Relationship between α and β
α and β values derived from the sonic database at SABS, HPM, PK, and IK are presented in Supplementary Table 1. The regression analysis of the α and β components in each soundscape fits into concave down quadratic regression models (Fig. 1). Table 1 summarises the quadratic regression models at the four sites. HPM, PK, and IK show matching patterns with comparable quadratic equation coefficients and standard deviations (Table 1). The consistently low standard deviation indicates fewer Power Spectral Density (PSD) fluctuations in the quadratic fit. While the regression model of SABS was slightly different from the others, the overall trends of the sites are comparable. The statistical significance (p-value < 0.05) and high R2 values (0.57, 0.85, 0.66, 0.65 for SABS, HPM, PK, and IK, respectively) of datasets describe sonic powers are fit for the regression models.
The αmaxβ and βmax of the fitted curves are given in Table 1. αmaxβ values describe the changing behaviour of soundscapes across anthrophonic (α) and biophonic (β) components. The highest βmax (2.26 Watts/Hz) was observed at SABS. The four sites showed almost identical αmaxβ (0.39–0.40) values.
Table 1 α - β regression model summary of the four sites
Site
|
α
|
α2
|
(Constant)
|
R2
|
βmax (Watts/Hz)
|
αmaxβ (Watts/Hz)
|
Salim Ali Bird Sanctuary (SABS)
|
4.11 (± 0.16)
|
-5.1 (± 0.17)
|
1.43 (± 0.02)
|
0.57
|
2.26
|
0.40
|
Hill Palace Museum (HPM)
|
3.45 (± 0.22)
|
-4.29 (± 0.17)
|
1.29 (± 0.06)
|
0.85
|
1.98
|
0.40
|
Poyil Kavu (PK)
|
3.42 (± 0.28)
|
-4.31 (± 0.25)
|
1.31 (± 0.07)
|
0.66
|
1.99
|
0.40
|
Iringole Kavu (IK)
|
3.35 (± 0.20)
|
-4.34 (± 0.19)
|
1.42 (± 0.04)
|
0.65
|
2.06
|
0.39
|
Significance of αmaxβ
PSD represents average sonic power during a specific time in a certain frequency range. It is a physical measure of information that leads to understanding the spatio-temporal dynamics of soundscapes. Mechanical and biological sounds are prevalent between 1–2 kHz and 2–8 kHz, respectively25,26. The frequency ranges are divided into 1 kHz frequency bins, and α and β estimate the vector normalised power spectral density of the anthrophony and biophony components by the sum of the power in these frequency bins. Since the prevalent anthrophonic range contains only one bin (1–2 kHz), the maximum α yields a power of 1 watt/Hz27. It explains the convergence of α at 1 in Fig. 1. The magnitude of β represents the intensity of the biophony and thus reveals specific characteristics of vocal organisms in a soundscape.
The Ordinary Least Square regression analysis of α and β components across all the sites fits into concave down quadratic functions. Biophony (β) increases with increasing anthrophony (α) to reach a maximum before decreasing. The empirical results presented here correspond well with the Lombard effect 28,29. The positive relationship of α and β at lower levels of α at all sites (Fig. 1) explicates biophonic adaptive resilience of birds to changing soundscapes. However, the biophonic resilience collapses to zero after βmax with increasing α (Fig. 1). Higher β is indicative of the intensified bird vocalisations at the study sites and indicates their presence.
Anthrophonic level in a landscape (α) is a proxy for the degree of disturbance and stress to non-human vocalising species therein. The notion of αmaxβ introduced in this paper is identical to the point corresponding to the vertex in Functional Calculus (corresponds to βmax). It is the critical point where a curve changes direction from increasing to decreasing. Geometrically αmaxβ is the point at which the axis of symmetry through the vertex of the quadratic curve cuts the x-axis (α). The identical αmaxβ observed at all the sites (Table 1) open the prospect of defining acoustic limits in protected terrestrial landscapes. Elevated anthrophonic levels disturb indicator species like birds. They either become alarmed and keep silent or move to another soundscape with lower anthrophony21,30. Constant αmaxβ at the four sites point to similarities in their soundscapes. We presume αmaxβ to be dependent on geography. All sites in the present study are located in the tropical monsoon region. We recommend αmaxβ as an indicator of anthropogenic tolerance level of sonic pressure in the sites.
Although several indices are available to study the presence and diversity of acoustic communities 18,31,32, we are yet to arrive at a standard metric to denote the sonic characteristic of natural soundscapes. We propose estimating αmaxβ from the α - β regression model of the soundscapes as a pragmatic way to define the threshold anthrophonic sound in protected landscapes. The α - β regression model can also be used to monitor habitat quality and act as a baseline for landscape conservation planning.
The α - β regression model of soundscape is a characteristic attribute of the terrestrial landscape. The estimated αmaxβ of protected landscapes (soundscapes) provides us with a metric that can be used as the permissible threshold of anthrophony in conservation planning. Reconfirmed in different locations and times, the α - β regression model of soundscape will lead to a quantitative framework to protect terrestrial habitats and species conservation.