The behavioral tests were performed with females of C. biguttulus. The animals were reared as the filial generation (F1) from eggs of individuals collected as adults near Göttingen, Germany. After adult molt females and males were held separately in plastic cages to ensure virginity. In this species the females respond to a male's song with a song of their own, thereby indicating their readiness to mate. This response song is an ideal criterion showing that a female has identified a song as belonging to a potential conspecific mating partner.

Electrophysiological experiments were performed on locusts, L. migratoria, that were bought from a commercial supplier (for details of the breeding and keeping procedures see Schmidt et al., 2008; Stange and Ronacher, 2012). We can homologize identified neurons between the two species on the basis of their characteristic morphology (Römer and Marquart, 1984; Stumpner and Ronacher, 1991). The homologous auditory neurons of the thoracic ganglia show quantitatively similar response patterns in both species (Neuhofer et al., 2008). In these experiments songs or song models of C. biguttulus were presented to both species, and neurons of the locust showed the same responses as neurons of C. biguttulus although these songs have, of course, no relevance for the locust (see also Ronacher and Stumpner, 1988; Sokoliuk et al., 1989). On the basis of this strong homology we can use recordings from L. migratoria neurons and compare their spike patterns with behavioral responses of C. biguttulus.

A digitally generated song envelope consisting of rectangular syllables of 72 ms duration separated by 12 ms pauses served as an attractive standard stimulus (Figure 1A). In order to systematically screen the detrimental effect of degradation at different syllable positions, we inserted perturbations of 24 ms either in the first, or in the middle, or in the last part of each syllable (Figure 1A). A perturbation consisted of 2 alternating accents and gaps, each of 6 ms duration and 12 dB higher or lower sound pressure relative to the syllable plateau. Earlier experiments had revealed that gaps within a syllable do markedly reduce the stimulus attractiveness; accentuations that occur at the end of a syllable have similar detrimental effects (Von Helversen, 1972, 1979; Ronacher and Stumpner, 1988; Von Helversen and von Helversen, 1997; for reviews see Ronacher et al., 2004; Ronacher and Stange, 2013).

The envelopes of all song models were convolved with the same carrier frequency (a broad band noise spectrum of 5–40 kHz). Sound intensity was calibrated with a half inch microphone (type 4133; Brüel and Kjær, Nærum, Denmark) and a measuring amplifier (type 2209, Brüel and Kjær) at the position of the animal. All four test patterns were presented with the same effective intensity (RMS) of 70 dB SPL; therefore, the peak and plateau intensities differed between stimuli (syllable plateau 70 dB for the standard stimulus and 65 dB for perturbed stimuli, Figure 1A). Yet, these intensities fall into the intensity range well accepted by C. biguttulus females (Von Helversen and von Helversen, 1994, 1997). The songs presented in the behavioral and electrophysiology tests comprised the same envelope structure but differed in length: 2772 ms (33 subunits; behavior) and 756 ms (9 subunits for electrophysiology), respectively.

Virgin C. biguttulus females were tested in a sound proof chamber at a constant temperature of 30 ± 2°C. The experiments were automatically conducted by a custom made program (written by M. Hennig in Labview 7.1, National Instruments) presenting songs in a pseudo-randomized order while recording the females' responses (for details of the apparatus and testing procedures see Schmidt et al., 2008). Each song was iterated 18 times. As a measure of stimulus attractiveness we used the percentage of responses normalized to the 18 presentations for each female. Out of these individual responses median response rates were calculated. Additionally, a negative control was presented, comprising the same carrier frequency and length as the standard signal, but lacking any syllable pause structure. In applying this negative control stimulus those females indicating a not discriminative behavior for song patterns could be detected. We therefore excluded from further analysis 11 of 44 females as they responded more than twice to the negative control. Applied statistic software was GraphPad Instat Version 3.06.

Auditory interneurons were recorded intracellularly in the frontal auditory neuropil of the metathoracic ganglion in both sexes of L. migratoria. During the experiments the torso of the animal was filled with a locust Ringer solution (Pearson and Robertson, 1981), to prevent the ganglia from drying. The temperature was kept constant at 30 ± 2°C. For the recordings we used glass microelectrodes (borosilicate, OØ = 1 mm, IØ = 0.58 mm, GC100F-10; Harvard Apparatus, LTD, USA), with capacities varying between 20 and 100 MΩ. They were filled with a fluorescent dye, a 3–5 % solution of Lucifer yellow (Sigma–Aldrich, Taufkirchen, Germany) in 0.5 M LiCl. Neural responses were amplified (10-fold, BRAMP-01 R, npi, USA) and recorded by a data-acquisition board (PCI-MIO-16E-4, 16 bit, National Instruments, USA) with a sampling rate of 20 kHz. The dye was injected into the recorded cell by applying hyperpolarizing current of 0.5–1 nA. Subsequently the thoracic ganglia were incubated in a fixation solution (4% paraformaldehyde), dehydrated and cleared in methyl salicylate. This procedure allowed an identification of the stained cells under a fluorescent microscope according to their characteristic morphology (Römer and Marquart, 1984; Stumpner and Ronacher, 1991).

Experiments were performed in a Faraday cage lined with reflection absorbing prisms. One of two speakers (frequency response 2–40 kHz, D21, Dynaudio, Denmark), which were placed laterally, at a distance of 30 cm from the animal's tympanal organ, emitted the sound signal. The acoustic stimuli were attenuated (PA5, Tucker-Davis Technologies, USA) and amplified (Raveland-XA600, Conrad Electronics, Germany). They were stored digitally and delivered by custom-made software (LabVIEW, National Instruments) using a 100-kHz D/A-conversion (PCI-MIO-16E-1, National Instruments). For this study ANs were analyzed which represent the third processing stage in the metathoracic ganglion and transmit the auditory information to the grasshopper's brain. We recorded four different types of ANs (AN1, AN4, AN3, AN12) from 25 animals (details of the response properties of these neurons can be found in Ronacher and Stumpner, 1988; Stumpner and Ronacher, 1991; Wohlgemuth and Ronacher, 2007). The direction from which the sound stimuli were presented depended on the side where the neurons were more sensitive to. With the exception of AN1 the ANs AN4, AN3, and AN 12 do not exhibit strong direction sensitivity. The AN1 was mostly recorded from the contralateral side (respective to the soma), the other neurons from both sides. Each song was presented within a looped order: standard stimulus, onset-perturbation, perturbation in the middle, then perturbation in the end, and starting again with the standard stimulus. Stimulus iteration was 8 times, each iteration comprised the full stimulus length (9 subunits).

Following Gold and Shadlen (2007) we use the experimental realizations of the count pattern in n = 8 ANs to fit a simple probabilistic model for the female's decision to respond to a calling song. This model is based on the log likelihood ratio (LR) of the song attractiveness given the AN population spike count. We computed for each syllable j separately the log LR as logLR±(j)=logP(c1(j),…,c8(j)|h+)P(c1(j),…,c8(j)|h−) where the denominator accounts for the probability that the a given count vector c₁(j), …, c₈(j) (test trial) across 8 neurons stems from the hypothesis h₊, which is represented by the probability distribution of counts estimated from the remaining trials given an attractive stimulus s₊. We then defined the decision variable as:

The decision variable is updated after each syllable k by taking the cumulative sum over the past log LR values up to the kth syllable. It represents a cumulative sum over the evidence for the presence of an attractive song. The larger DV the more likely is the presence of an attractive song over an unattractive song.

For any combination of n = 8 selected ANs, two of each type, we compute for each single song presentation (test trial) the LR and the DV based on the remaining trials (leave-one-out). We repeat this for all possible combinations of 8 neurons that comprise 2 neurons of each type of AN representing input from both ears. We next introduced a decision threshold θ on DV. For a single trial, i.e., a particular song presentation, a behavioral response is elicited if DV(k) > θ in any k. This approach allows us to simulate the female single trial response behavior based on the experimentally recorded AN population activity.

We compared the performance of the simulated animal decisions to the actual animal performance in the behavioral experiments. For a given value of θ the true positive (TP) rate is defined as the fraction of correct detections, i.e., threshold crossings in the presence of an attractive song over all presentations of an attractive song. The false positive (FP) rate quantifies the fraction of false alarms, i.e., the threshold crossings in the presence of an unattractive song over all presentations of an unattractive song. TP and FP rates depend on the choice of θ. We thus computed the receiver operating characteristic (ROC) that represents the TP rate as a function of the FP rate for varying θ (Wiley, 2006). We measure the area under the ROC to quantify the model performance independent of the behavioral threshold θ.

In behavioral tests we investigated how degradation at specific positions within the signal does affect signal recognition. We compared the responses of C. biguttulus females to four stimulus types (Figure 1A): (i) standard stimulus without perturbation, (ii) with perturbation during the first third of the syllable (“onset”), (iii) during the second third (“middle”), and (iv) during the last third (“end”). Figure 1B shows the distribution of response rates across individual females to all four stimuli (see Materials and Methods). The standard stimulus was highly attractive (median: 83%), although individual females differed considerably in their response rate (compare quartile ranges and see variance in Figure 1C). Females showed similar high response rates toward the stimulus with onset perturbation, whereas the same perturbation in the middle or the end of a syllable led to a behavioral rejection (median response levels of <10%). Only 3 out of 33 females responded to the latter stimuli in more than 50% of the stimulus presentations.

In order to further analyze differences in attractiveness we pairwise compared stimulus responses in individual females. For each female, the response rates for any two stimuli (see left column in Figure 2) were subtracted. Thus, it could be shown that the responses to the onset stimulus did not differ significantly from the responses to the standard (top row, Figure 2); the same is true for the comparison of the stimuli perturbed in the second and third part of the syllable (lowest row, Figure 2). In contrast, the responses to the unperturbed song and the song with middle and end perturbations differed significantly (p < 0.001; Friedman and Dunn's Multiple Comparison Test), and in both cases the median difference was about 60%. Similar results were found for the comparison between the onset perturbed stimulus and the other two perturbed stimuli (median differences >50%, p < 0.001).

Grasshoppers have to make their decisions based on the information about the environment provided by the sensory and higher order neurons of the auditory pathway. The clear separation into two behavioral stimulus classes raises the question of how the different stimuli and the different behavioral classes are represented and discriminated within the grasshopper's nervous system. We address this question in intracellular in vivo recordings of identified ANs during repeated presentations of all four songs. To quantify the encoded information we apply a single-trial decoding approach to the neural spiking activity using a Bayesian classifier. We first decode the identity of the auditory stimulus before we predict the behavioral class (attractive vs. non-attractive).

Thus far we have shown that a population of ANs carries a significant amount of information about the behavioral relevance of the stimulus that allowed for a binary classification of the attractive vs. the unattractive stimulus class based on the neurons' spike count (Figure 6C). Here we introduce a simple model of decision making inspired by Gold and Shadlen (2007). In our model we interpret the population spike count of the ANs as sensory evidence about the behaviorally relevant cues that indicate an attractive calling song (see Materials and Methods). Our results in Figure 6B indicate that this information is encoded in a persistent and stable manner across syllables. We thus hypothesize that a decision circuit at a higher processing level makes use of this stable representation at the sensory level by accumulating evidence across successive syllables.

Formally, our model (c.f. Materials and Methods, Model of Decision Making) assumes that the AN population firing rate for each syllable provides an independent piece of evidence about the behaviorally relevant cues. For each single trial spike count pattern in a population of 8 neurons and for each syllable separately we computed the log LR for the presence of an attractive song over the presence of an unattractive song. In a second step we integrated the log LR across syllables. We then define the decision variable (DV) as the time integral over the log LR. Positive values of the DV indicate that the presence of an attractive stimulus is more likely than the presence of an unattractive stimulus and vice versa for negative values of the DV.

Figure 7A shows the DV as a function of time based on the measured neuronal response patterns. In the case of attractive calling songs (red) the average DV is positive already during the first syllable and shows an overall increase over the 9 syllables. For trials in which an unattractive song was presented the average DV (black) steadily decreased across syllables. The individual single trial curves of the DV show a variable behavior (Figure 7A). In order to simulate the behavioral decision we introduced a decision threshold on the DV. In each single trial a response is simulated if the log LR value crosses this threshold during any of the syllables.

In the cases of an attractive (unattractive) trial we count a threshold crossing as TP or FP result, respectively. We then computed the TP and FP rates in dependence on the threshold value. The TP rate of the model relates to the female response rate for attractive song presentations in animal experiments, the FP rate relates to the female response rate to unattractive songs (Figure 1B). As shown in Figure 7B the FP rate drops sharply and much faster than the TP rate when increasing the decision threshold.

How does the model performance compare quantitatively to the behavioral experiments? The median female response rates were 83% for attractive stimuli and 6% for unattractive stimuli (Figure 1B). A variation of the decision boundary in our model corresponding to a variation of the TP rate in the range of 80–85% corresponds to FP rates in the range of 3–4% (Figure 7B). This indicates that the behavioral decisions based on the neural recordings from a population of 8 ANs and the simple decision model presented here are, on average, comparable to the average performance in the behavioral experiments with female grasshoppers.

The ROC in Figure 7C quantifies the model performance independent of the threshold. Integrating over the ROC (area under ROC) yielded a high value of 0.97 indicating that this decision model based on the neuronal population spike count performs very well in making correct detections of attractive calling songs and in avoiding false alarms in the case of unattractive calling songs.

We evaluated the information about stimulus and behavioral contingency using a simple measure of neuronal activity: the total spike count during stimulus presentation. For single neurons we obtained only poor decoding performances. The full time-resolved firing rate estimate over the stimulus duration carries much more stimulus information and naturally results in much higher decoding performances (Figure S3). However, in the realistic scenario of decoding the spike counts from a population of neurons the performance increased significantly as compared to the single neuron case. For the maximum population size of 8 ANs we obtained on average MCC = 0.69 for predicting the behavioral class (Figure 6C). We grouped maximally 8 neurons, two of each of the morphological types that had been recorded in our experiments. This represents a realistic subpopulation of ANs from an individual animal. We can expect that the decoding from an intact population of at least 20 morphologically distinct ANs per hemisphere in the grasshopper would reach considerably higher decoding performances, indicating that the relevant stimulus features are represented by a combinatorial rate code in the AN population. These results are particularly interesting in view of recent papers investigating different aspects of the grasshopper's auditory pathway. Clemens et al. (2011) provided evidence that between the local and ascending neurons, i.e., between the second and third processing stage, the coding principle changes from a summed population code to a labeled-line population code where the population's information is maximal if a decoder takes into account neuronal identity. At the level of the AN population, the temporal sparseness as well as the population sparseness increases (Clemens et al., 2012). At the same time, integrated spike rate information gains in significance compared to spike timing information (Clemens et al., 2011, 2012; see also Wohlgemuth and Ronacher, 2007; Creutzig et al., 2009; Ronacher, 2014) which fits our results. In addition, the use of a spike count code would also explain why the remarkable imprecise spike timing found in ANs (Vogel et al., 2005) does not impair the precise evaluation of song features in the millisecond range as observed in behavioral tests (Von Helversen, 1979; Ronacher and Stumpner, 1988; Ronacher and Stange, 2013; Ronacher, 2014).

We found that the across syllables information is encoded persistently and reliably in the AN population rate and we hypothesize that the role the grasshopper's auditory system is to provide stable sensory evidence that can be evaluated in the brain. The performance of the Bayesian classifier depends on both, the encoding rate signal and the noise. We found that the Fano factor of ANs, which estimates the noise as trial-by-trial variability of the spike number (Nawrot, 2010), is constant across time, indicating a constant level of noise in the peripheral auditory system (Figure S2). The absolute values of the Fano factor match previous results showing that variability of spike trains increases from receptor neurons to the ANs (Ronacher et al., 2004; Vogel et al., 2005; Vogel and Ronacher, 2007; Neuhofer et al., 2011), which on average showed a reduced performance in stimulus classification compared to LNs (Wohlgemuth and Ronacher, 2007). Using song models that were progressively degraded, Neuhofer et al. (2011) could estimate the respective contributions of external signal degradation and the trial-to-trial variability of spike trains caused by intrinsic neuronal noise. Intrinsic neuronal noise had a very strong impact on the spike train variability, in particular in ANs, thus likely affecting the representation of acoustic signals along the auditory pathway, and thus also the discrimination and recognition of grasshopper songs (Ronacher, 2014).

At the level of ANs that provide the sole auditory input to the grasshopper's brain we found a steady representation of information about the stimulus and its behavioral relevance in the population spike count. We devised a simple decision making model that integrates evidence over time generating a decision variable, which eventually may reach a decision threshold to elicit a behavioral response. Such models have previously been formulated for alternative choices in sensory decision tasks (e.g., Gold and Shadlen, 2007; Beck et al., 2008; Drugowitsch and Pouget, 2012). The model integrates the estimated Bayesian likelihood across successive syllables and, by crossing a decision threshold allows to form behavioral decisions. In the grasshopper, recognition, and evaluation of a conspecific calling song simplifies to the female's decision between showing or not showing her response behavior depending on whether and when the evidence reaches a threshold. In a neuroethological context as well as in controlled behavioral experiments animals can modulate their behavioral response level (Von Helversen and von Helversen, 1994, 1997; Wirmer et al., 2010). In our model this could be realized by a modulation of response threshold, e.g., through neuromodulators in the relevant brain circuit (Heinrich et al., 2001; Wirmer et al., 2010).

Our model presented here is based on neural recordings in the auditory pathway and thus extends on approaches that model female response behavior based on the auditory stimuli alone. Clemens and Ronacher (2013) devised an abstract linear-nonlinear cascade model: In a first step the model continuously extracts characteristic stimulus features from the sound stimulus by use of linear filters. In the second step the model transforms each filter output with a non-linear function. The resulting signals are then integrated across features and over the whole stimulus period, neglecting the exact temporal position of specific song features. Their model was able to predict behavioral responses with high reliability (r² = 0.87) with a set of only two distinct song features. This serial structure of (i) extraction of sensory evidence, and (ii) subsequent temporal integration over this evidence is paralleled in our model and the model proposed by Clemens and Ronacher (2013).

If we assume a time-integrating algorithm in the grasshopper's brain, what could be the underlying neuronal mechanism? The relevant time span is indicated by the duration of the reported response times in the range of typically several hundreds of milliseconds. One cellular mechanism that could serve this task is short-term synaptic plasticity. Fascilitation and depression at synapses are governed by processes with typical time constants in the right order of magnitude and they have repeatedly been suggested to be involved in decision making processes (Mongillo et al., 2008; Martínez-García et al., 2011) including a suggested algorithm for auditory pattern recognition in the cricket's central brain (Rost et al., 2013).

In summary, our results support the hypothesis of a population rate code in ANs that project the acoustic information to the central brain (see Clemens et al., 2011, 2012). The information about the behavioral relevance of a stimulus is well represented in the population rate and this information is constantly present throughout the stimulus presentation. The good performance of our decision model suggests a computational process located within the grasshopper brain that infers the behaviorally relevant information and integrates this evidence over time to reach a behavioral decision based on accumulated evidence.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.