Recent advances in DNA sequencing allows us to observe the evolution of populations in real time by tracking the change in the frequencies of variant nucleotides through time, particularly for microbes and viruses that reproduce asexually. To understand the causes and patterns of evolutionary changes through DNA sequence data, it is important to define and use an appropriate parameter to summarize the evolutionary dynamics of a population. Temporal clustering of fixations, occurring when multiple alleles at different loci are fixed together due to various evolutionary forces, can be quantified by the index of dispersion (IOD = variance/mean). In the previous study, IODs of asexual populations under neutral equilibrium or under recurrent positive selection were shown to be sufficiently larger than one, indicating that temporal clustering of fixation events occurs on wide parameter space for asexually evolving systems. In this study, we ran simulations and recorded times at which mutant alleles reach an intermediate threshold frequency. The temporal clustering of these events is also quantified by IOD. We obtained IODs for ten different threshold frequencies, under both neutral and selection models. There is a qualitative difference in neutral vs. selection models in the relationship between the threshold frequency and IOD: increase in IOD with increasing threshold frequency is much steeper in the neutral model than in selection models. This result may allow us to assess the presence of recurrent positive selection in asexually-evolving populations with genomic data. We also elaborate on theoretical explanation for this result in terms of genetic hitchhiking and clonal interference.