In order to establish the fact that feature economy is the key factor that drives the co-occurrence patterns of the consonants it is necessary to show that the communi- ties obtained from PhoNet exhibit a significantly lower feature entropy than the case
where the consonant inventories are assumed to have been generated randomly. For this purpose, we construct a random version of PhoNet (henceforth PhoNetrand) and
compare the communities obtained from it with those obtained from PhoNet in terms of feature entropy. We construct PhoNetrand as follows. Let the frequency of occur-
rence for each consonant C in UPSID be denoted by fC. Let there be 317 bins each
corresponding to a language in UPSID. fC bins are then chosen uniformly at random
and the consonant C is packed into these bins. Thus the consonant inventories of the 317 languages corresponding to the bins are generated4. Note that in such ran-
domly constructed inventories the effect of feature economy should not be prevalent as there is no strict co-occurrence principle that plays a role in the process of inven- tory construction. Therefore, feature entropy in this case should be no better than what is expected by random chance. One can build PhoNetrand from these randomly
generated consonant inventories in a procedure similar to that used for constructing PhoNet. The entire idea of constructing PhoNetrand is summarized in Algorithm 5.2.
Algorithm 5.2: Algorithm to construct PhoNetrand
for each consonant C do for i = 1 to fC do
Choose, uniformly at random, one of the 317 bins each of which corresponds to a language in UPSID;
Pack the consonant C into the bin so chosen if it has not been already packed into this bin earlier;
end end
Construct PhoNetrand, similarly as PhoNet, from the new consonant
inventories (each bin corresponds to a new inventory) ;
We can apply the MRad algorithm to extract the communities from PhoNetrand
similarly as in the case of PhoNet. Figure 5.6 illustrates, for all the communities obtained from PhoNet and PhoNetrand, the average feature entropy exhibited by the
communities of a particular size (y-axis) versus the community size (x-axis). The “average feature entropy exhibited by the communities of a particular size” can be
Figure 5.6: Average feature entropy of the communities of a particular size versus the community size for PhoNet as well as PhoNetrand
calculated as follows. Let there be n communities of a particular size s obtained at all the different values of η. The average feature entropy of the communities of size s is
1 n
Pn
i=1FEi where FEi signifies the feature entropy of the i
th community of size s. The
curves in the figure make it quite clear that the average feature entropy exhibited by the communities of PhoNet are substantially lower than that of PhoNetrand(especially
for a community size ≤ 20). As the community size increases, the difference in the average feature entropy of the communities of PhoNet and PhoNetrand gradually
diminishes. This is mainly because of the formation of a giant community, which is similar for both PhoNet as well as PhoNetrand. The above result indicates that the
consonant communities in PhoNet are far more economic than what is expected by random chance. Note that if in contrast, the communities exhibit a feature entropy that is higher than that reflected by the randomly generated inventories then one can argue that on an average the features are more discriminative than expected by chance pointing to the prevalence of high perceptual contrast among the constituent nodes in the community (this shall become apparent from the analysis of the vowel communities presented in the next chapter).
Figure 5.7: Average occurrence ratio (Oav) versus the feature entropy of the communities
consonants forming communities in PhoNet occur in real languages in such groups so as to minimize feature entropy. Figure 5.7 shows the scatter plot of the average occurrence ratio of the communities obtained from PhoNet (y-axis) versus the feature entropy of these communities (x-axis). Each point in this plot corresponds to a single community. The plot clearly indicates that the communities exhibiting lower feature entropy have a higher average occurrence ratio. For communities having feature entropy less than or equal to 3 the average occurrence ratio is never less than 0.7 which means that the consonants forming these communities occur together on an average in 70% or more of the world’s languages. As feature entropy increases this ratio gradually decreases until it is almost close to 0 when feature entropy is around 10. Once again, this result fosters the fact that the driving force for the community formation is the principle of feature economy and languages indeed tend to choose consonants in order to maximize the combinatorial possibilities of the distinctive features, which are already available in the inventory.