Characteristics and applications of beta acoustic indices

doi:10.17520/biods.2022513

Abstract

Abstract:

Background & Aims: In recent years, with recording equipment becoming more accessible to researchers through improved performance and reduced prices, habitat and biodiversity assessment conducted through audio recording has developed rapidly. An acoustic index is the quantification of the overall characteristics of sound, which is influenced by both the habitat characteristics and the composition and abundance of species in the study area. Therefore, there is a correlation, at least in theory, amongst acoustic indices, habitat, and biodiversity. An acoustic index can be divided into two categories: reflecting the information within the recordings and comparing the differences between different recordings, which are named an alpha acoustic index and beta acoustic index, respectively. With the increase of utilizing recording monitoring equipment in studies, the demand for comparing acoustic indices at different times and places has also increased. Therefore, the development and application of the beta acoustic index is an important direction of acoustic index research. Here, we introduced some commonly used beta acoustic indices, and explored the mathematical properties (non-negativity, self-identity, symmetry, triangle inequality, finiteness) of these indices. We also summarized applications of these beta acoustic indices by conducting a systematic literature review.

Results & Discussion: In this paper, we introduced 11 commonly utilized beta acoustic indices: mutual information index (MI), relative frequency dissimilarity index (RF), temporal dissimilarity index (TD), spectral dissimilarity index (SD), acoustic dissimilarity index (AD), Kolmogorov-Smirnov distance index (KS), Kullback-Leibler distance index (KL), cumulative spectral dissimilarity index (CS), correlation-based dissimilarity index (CB), Itakura-Saito distance index (IS), and log-spectral distance index (LS). Three of these indices (RF, KS, CS) satisfy all the properties (non-negativity, self-identity, symmetry, triangle inequality, finiteness), and another three indices (TD, SD, LS) satisfy the metric properties (non-negativity, self-identity, symmetry, triangle inequality). Cross-reference searches were conducted in the Web of Science database (www.webofscience.com, accessed on 2022-10-20), and 14 articles were found concerning the application of beta acoustic indices. Amongst these articles, SD was used most frequently in seven articles; AD and CS were used in five and four articles, respectively, while other beta acoustic indices were used no more than three times. The application of beta acoustic indices mainly focused on three aspects: the changes in time rhythm, habitat characteristics, or biological composition.

Prospect: We pointed out three areas in need of urgent development in the study/application of beta acoustic indices: designing new indices, optimizing the algorithm for existing indices, and strengthening empirical research.

Key words: acoustic monitoring, acoustic index, biodiversity, bioacoustics, metric

Yimei Zhang, Yanyi Wang, Yan He, Bing Zhou, Miao Tian, Canwei Xia. Characteristics and applications of beta acoustic indices[J]. Biodiv Sci, 2023, 31(1): 22513.

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URL: https://www.biodiversity-science.net/EN/10.17520/biods.2022513

https://www.biodiversity-science.net/EN/Y2023/V31/I1/22513

Figures/Tables 3

Table 1 Description of the commonly used beta acoustic indices

声学指数 Acoustic index	计算公式 Computing formula	公式中符号的含义 Meaning of symbols in the formula	参考文献 Reference
交互信息指数 Mutual information index (MI)	$MI?=? H 1 + H 2 ? H 1 ∪ 2$	H₁, H₂, $H 1 ∪ 2$ 分别为两段声音各自及合并后的Shannon指数 H₁, H₂, $H 1 ∪ 2$ are the Shannon index of each sound and the joint sound	2004
相对频谱差异指数 Relative frequency dissimilarity index (RF)	$RF = 1 ? 1 n ∑ ? min x i, ? y i max x i, ? y i$	x_i, y_i分别为两段声音各自频段的相对音强 x_i, y_i are the relative sound intensity in each frequency band of each sound	2006
时间差异指数 Temporal dissimilarity index (TD)	$TD?=? 12 ∑ ? s i ? t i$	s_i, t_i分别为两段声音各自时段的相对音强 s_i, t_i are the relative sound intensity in each time period of each sound	2008
频谱差异指数 Spectral dissimilarity index (SD)	$SD?=? 12 ∑ ? x i ? y i$	同RF Same as in the formula of RF	2008
声音差异指数 Acoustic dissimilarity index (AD)	$AD?=?TD? × ?SD$	TD和SD的乘积 Product of TD and SD	2008
Kolmogorov-Smirnov距离指数 Kolmogorov-Smirnov distance index (KS)	$KS?=? m a x X i ? Y i$	X_i, Y_i分别为两段声音每个频率的累积音强 X_i, Y_i are the cumulative sound intensity in each frequency of each sound	2013a
Kullback-Leibler距离指数 Kullback-Leibler distance index (KL)	$KL?=? 12 ∑ ? x i × log x i y i + ∑ ? y i × log y i x i$	同RF Same as in the formula of RF	2013a
累积频谱差异指数 Cumulative spectral dissimilarity index (CS)	$CS? = 1 n ∑ ? X i ? Y i$	同KS Same as in the formula of KS	2014
相关差异指数 Correlation-based dissimilarity index (CB)	$CB?=? 1 ? ∑ ? x i × y i ∑ ? x i 2 × ∑ ? y i 2$	同RF Same as in the formula of RF	2014
Itakura-Saito距离指数 Itakura-Saito distance index (IS)	$IS?=? 12 ∑ ? x i y i ? log x i y i ? 1 + ∑ ? y i x i ? log y i x i ? 1$	同RF Same as in the computing of RF	2018
对数频谱距离指数 Log-spectral distance index (LS)	$LS?=? ∑ ? 10 × log x i y i 2$	同RF Same as in the formula of RF	2018

Table 1 Description of the commonly used beta acoustic indices

声学指数 Acoustic index	计算公式 Computing formula	公式中符号的含义 Meaning of symbols in the formula	参考文献 Reference
交互信息指数 Mutual information index (MI)	$MI?=? H 1 + H 2 ? H 1 ∪ 2$	H₁, H₂, $H 1 ∪ 2$ 分别为两段声音各自及合并后的Shannon指数 H₁, H₂, $H 1 ∪ 2$ are the Shannon index of each sound and the joint sound	2004
相对频谱差异指数 Relative frequency dissimilarity index (RF)	$RF = 1 ? 1 n ∑ ? min x i, ? y i max x i, ? y i$	x_i, y_i分别为两段声音各自频段的相对音强 x_i, y_i are the relative sound intensity in each frequency band of each sound	2006
时间差异指数 Temporal dissimilarity index (TD)	$TD?=? 12 ∑ ? s i ? t i$	s_i, t_i分别为两段声音各自时段的相对音强 s_i, t_i are the relative sound intensity in each time period of each sound	2008
频谱差异指数 Spectral dissimilarity index (SD)	$SD?=? 12 ∑ ? x i ? y i$	同RF Same as in the formula of RF	2008
声音差异指数 Acoustic dissimilarity index (AD)	$AD?=?TD? × ?SD$	TD和SD的乘积 Product of TD and SD	2008
Kolmogorov-Smirnov距离指数 Kolmogorov-Smirnov distance index (KS)	$KS?=? m a x X i ? Y i$	X_i, Y_i分别为两段声音每个频率的累积音强 X_i, Y_i are the cumulative sound intensity in each frequency of each sound	2013a
Kullback-Leibler距离指数 Kullback-Leibler distance index (KL)	$KL?=? 12 ∑ ? x i × log x i y i + ∑ ? y i × log y i x i$	同RF Same as in the formula of RF	2013a
累积频谱差异指数 Cumulative spectral dissimilarity index (CS)	$CS? = 1 n ∑ ? X i ? Y i$	同KS Same as in the formula of KS	2014
相关差异指数 Correlation-based dissimilarity index (CB)	$CB?=? 1 ? ∑ ? x i × y i ∑ ? x i 2 × ∑ ? y i 2$	同RF Same as in the formula of RF	2014
Itakura-Saito距离指数 Itakura-Saito distance index (IS)	$IS?=? 12 ∑ ? x i y i ? log x i y i ? 1 + ∑ ? y i x i ? log y i x i ? 1$	同RF Same as in the computing of RF	2018
对数频谱距离指数 Log-spectral distance index (LS)	$LS?=? ∑ ? 10 × log x i y i 2$	同RF Same as in the formula of RF	2018

Table 2 Mathematical properties of beta acoustic indices

声学指数Acoustic index^*	非负性 Non-negativity	同一性 Self-identity	对称性 Symmetry	直递性 Triangle inequality	有限性 Finiteness
MI	否 No	否 No	是 Yes	否 No	是 Yes
RF	是 Yes	是 Yes	是 Yes	是 Yes	是 Yes
TD	是 Yes	是 Yes	是 Yes	是 Yes	否 No
SD	是 Yes	是 Yes	是 Yes	是 Yes	否 No
AD	是 Yes	否 No	是 Yes	否 No	否 No
KS	是 Yes	是 Yes	是 Yes	是 Yes	是 Yes
KL	是 Yes	是 Yes	是 Yes	否 No	否 No
CS	是 Yes	是 Yes	是 Yes	是 Yes	是 Yes
CB	是 Yes	是 Yes	是 Yes	否 No	是 Yes
IS	是 Yes	是 Yes	是 Yes	否 No	否 No
LS	是 Yes	是 Yes	是 Yes	是 Yes	否 No

Table 3 The application of beta acoustic indices

声学指数 Acoustic index^*	生物学意义 Biological significance	文献 Reference
AD	反映物种(鸟类、两栖类、昆虫)组成不同 Difference in species (birds, amphibians, insects) composition	2008
AD	反映生境差异(成熟森林、幼林、林地-农田交错带的比较) Difference in habitat comparison among mature forest, young forest, and forest-cropland ecotone	2012
SD	反映日节律 Daily rhythm	2013a
SD, KS, KL, CB	反映鸟类物种数量不同 Difference in the number of bird species	2013b
CB, KL, SD, KS, CS	反映鸟类物种数量不同 Difference in the number of bird species	2014
SD	反映日节律、生境差异(林下层和树冠层的比较) Daily rhythm, difference in habitat comparison between understory and canopy	2014
AD	反映生境差异(清除、再生、残留植被的比较) Difference in habitat comparison among cleared, regrowth and remnant vegetation conditions	2018
SD, CS	反映月相变化、生境差异(有无入侵生物啮齿类和狐狸) Lunar rhythm, difference in habitat have or not have invasive species rats and foxes	2020
SD, CS	反映日节律、生境差异(油棕种植园和周围森林的比较) Daily rhythm, difference in habitat comparison between oil palm plantation and surrounding forests	2020
AD	反映日节律和季节变化 Daily rhythm, seasonal variation	2022
SD, TD, CS, AD, KS, CB, MI, LS, RF	反映生境差异(混交林、落叶林的比较) Difference in habitat comparison between mixed-use corridor and deciduous forest	2022

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