar modulation frequencies will produce an amplitude-modulated pattern in the time domain. In the frequency domain, however, such a pattern will reveal a center frequency with two side peaks of different amplitudes only in the high but not the low frequency range (Yost, 2000). Present evidence does not support processing in the frequency domain for the pulse filter (Hennig, 2009). However, it is still conceivable that the pulse filter may respond to high modulation frequencies that are typical for such an amplitude-modulated pattern and thus produce a response similar to the output of the chirp filter. To test this hypothesis, female crickets were tested with patterns constructed by the addition of sine waves. Because of the continuous nature of the stimuli, it was possible not only to control for emergent properties between different time scales, but also to describe the robustness of pattern detection against masking by reduced modulation depth.

In the first set of experiments, a basic stimulus was generated by the addition of two modulation frequencies at the same amplitude: 3 Hz, equivalent to a chirp period of 333 ms, and 25 Hz, equivalent to a pulse period of 40 ms, to which female crickets responded well. However, the stimulus envelope did not contain clear pauses between chirps, but showed a continuous modulation of pulse amplitude (see pattern 1 in Fig. 6). Female crickets responded to such a pattern with high scores (Fig. 6). For further tests, one modulation frequency was kept constant, while the other was varied (see patterns 2 and 3 in Fig. 6). The responses of females showed tuning curves for the particular modulation frequencies known from the present and earlier studies, despite the reduced modulation depth of all stimuli (Fig. 6). At the optima (3 and 30 Hz in Fig. 6), the respective response scores were also high and showed that both the pulse and the chirp filter were activated by these stimuli. If only a single modulation frequency was presented in the low or high frequency range, the responses were reduced, similar to the results obtained above [grey lines in Fig. 6; cf. fig. 6 from Hennig (Hennig, 2009)]. The responses dropped to low levels when intermediate modulation frequencies were mixed with attractive modulation frequencies (e.g. 10 Hz added to 3 or 25 Hz; see patterns 2 and 3 in Fig. 6). Because the scores to these patterns were lower than the response to the attractive modulation frequency alone (1′ or 1″ in Fig. 6), this observation also suggested an inhibitory influence on the mechanism of pattern detection.

In a second series of tests, an amplitude-modulated pattern was produced by the addition of three neighbouring modulation frequencies (patterns 1–3 in Fig. 7). The spectra of such stimuli revealed a center frequency (f_c) with two side bands at half amplitude with a frequency difference of d_f (Fig. 7) and a constant phase of 0 deg. By varying d_f, a chirp-like pattern with trains of pulses of varying amplitude was produced (patterns 1–3 in Fig. 7). The frequency difference d_f corresponded to the period of the slow-amplitude modulation observed in the time domain. It should be noted that the mean of the amplitude distribution of these patterns was at 0.5 and consequently the sections between apparent chirps were not silent but filled with the carrier frequency. Female crickets responded to such patterns with high scores, if the center frequency f_c was at 25–30 Hz and the beat frequency was between 3 and 4 Hz (open circles in Fig. 7; see for example pattern 2). In Fig. 7, the data from previous experiments are indicated by grey lines that show the responses to single modulation frequencies in the low and high frequency range (Hennig, 2009). The responses to sinusoidal patterns with a single modulation frequency and clear, unmodulated pauses between pulse trains (chirps, see pattern 4 in Fig. 7) are also shown as grey line with small black squares (Hennig, 2009). By comparison, responses to a beat pattern with a center frequency of 25 Hz and side bands at a d_f of 3 Hz (pattern 2 in Fig. 7) revealed similar best responses at 25–30 Hz as the scores for a sinusoidal pattern with clear pauses between chirps. For sinusoidal pulse patterns, only the high-frequency cut-off was at a lower modulation frequency (pattern 4 in Fig. 7). In part, this difference in the tuning of the responses may be due to the clear (pattern 4) and filled pauses (pattern 2 in Fig. 7) between chirps. Beat patterns also elicited higher response scores than single modulation frequencies (grey lines in Fig. 7), indicating that both the pulse and the chirp filter in the auditory pathway of female crickets were activated. In the frequency range below 10 Hz, stimuli were constructed by a constant center frequency of 25 Hz and by variation of the sidebands d_f. Responses of females revealed a broad range of accepted patterns between 2 and 5 Hz (patterns 1 and 2, Fig. 7), similar to the data shown in Fig. 4.

The construction of stimuli by modulation frequencies requires two parameters for each frequency: their amplitude and their phase relative to other frequencies. By sole variation of phase it is possible to leave the amplitude spectrum unchanged, but to vary the temporal pattern. It is then possible to distinguish between processing in the frequency and the time domain. If females respond to changes in phase, they process the patterns in the time domain. If females are insensitive to variation in phase, processing in the frequency domain is likely. For the beat patterns 1–3 used in Fig. 7, the phase of the center frequency f_c was now shifted by 90 deg, which left the amplitude spectrum unchanged but led to patterns with a continuous series of pulses rather than groups of pulses (patterns 2′ and 3′ in Fig. 7). The introduced phase difference thus changed the stimulus from an amplitude-modulated pattern to a frequency-modulated pattern, as the pulse period wobbles around the period of the center frequency f_c with only a minor amplitude modulation (patterns 2′ and 3′ in Fig. 7) (Hartmann, 1997; Yost, 2000). On average, the response of females to such stimuli (open squares in Fig. 7) dropped to the same level as the responses to patterns with single modulation frequencies and also revealed the same tuning. Therefore, these responses indicated that only the pulse filter of female crickets was activated and that female crickets operate in the time domain, because the response was reduced when the phase of f_c was changed. Also, the scores of females for patterns with modulation frequencies lower and higher than 25 Hz was reduced below the response to the activation of the chirp filter alone (see dashed line in Fig. 7). As before, this reduction indicated an inhibitory effect of unattractive modulation frequencies (see Figs 4, 6).

Although at the population level of all females tested a significant reduction in the response to stimuli with a changed phase of f_c was observed (Fig. 7), there were remarkable differences in individual responses (Fig. 8A). Some females showed a tuning to the center frequency just as for stimuli with a chirp-like structure, whereas others remained at low response scores for all center frequencies. Intermediate response levels were also observed (Fig. 8A). To directly compare the responses of females to the two patterns with a center frequency of 25 Hz, but different phases, the individual scores to these patterns were plotted versus the response to the attractive control pattern constructed from rectangular pulses with a chirp-like structure (Fig. 8B,C). For a pattern with a phase of 0 deg (pattern 2 in Fig. 7), all females revealed high scores, whereas for a pattern with a phase of 90 deg the scores were distributed from low to high attractiveness (Fig. 8B). Some of these females were also tested with a pattern that contained only a single modulation frequency of 25 Hz (Fig. 8C) that corresponded to a continuous pulse pattern as tested previously (Fig. 4). Four females with low response scores to a continuous modulation frequency of 25 Hz showed an AND-type response, as they also exhibited low scores to a modulation frequency of 3 Hz (encircled AND-range in Fig. 8C). Two of three females with high response scores corresponded to the OR-type, as they showed high scores to a modulation frequency 3 Hz (encircled OR-range in Fig. 8C). Conceptually, those females that exhibited low scores for patterns with a phase of f_c of 90 deg appeared to operate in the time domain, whereas females with a high score seemed to operate in the frequency domain. However, this discrepancy is explained by the previously observed range of responses to continuous pulse trains and to patterns with pulses grouped in chirps (Fig. 5). On average, the same reduction of scores occurred when the pattern was changed from a chirp-like pattern to a continuous pulse train (Fig. 5A, Fig. 7; compare responses to patterns 2 and 2′). Similarly, individual responses to continuous pulse trains varied between low and high scores (Fig. 5B, Fig. 8). From the perspective of parallel processing, the females that appeared to process the pattern in the frequency domain (Fig. 8C) corresponded to the OR-type, as the activation of the pulse filter alone sufficed to elicit positive phonotaxis. In that sense, for these females, both descriptions are equivalent: in the frequency domain, the phase responsible for the chirped beat pattern was not important; in the time domain, the activation of the chirp filter was not required by an OR-type female. However, the mean response of all females was reduced if the phase of f_c was changed (Fig. 7) or if the chirp pattern was not present (Figs 4, 5). Therefore, by their mean response, female crickets indicated processing in the time domain both by the pulse and the chirp filter.

The first goal of the present study was to determine the crucial cues in the time domain that are required for a response of the chirp filter. The response profile of females showed that the chirp filter was activated over a range of chirp and pause durations (100–400 ms; Fig. 1, Fig. 3A). This area of responses to chirp periods between 200 and 500 ms was limited by the duty cycle that also set the limits of activation for short chirp durations and pause durations (Fig. 1C,D, Fig. 3A). The duty cycle is therefore the crucial cue for detection (Fig. 1C) and separation (Fig. 1D) of chirps. The chirp profile showed that the chirp duty cycle and the chirp period emerged as the most important cues for detection of the chirp pattern (Figs 1, 3).

Over the range of combinations of chirps and pause durations measured (up to 1000 ms), there was a distinct reduction in phonotactic response for long pause durations, but for long chirp durations the responses of females remained at an elevated level (Fig. 3). Interestingly, the signals of males did not extend into that range of the chirp filter (Figs 1, 3) (Ferreira and Ferguson, 2002). The observed range of responses encompassed the previously described preferences for chirp period (Wendler, 1990; Trobe et al., 2011; Doherty, 1985a). The response of a bushcricket to variation of verses (chirps) on the long time scale revealed a similar response profile but was tuned to a higher range of chirp periods between 4 and 16 s (Deily and Schul, 2009). Similarly to G. bimaculatus, this species of bushcricket requires a pattern with amplitude modulations on two time scales, but at a higher modulation depth of in excess of 18 dB between chirps (Deily and Schul, 2009). For the cricket G. bimaculatus, a modulation depth of 50% (6 dB) was still sufficient to extract the periodical signals from a masking background, regardless of whether there was a pulse modulation (Fig. 6) or a continuous sound level (Fig. 7). Such a robustness of the pattern processing network for periodical signals is remarkable, as noise in the frequency range of the relevant signal is known to be most detrimental for the detection of song patterns in grasshoppers (Ronacher et al., 2000; Ronacher and Hoffmann, 2003; Ronacher et al., 2004).

Given the large amount of data on both the pulse (Schildberger, 1984; Hedwig and Poulet, lr2004; Hennig, 2009) and the chirp filter (Tschuch, 1977; Doherty, 1985a), the following section summarizes the commonalities and the differences between the two filters. Both filters operate in the time domain (Fig. 7) (Hennig, 2009) and exhibit bandpass properties for period duration if the duty cycle of a stimulus is kept constant at 50% (Fig. 3) (Schildberger, 1984; Hennig, 2009). Best tuning is observed with a difference of approximately one order of magnitude: 30–40 ms for the pulse filter, and 300–400 ms for the chirp filter (Figs 1, 3). However, the response profiles differ: the pulse filter exhibits a tuning to the pulse period and is limited by the duty cycle (Tschuch, 1977; Hennig, 2009), whereas the chirp filter exhibits mostly a duty cycle preference over a various combinations of durations and pauses (Fig. 3). The limitation by the duty cycle sets the different limits of temporal resolution for both filters: 4–8 ms for the pulse filter (Marsat and Pollack, 2004; Sabourin et al., 2008) and ca. 40–80 ms for the chirp filter (Fig. 1D). The integration time also differs by one order of magnitude between both filters. Although three pulses equivalent to a time of 100 ms are required for the pulse filter to be activated, the chirp filter has an integration time of 1–2 s (Poulet and Hedwig, 2005). Both profiles have a sustained level of responses at high duty cycles given by long pulse or chirp durations in common (Fig. 3) (Hennig, 2009). Both filters reveal the same robustness to different modulation depths and are activated at masking levels of 50% [6 dB (Pollack, 1988)], which is similar to levels known from bushcrickets (Schul and Fritsch, 1999) and has also been observed in grasshoppers (Helversen et al., 2004). The sharpness of tuning as measured by the Q-value (best frequency divided by the bandwidth at the 50% level) is moderate but similar for both filters. The pulse filter reached values of ca. 1.0 at Q_50% and the chirp filter Q_50%-values between 0.5 and 1.0 (Fig. 4).

Given this long list of filter attributes, there are remarkable commonalities between the two filters, except for minor differences in the response profile. The major difference between both filters is one order of magnitude with respect to the time scale on which they operate, their temporal resolution and their integration time. Do these phenomenological commonalities indicate a common neuronal basis for both filters or even that the properties of the chirp filter emerge from the pulse filter? On present evidence it appears unlikely that the chirp filter phenotype emerges from a pulse filter property, because neither the Fourier-based analysis suggested that (Fig. 7) nor was the observed integration time constant over consecutive pulses (Fig. 1C) of sufficient duration to suggest such a scenario. Nevertheless, in terms of neurons, both filters may well share a common basis, but employ different neuronal properties (e.g. network properties for short time scale, synaptic weights for long time scale). It is thus not excluded that resonant properties may contribute to filter properties on the long time scale [see also resonant properties of the pulse filter in a bushcricket (Bush and Schul, 2006)].

In the simplest scenario, the outputs of both filters are combined in an all-or-none manner. If both filters are activated above threshold, a hypothetical detector neuron would respond and ultimately initiate positive phonotactic orientation (Fig. 4C, D). Indeed, the response profile of female crickets suggested such an AND-operation, because both filters had to be activated (Figs 3, 4, 6, 7) (Doherty, 1985a; Hennig, 2009). The distribution of individual preferences (Fig. 5B) suggested a continuum between females in terms of threshold, although the pulse filter revealed a lower threshold (or higher gain) on average (Fig. 5A). For single tests or single individuals, a response to activation of either filter alone was also observed (Fig. 5B, upper right corner; Fig. 8) and has been reported previously (Tschuch, 1977; Thorson et al., 1982; Hennig, 2009). For those cases, the integration process would correspond to an OR-type operation.

Several experiments suggested that there are inhibitory effects of both filters if unattractive signal ranges were presented (Figs 4, 6, 7). The output of the pulse filter to unattractive pulse periods (66 ms) reduced the response level below the activation obtained for the chirp pattern alone with unmodulated structure (Fig. 4A,B, Figs 6, 7). Conversely, the response to attractive periods was reduced if an unattractive chirp period was presented (Fig. 4A). At the level of processing of carrier frequencies by interneurons, a suppression of responses is known for different carrier frequencies (Stumpner, 1997). However, at the level of pattern processing, there do not appear to be many examples for which such an inhibition of responses to unattractive features of a song pattern was described. A notable exception is gap detection in female grasshoppers (von Helversen and von Helversen, 1997; Ronacher and Stumpner, 1988). Recent reports about the receptive fields of visual interneurons showed that a broadly tuned inhibition serves to sharpen response profiles by changing the balance between excitation and inhibition (Xing et al., 2011; Isaacson and Scanziani, 2011). Similarly, the observed suppression of responses for the pulse and the chirp filter may serve to sharpen the response profiles of both filters by a broadly tuned inhibition.

In summary, the female crickets fuse the two time scales by a weighted AND-like operation of two modules, the pulse and the chirp filter. Processing on the long time scale therefore forms an important and integral part in the discrimination of acoustic signals that serve to maintain isolation between different species of crickets.

We thank Jan Clemens, Florian Rau and Bernhard Ronacher for critical reading of the manuscript. We also gratefully acknowledge the careful reading and constructive criticism of the manuscript by two anonymous referees.