*3.3. Gene Duplication Analysis and Evolutionary Rate Calculation*

In the present study, a total of 18 (18/25; 72%) maize HSF genes were shown to be duplicated (Table 3). Further, only one pair of a gene (*ZmHSF-01*/*Zm-HSF-04*) appeared to be tandemly duplicated, which was recognized on chromosome number 1 (Figure 3). The rest of duplicated genes were all segmentally duplicated, with eight different clusters containing 16 genes. These genes were recognized on chromosomes 1–9. Moreover, the molecular evolutionary rate of tandemly and segmentally duplicated HSF genes was calculated to gain insights into the selective constraints on the duplicated HSF genes. The ratio of Ka and Ks substitution rate is an effective method to investigate the selective constraint among duplicated gene pairs [64]. Hence, in the present study, Ka, Ks, and Ka/Ks values for each paralogous gene pair were calculated (Table 3). Here, 18 *Zm*HSF genes were shown to be duplicated. The Ka/Ks ratio for duplicated *Zm*HSF genes ranged from 0.3415 to 0.7572. All the HSF genes in the present study have Ka/Ks value < 1.

**Table 3.** Duplicated gene pairs, non-synonymous substitution rate (Ka), synonymous substitution rate (Ks), nonsynonymous to synonymous substitution rate ratio (Ka/Ks), estimated time of duplication event in a million years ago (MYA), and mode of gene duplication.


**Figure 3.** Circular illustration of the maize genome. The paralogous HSF genes are connected with grey lines. The red lines on top of the chromosomal bar represent the position of HSFs.

The outcome suggests that these genes were under strong purifying selection pressure by natural selection during the course of evolution. Further, the divergence periods of tandemly and segmentally duplicated *ZmHSF* genes were estimated to range from 5.96 to 38.04 with an average of 20.89 million years ago (MYA). Some paralogous gene pairs (*ZmHSF-02*/*ZmHSF-24*, *ZmHSF-09*/*ZmHSF21*, and *ZmHSF-16*/*ZmHSF20*) appeared to be recently duplicated (Table 3). The grass species are estimated to have diverged around 56–73 MYA [65,66]. In the present analysis, all the *HSF* genes in maize appeared to have duplicated after the divergence of grass species. Further, most of the HSF genes in maize are paralogs, and it can be concluded that duplication events (primarily segmental) played a significant role in the expansion of the *HSF* gene family in maize.
