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Good day. Finished invariance introduction paragraph. Added more sources.

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@ -7,6 +7,17 @@
year={2001},
}# Cited
@article{barbour2011intensity,
title={Intensity-invariant coding in the auditory system},
author={Barbour, Dennis L},
journal={Neuroscience \& Biobehavioral Reviews},
volume={35},
number={10},
pages={2064--2072},
year={2011},
publisher={Elsevier}
}# Cited
@article{bauer1987separate,
title={Separate localization of sound recognizing and sound producing neural mechanisms in a grasshopper},
author={Bauer, Maria and von Helversen, Otto},
@ -22,7 +33,19 @@
volume={24},
pages={113--136},
year={2008},
}
}# Cited
@article{benda2021neural,
title={Neural adaptation},
author={Benda, Jan},
journal={Current Biology},
volume={31},
number={3},
pages={R110--R116},
year={2021},
publisher={Elsevier}
}# Cited
@article{bhavsar2017brain,
title={Brain regions for sound processing and song release in a small grasshopper},
author={Bhavsar, Mit Balvantray and Stumpner, Andreas and Heinrich, Ralf},
@ -95,7 +118,8 @@
volume={22},
pages={1493--1510},
year={2010},
}
}# Cited
@article{creutzig2009timescale,
title={Timescale-invariant representation of acoustic communication signals by a bursting neuron},
author={Creutzig, Felix and Wohlgemuth, Sandra and Stumpner, Andreas and Benda, Jan and Ronacher, Bernhard and Herz, Andreas VM},
@ -103,7 +127,8 @@
volume={29},
pages={2575--2580},
year={2009},
}
}# Cited
@article{eberhard2015temperature,
title={A temperature rise reduces trial-to-trial variability of locust auditory neuron responses},
author={Eberhard, Monika JB and Schleimer, Jan-Hendrik and Schreiber, Susanne and Ronacher, Bernhard},
@ -125,6 +150,27 @@
publisher={Springer}
}# Cited
@article{einhaupl2011attractiveness,
title={Attractiveness of grasshopper songs correlates with their robustness against noise},
author={Einh{\"a}upl, Anne and Stange, Nicole and Hennig, R Matthias and Ronacher, Bernhard},
journal={Behavioral Ecology},
volume={22},
number={4},
pages={791--799},
year={2011},
publisher={Oxford University Press}
}
@article{elsner1968neuromuskularen,
title={Die neuromuskul{\"a}ren Grundlagen des Werbeverhaltens der roten Keulenheuschrecke Gomphocerippus rufus (L.)},
author={Elsner, Norbert},
journal={Zeitschrift f{\"u}r vergleichende Physiologie},
volume={60},
number={3},
pages={308--350},
year={1968},
publisher={Springer}
}# Cited
@article{fisch2012channel,
title={Channel noise from both slow adaptation currents and fast currents is required to explain spike-response variability in a sensory neuron},
author={Fisch, Karin and Schwalger, Tilo and Lindner, Benjamin and Herz, Andreas VM and Benda, Jan},
@ -132,7 +178,7 @@
volume={32},
pages={17332--17344},
year={2012},
}# Cited
}
@article{gollisch2002energy,
title={Energy integration describes sound-intensity coding in an insect auditory system},
@ -234,6 +280,16 @@
year={2004},
}# Cited
@article{hennig2004processing,
title={Processing of auditory information in insects},
author={Hennig, RM and Franz, A and Stumpner, A},
journal={Microscopy research and technique},
volume={63},
number={6},
pages={351--374},
year={2004},
publisher={Wiley Online Library}
}
@article{hennig2014time,
title={Time and timing in the acoustic recognition system of crickets},
author={Hennig, R Matthias and Heller, Klaus-Gerhard and Clemens, Jan},
@ -251,6 +307,13 @@
year={2009},
}# Cited
@article{hildebrandt2010neural,
title={Neural adaptation in the auditory pathway of crickets and grasshoppers},
author={Hildebrandt, Kai Jannis},
year={2010},
publisher={Humboldt-Universit{\"a}t zu Berlin, Mathematisch-Naturwissenschaftliche Fakult{\"a}t I}
}
@article{hildebrandt2015neural,
title={A neural mechanism for time-window separation resolves ambiguity of adaptive coding},
author={Hildebrandt, K Jannis and Ronacher, Bernhard and Hennig, R Matthias and Benda, Jan},
@ -396,7 +459,8 @@
pages={345--373},
year={1978},
publisher={Springer}
}
}# Cited
@article{miller1977directional,
title={Directional hearing in the locust Schistocerca gregaria Forsk{\aa}l (Acrididae, Orthophera)},
author={Miller, Lee A},
@ -432,6 +496,15 @@
publisher={University of Michigan Museum of Zoology}
}# Cited
@article{ozeri2018fast,
title={Fast intensity adaptation enhances the encoding of sound in Drosophila.},
author={Ozeri-Engelhard, Nofar and Clemens, Jan and Murthy, Mala},
journal={Nature Communications},
volume={9},
number={1},
year={2018}
}# Cited
@article{prinz2002temporal,
title={Temporal modulation transfer functions in auditory receptor fibres of the locust (Locusta migratoria L.)},
author={Prinz, P and Ronacher, B},
@ -462,6 +535,17 @@
year={1976},
}# Cited
@article{romer1976informationsverarbeitung,
title={Die Informationsverarbeitung tympanaler Rezeptorelemente von Locusta migratoria (acrididae, orthoptera)},
author={R{\"o}mer, Heiner},
journal={Journal of comparative physiology},
volume={109},
number={1},
pages={101--122},
year={1976},
publisher={Springer}
}# Cited
@article{romer1985responses,
title={Responses to model songs of auditory neurons in the thoracic ganglia and brain of the locust},
author={R{\"o}mer, Heiner and Seikowski, Ulrich},
@ -580,7 +664,7 @@
pages={309--318},
year={2012},
publisher={Springer}
}
}# Cited
@article{stumpner1994song,
title={{Song production and song recognition in a group of sibling grasshopper species (Chorthippus dorsatus, Ch. dichrous and Ch. loratus: Orthoptera, Acrididae)}},

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@ -65,6 +65,104 @@
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\field{title}{Die neuromuskulären Grundlagen des Werbeverhaltens der roten Keulenheuschrecke Gomphocerippus rufus (L.)}
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@ -1270,6 +1418,82 @@
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\field{title}{Song recognition and song pattern in a shorthorned grasshopper}
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69
main.bcf
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@ -2363,9 +2363,9 @@
</bcf:bibdata>
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<bcf:citekey order="2" intorder="1">helversen1993absolute</bcf:citekey>
<bcf:citekey order="3" intorder="1">helversen1997recognition</bcf:citekey>
<bcf:citekey order="4" intorder="1">helversen1988interaural</bcf:citekey>
<bcf:citekey order="2" intorder="1">stange2012grasshopper</bcf:citekey>
<bcf:citekey order="3" intorder="1">helversen1988interaural</bcf:citekey>
<bcf:citekey order="4" intorder="1">elsner1968neuromuskularen</bcf:citekey>
<bcf:citekey order="5" intorder="1">greenfield1993acoustic</bcf:citekey>
<bcf:citekey order="6" intorder="1">otte1970comparative</bcf:citekey>
<bcf:citekey order="7" intorder="1">tishechkin2016acoustic</bcf:citekey>
@ -2381,32 +2381,47 @@
<bcf:citekey order="17" intorder="1">helversen1977stridulatory</bcf:citekey>
<bcf:citekey order="18" intorder="1">stumpner1994song</bcf:citekey>
<bcf:citekey order="19" intorder="1">helversen1997recognition</bcf:citekey>
<bcf:citekey order="20" intorder="1">helversen1993absolute</bcf:citekey>
<bcf:citekey order="21" intorder="1">balakrishnan2001song</bcf:citekey>
<bcf:citekey order="22" intorder="1">helversen2004acoustic</bcf:citekey>
<bcf:citekey order="23" intorder="1">helversen1972gesang</bcf:citekey>
<bcf:citekey order="20" intorder="1">helversen1972gesang</bcf:citekey>
<bcf:citekey order="21" intorder="1">helversen1993absolute</bcf:citekey>
<bcf:citekey order="22" intorder="1">balakrishnan2001song</bcf:citekey>
<bcf:citekey order="23" intorder="1">helversen2004acoustic</bcf:citekey>
<bcf:citekey order="24" intorder="1">helversen1997recognition</bcf:citekey>
<bcf:citekey order="25" intorder="1">skovmand1983song</bcf:citekey>
<bcf:citekey order="26" intorder="1">clemens2013computational</bcf:citekey>
<bcf:citekey order="27" intorder="1">clemens2013feature</bcf:citekey>
<bcf:citekey order="28" intorder="1">ronacher2015computational</bcf:citekey>
<bcf:citekey order="29" intorder="1">rehbein1974structure</bcf:citekey>
<bcf:citekey order="30" intorder="1">kalmring1975afferent</bcf:citekey>
<bcf:citekey order="31" intorder="1">rehbein1976auditory</bcf:citekey>
<bcf:citekey order="32" intorder="1">eichendorf1980projections</bcf:citekey>
<bcf:citekey order="33" intorder="1">clemens2011efficient</bcf:citekey>
<bcf:citekey order="34" intorder="1">clemens2011efficient</bcf:citekey>
<bcf:citekey order="35" intorder="1">clemens2011efficient</bcf:citekey>
<bcf:citekey order="36" intorder="1">michelsen1971frequency</bcf:citekey>
<bcf:citekey order="37" intorder="1">windmill2008time</bcf:citekey>
<bcf:citekey order="38" intorder="1">malkin2014energy</bcf:citekey>
<bcf:citekey order="39" intorder="1">machens2001discrimination</bcf:citekey>
<bcf:citekey order="40" intorder="1">machens2001representation</bcf:citekey>
<bcf:citekey order="41" intorder="1">suga1960peripheral</bcf:citekey>
<bcf:citekey order="42" intorder="1">gollisch2002energy</bcf:citekey>
<bcf:citekey order="43" intorder="1">hildebrandt2009origin</bcf:citekey>
<bcf:citekey order="44" intorder="1">clemens2010intensity</bcf:citekey>
<bcf:citekey order="45" intorder="1">fisch2012channel</bcf:citekey>
<bcf:citekey order="26" intorder="1">creutzig2009timescale</bcf:citekey>
<bcf:citekey order="27" intorder="1">creutzig2010timescale</bcf:citekey>
<bcf:citekey order="28" intorder="1">helversen1972gesang</bcf:citekey>
<bcf:citekey order="29" intorder="1">michelsen1978sound</bcf:citekey>
<bcf:citekey order="30" intorder="1">lang2000acoustic</bcf:citekey>
<bcf:citekey order="31" intorder="1">benda2008spike</bcf:citekey>
<bcf:citekey order="32" intorder="1">barbour2011intensity</bcf:citekey>
<bcf:citekey order="33" intorder="1">ozeri2018fast</bcf:citekey>
<bcf:citekey order="34" intorder="1">benda2021neural</bcf:citekey>
<bcf:citekey order="35" intorder="1">romer1976informationsverarbeitung</bcf:citekey>
<bcf:citekey order="36" intorder="1">gollisch2002energy</bcf:citekey>
<bcf:citekey order="37" intorder="1">hildebrandt2009origin</bcf:citekey>
<bcf:citekey order="38" intorder="1">clemens2010intensity</bcf:citekey>
<bcf:citekey order="39" intorder="1">clemens2010intensity</bcf:citekey>
<bcf:citekey order="40" intorder="1">hildebrandt2009origin</bcf:citekey>
<bcf:citekey order="41" intorder="1">clemens2013computational</bcf:citekey>
<bcf:citekey order="42" intorder="1">clemens2013feature</bcf:citekey>
<bcf:citekey order="43" intorder="1">ronacher2015computational</bcf:citekey>
<bcf:citekey order="44" intorder="1">rehbein1974structure</bcf:citekey>
<bcf:citekey order="45" intorder="1">kalmring1975afferent</bcf:citekey>
<bcf:citekey order="46" intorder="1">rehbein1976auditory</bcf:citekey>
<bcf:citekey order="47" intorder="1">eichendorf1980projections</bcf:citekey>
<bcf:citekey order="48" intorder="1">clemens2011efficient</bcf:citekey>
<bcf:citekey order="49" intorder="1">clemens2011efficient</bcf:citekey>
<bcf:citekey order="50" intorder="1">clemens2011efficient</bcf:citekey>
<bcf:citekey order="51" intorder="1">michelsen1971frequency</bcf:citekey>
<bcf:citekey order="52" intorder="1">windmill2008time</bcf:citekey>
<bcf:citekey order="53" intorder="1">malkin2014energy</bcf:citekey>
<bcf:citekey order="54" intorder="1">machens2001discrimination</bcf:citekey>
<bcf:citekey order="55" intorder="1">machens2001representation</bcf:citekey>
<bcf:citekey order="56" intorder="1">suga1960peripheral</bcf:citekey>
<bcf:citekey order="57" intorder="1">gollisch2002energy</bcf:citekey>
<bcf:citekey order="58" intorder="1">hildebrandt2009origin</bcf:citekey>
<bcf:citekey order="59" intorder="1">clemens2010intensity</bcf:citekey>
<bcf:citekey order="60" intorder="1">fisch2012channel</bcf:citekey>
</bcf:section>
<!-- SORTING TEMPLATES -->
<bcf:sortingtemplate name="nyt">

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[0] Config.pm:307> INFO - This is Biber 2.19
[0] Config.pm:310> INFO - Logfile is 'main.blg'
[35] biber:340> INFO - === Di Jan 13, 2026, 15:04:23
[43] Biber.pm:419> INFO - Reading 'main.bcf'
[69] Biber.pm:979> INFO - Found 38 citekeys in bib section 0
[75] Biber.pm:4419> INFO - Processing section 0
[35] biber:340> INFO - === Do Jan 15, 2026, 16:37:11
[42] Biber.pm:419> INFO - Reading 'main.bcf'
[69] Biber.pm:979> INFO - Found 49 citekeys in bib section 0
[74] Biber.pm:4419> INFO - Processing section 0
[79] Biber.pm:4610> INFO - Looking for bibtex file 'cite.bib' for section 0
[80] bibtex.pm:1713> INFO - LaTeX decoding ...
[105] bibtex.pm:1519> INFO - Found BibTeX data source 'cite.bib'
[226] UCollate.pm:68> INFO - Overriding locale 'en-US' defaults 'normalization = NFD' with 'normalization = prenormalized'
[227] UCollate.pm:68> INFO - Overriding locale 'en-US' defaults 'variable = shifted' with 'variable = non-ignorable'
[227] Biber.pm:4239> INFO - Sorting list 'nyt/global//global/global' of type 'entry' with template 'nyt' and locale 'en-US'
[227] Biber.pm:4245> INFO - No sort tailoring available for locale 'en-US'
[242] bbl.pm:660> INFO - Writing 'main.bbl' with encoding 'UTF-8'
[249] bbl.pm:763> INFO - Output to main.bbl
[249] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_G7r3/347c261ec4135a5723bef5c751f5078f_99898.utf8, line 10, warning: 6 characters of junk seen at toplevel
[249] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_G7r3/347c261ec4135a5723bef5c751f5078f_99898.utf8, line 35, warning: 6 characters of junk seen at toplevel
[249] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_G7r3/347c261ec4135a5723bef5c751f5078f_99898.utf8, line 50, warning: 6 characters of junk seen at toplevel
[249] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_G7r3/347c261ec4135a5723bef5c751f5078f_99898.utf8, line 91, warning: 6 characters of junk seen at toplevel
[249] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_G7r3/347c261ec4135a5723bef5c751f5078f_99898.utf8, line 128, warning: 6 characters of junk seen at toplevel
[249] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_G7r3/347c261ec4135a5723bef5c751f5078f_99898.utf8, line 137, warning: 6 characters of junk seen at toplevel
[249] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_G7r3/347c261ec4135a5723bef5c751f5078f_99898.utf8, line 146, warning: 6 characters of junk seen at toplevel
[250] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_G7r3/347c261ec4135a5723bef5c751f5078f_99898.utf8, line 157, warning: 6 characters of junk seen at toplevel
[250] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_G7r3/347c261ec4135a5723bef5c751f5078f_99898.utf8, line 168, warning: 6 characters of junk seen at toplevel
[250] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_G7r3/347c261ec4135a5723bef5c751f5078f_99898.utf8, line 177, warning: 6 characters of junk seen at toplevel
[250] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_G7r3/347c261ec4135a5723bef5c751f5078f_99898.utf8, line 186, warning: 6 characters of junk seen at toplevel
[250] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_G7r3/347c261ec4135a5723bef5c751f5078f_99898.utf8, line 197, warning: 6 characters of junk seen at toplevel
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[250] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_G7r3/347c261ec4135a5723bef5c751f5078f_99898.utf8, line 217, warning: 6 characters of junk seen at toplevel
[250] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_G7r3/347c261ec4135a5723bef5c751f5078f_99898.utf8, line 228, warning: 6 characters of junk seen at toplevel
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[250] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_G7r3/347c261ec4135a5723bef5c751f5078f_99898.utf8, line 435, warning: 6 characters of junk seen at toplevel
[250] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_G7r3/347c261ec4135a5723bef5c751f5078f_99898.utf8, line 456, warning: 6 characters of junk seen at toplevel
[250] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_G7r3/347c261ec4135a5723bef5c751f5078f_99898.utf8, line 465, warning: 6 characters of junk seen at toplevel
[250] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_G7r3/347c261ec4135a5723bef5c751f5078f_99898.utf8, line 496, warning: 6 characters of junk seen at toplevel
[250] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_G7r3/347c261ec4135a5723bef5c751f5078f_99898.utf8, line 534, warning: 6 characters of junk seen at toplevel
[250] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_G7r3/347c261ec4135a5723bef5c751f5078f_99898.utf8, line 543, warning: 6 characters of junk seen at toplevel
[250] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_G7r3/347c261ec4135a5723bef5c751f5078f_99898.utf8, line 564, warning: 6 characters of junk seen at toplevel
[250] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_G7r3/347c261ec4135a5723bef5c751f5078f_99898.utf8, line 594, warning: 6 characters of junk seen at toplevel
[250] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_G7r3/347c261ec4135a5723bef5c751f5078f_99898.utf8, line 603, warning: 6 characters of junk seen at toplevel
[250] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_G7r3/347c261ec4135a5723bef5c751f5078f_99898.utf8, line 620, warning: 6 characters of junk seen at toplevel
[250] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_G7r3/347c261ec4135a5723bef5c751f5078f_99898.utf8, line 629, warning: 6 characters of junk seen at toplevel
[250] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_G7r3/347c261ec4135a5723bef5c751f5078f_99898.utf8, line 654, warning: 6 characters of junk seen at toplevel
[250] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_G7r3/347c261ec4135a5723bef5c751f5078f_99898.utf8, line 671, warning: 6 characters of junk seen at toplevel
[250] Biber.pm:133> INFO - WARNINGS: 36
[108] bibtex.pm:1519> INFO - Found BibTeX data source 'cite.bib'
[254] UCollate.pm:68> INFO - Overriding locale 'en-US' defaults 'variable = shifted' with 'variable = non-ignorable'
[254] UCollate.pm:68> INFO - Overriding locale 'en-US' defaults 'normalization = NFD' with 'normalization = prenormalized'
[254] Biber.pm:4239> INFO - Sorting list 'nyt/global//global/global' of type 'entry' with template 'nyt' and locale 'en-US'
[254] Biber.pm:4245> INFO - No sort tailoring available for locale 'en-US'
[273] bbl.pm:660> INFO - Writing 'main.bbl' with encoding 'UTF-8'
[281] bbl.pm:763> INFO - Output to main.bbl
[281] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_x7Wz/347c261ec4135a5723bef5c751f5078f_156259.utf8, line 10, warning: 6 characters of junk seen at toplevel
[281] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_x7Wz/347c261ec4135a5723bef5c751f5078f_156259.utf8, line 21, warning: 6 characters of junk seen at toplevel
[281] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_x7Wz/347c261ec4135a5723bef5c751f5078f_156259.utf8, line 38, warning: 6 characters of junk seen at toplevel
[281] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_x7Wz/347c261ec4135a5723bef5c751f5078f_156259.utf8, line 49, warning: 6 characters of junk seen at toplevel
[281] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_x7Wz/347c261ec4135a5723bef5c751f5078f_156259.utf8, line 58, warning: 6 characters of junk seen at toplevel
[281] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_x7Wz/347c261ec4135a5723bef5c751f5078f_156259.utf8, line 73, warning: 6 characters of junk seen at toplevel
[281] Biber.pm:131> WARN - BibTeX subsystem: /tmp/biber_tmp_x7Wz/347c261ec4135a5723bef5c751f5078f_156259.utf8, line 114, warning: 6 characters of junk seen at toplevel
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@ -93,10 +93,11 @@ formalization of the underlying structures and mechanisms.
One sensory system about which extensive information has been gathered over the
years is the auditory system of grasshoppers~(\textit{Acrididae}). Grasshoppers
rely on their sense of hearing primarily for intraspecific communication, which
includes mate attraction and evaluation~(\bcite{helversen1972gesang},
\bcite{helversen1993absolute}, \bcite{helversen1997recognition}), sender
localization~(\bcite{helversen1988interaural}), courtship display~(SOURCE),
rival deterrence~(\bcite{greenfield1993acoustic}), and loss-of-signal predator
includes mate attraction~(\bcite{helversen1972gesang}) and
evaluation~(\bcite{stange2012grasshopper}), sender
localization~(\bcite{helversen1988interaural}), courtship
display~(\bcite{elsner1968neuromuskularen}), rival
deterrence~(\bcite{greenfield1993acoustic}), and loss-of-signal predator
alarm~(SOURCE). In accordance with this rich behavioral repertoire,
grasshoppers have evolved a variety of sound production mechanisms to generate
acoustic communication signals for different contexts and ranges using their
@ -131,34 +132,62 @@ forewings~(\bcite{helversen1977stridulatory}, \bcite{stumpner1994song},
a brief pulse of sound. Multiple pulses make up a syllable; and the alternation
of syllables and relatively quiet pauses forms a characteristic, through noisy,
waveform pattern. Song recognition depends on certain temporal and structural
properties of this pattern, such as the slope of pulse
onsets~(\bcite{helversen1993absolute}), the accentuation of syllable
onsets~(\bcite{balakrishnan2001song}, \bcite{helversen2004acoustic}), and the
ratio of syllable duration to pause duration~(\bcite{helversen1972gesang}).
This signal design
parameters of this pattern, such as the duration of syllables and
pauses~(\bcite{helversen1972gesang}), the slope of pulse
onsets~(\bcite{helversen1993absolute}), and the accentuation of syllable onsets
relative to the preceeding pause~(\bcite{balakrishnan2001song},
\bcite{helversen2004acoustic}). The amplitude modulation, or envelope, of the
song is sufficient for recognition~(\bcite{helversen1997recognition}). However,
the essential recognition cues can vary considerably with external physical
factors, which requires the auditory system to be invariant to such variations
in order to reliably recognize songs under different conditions. For instance,
the temporal structure of grasshopper songs warps with
temperature~(\bcite{skovmand1983song}). The auditory system can compensate for
this variability by reading out relative temporal relationships rather than
absolute time intervals~(\bcite{creutzig2009timescale},
\bcite{creutzig2010timescale}), as those remain relatively constant across
different temperatures~(\bcite{helversen1972gesang}). Another, perhaps even
more fundamental external source of song variability lays in the attenuation of
sound intensity with increasing distance to the sender. Sound attenuation
depends on both the frequency content of the signal and the vegetation of the
habitat~(\bcite{michelsen1978sound}). For the receiving auditory system, this
has two major implications. First, the amplitude dynamics of the song pattern
are steadily degraded over distance, which limits the effective communication
range of grasshoppers to~\mbox{1\,-\,2\,m} in their typical grassland
habitats~(\bcite{lang2000acoustic}). Second, the overall intensity level of
songs at the receiver's position varies depending on the location of the
sender, which should ideally not affect the recognition of the song pattern.
This neccessitates that the auditory system achieves a certain degree of
intensity invariance --- a time scale-selective sensitivity to faster amplitude
dynamics and simultaneous insensitivity to slower, more sustained amplitude
dynamics. Intensity invariance in different auditory systems is often
associated with neuronal adaptation~(\bcite{benda2008spike},
\bcite{barbour2011intensity}, \bcite{ozeri2018fast}), which represents an
important principle of dynamic sensory systems in
general~(\bcite{benda2021neural}). In the grasshopper auditory system, a number
of neuron types along the processing chain exhibit spike-frequency adaptation
in response to sustained stimulus
intensities~(\bcite{romer1976informationsverarbeitung},
\bcite{gollisch2002energy}, \bcite{hildebrandt2009origin},
\bcite{clemens2010intensity}) and thus likely contribute to the emergence of
intensity-invariant song representations. This means that intensity invariance
is not the result of a single processing step but rather a gradual process, in
which different neuronal populations contribute to varying
degrees~(\bcite{clemens2010intensity}) and by different
mechanisms~(\bcite{hildebrandt2009origin}). Approximating this process within a
functional model framework thus requires a considerable amount of
simplification. In this work, we demonstrate that even a small number of basic
physiologically inspired signal transformations --- specifically, pairs of
nonlinear and linear operations --- is sufficient to achieve a meaningful
degree of intensity invariance. Due to the critical role of intensity-invariant
representations for reliable song recognition, these transformations are at the
core of the proposed model framework.
The
amplitude modulation, or envelope, of the song is sufficient for successful
recognition~(\bcite{helversen1997recognition}). Because grasshoppers are
poikilothermic, the temporal structure of their songs warps with
temperature~(\bcite{skovmand1983song}), which poses a major challenge for the
auditory system.
Songs = Amplitude-modulated (AM) broad-band acoustic signals\\
- Generated by stridulatory movement of hindlegs against forewings\\
- Shorter time scales: Characteristic temporal waveform pattern\\
- Longer time scales: High degree of periodicity (pattern repetition)\\
- Sound propagation: Signal intensity varies strongly with distance to sender\\
- Ectothermy: Temporal structure warps with temperature\\
$\rightarrow$ Sensory constraints imposed by properties of the acoustic signal itself
Multi-species, multi-individual communally inhabited environments\\
- Temporal overlap: Simultaneous singing across individuals/species common\\
- Frequency overlap: No/hardly any niche speciation into frequency bands\\
- Frequency overlap: Little speciation into frequency bands (likely unused)\\
- "Biotic noise": Hetero-/conspecifics ("Another one's songs are my noise")\\
- "Abiotic noise": Wind, water, vegetation, anthropogenic\\
- Effects of habitat structure on sound propagation (landscape - soundscape)\\