Information analysis of Bat Calls

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Figure 1 Figure 2 Figure 3 Figure 4

Table 1 Table 2

Strong's method[1], which is originally used to quantify the information flow of neural spikes, is applied here to quantify the information flow of bat calls. See Figure 1 for the basic procedure of the method.

The word distribution curve is highly skewed, with word '0'(no calls) mostly frequent. See Figure 2.

As described in Figure 1, we can compute the entropy rate, the upper limit of information rate, from the word distribution. The result is shown in Table 1 and plotted in Figure 3.

The entropy carried by one call, calculated as entropy rate divided by call rate(# of calls/second), is around 11 bits. See Figure 4.

The number of calls in each time period is shown in Table 2.

Table 1: Entropy rate, word length and resolution time

　 　 Word length, L 　 　 　 　 　 　 　 　 　
dt, resolution time (sample number) 1 2 4 8 16 32 64 128 256 512 1024
　 1/dt 1/L 1 0.5 0.25 0.125 0.0625 0.03125 0.015625 0.007813 0.003906 0.001953 0.000977
1 1 6253.109 3233.886 1725.256 970.7849 593.1362 403.4452 307.9917 255.9366 216.0363 176.611 138.2248
2 0.5 3141.188 1668.18 931.4389 562.5991 377.2187 284.0313 235.2077 200.8773 168.0936 134.3031 76.30811
4 0.25 1585.328 879.1243 525.7785 348.0229 258.5257 212.6669 183.1523 155.6715 127.1416 75.83113 37.3722
8 0.125 807.1699 479.1908 314.2585 230.8473 188.3732 163.5045 141.0036 116.7948 74.55674 37.36607 17.70387
16 0.0625 417.7212 273.4723 200.0266 162.5408 141.6004 124.6624 104.9039 71.96718 37.34501 17.70329 8.192154
32 0.03125 222.2294 163.0269 131.9232 115.1208 103.6586 89.81683 66.10328 37.18704 17.70201 8.192154 3.757358
64 0.015625 122.5621 100.5938 88.01354 80.24803 72.35149 56.69554 35.94052 17.69125 8.192154 3.757358 1.710445
128 0.007813 69.84474 63.66814 58.55898 53.87305 45.40555 32.44407 17.52786 8.192154 3.757358 1.710445 0.771113
256 0.003906 40.2175 39.46258 36.79202 32.25621 26.71512 16.663 8.177164 3.757358 1.710445 0.771113 0.343604
512 0.001953 21.48902 21.17389 20.16933 18.04039 14.51712 8.031109 3.757358 1.710445 0.771113 0.343604 0.150773
1024 0.000977 7.179716 6.745139 6.490494 6.254051 5.452181 3.591465 1.710152 0.771113 0.343604 0.150773 0.064872

　

Table 2: Number of calls

　

Time(min) Call Number total calls
5 3681 3681
10 3152 6833
15 3042 9875
20 3044 12919
25 3195 16114
30 3279 19393
35 3169 22562
40 3280 25842
45 3065 28907
50 3107 32014
55 3307 35321
60 3123 38444
65 3333 41777
70 3288 45065
75 3346 48411
80 3683 52094
85 3704 55798
90 3674 59472
95 3530 63002
100 3530 66532
105 3172 69704
110 3104 72808
115 3141 75949

　

　

References:

[1] Strong et al., "Entropy and information in neural spike trains", Phys Rev Lett 80: 197-200 (1998)