I did a Google search on the author's name, found a wee bit, but not the article.
PubMed does have an abstract:
The most widely used evolutionary model for phylogenetic trees is the equal-rates Markov (ERM) model. A problem is that the ERM model predicts less imbalance than observed for trees inferred from real data; in fact, the observed imbalance tends to fall between the values predicted by the ERM model and those predicted by the proportional-to-distinguishable-arrangements (PDA) model. Here, a continuous multi-rate (MR) family of evolutionary models is presented which contains entire subfamilies corresponding to both the PDA and ERM models. Furthermore, this MR family covers an entire range from 'completely balanced' to 'completely unbalanced' models. In particular, the MR family contains other known evolutionary models. The MR family is very versatile and virtually free of assumptions on the character of evolution; yet it is highly susceptible to rigorous analyses. In particular, such analyses help to uncover adaptability, quasi-stabilization and prolonged stasis as major possible causes of the imbalance. However, the MR model is functionally simple and requires only three parameters to reproduce the observed imbalance.Asymmetry in the branches shouldn't be too unexpected. In a simple random walk in 1-d (moving left or right with equal probability), it's highly likely that any individual walk with be biased in one direction or the other. The totalitiy of walks is symmetric, however. The same thing should happen with trees.
IF I understand this article correctly, it sounds like it could be summarized as saying: "the species that branches first, branches more often."
Or, it is as if with every speciation event, the branches each receive a lottery ticket; the more branches, the more lottery tickets in your family. The more tickets, the greater the odds that your family will frequently win the lottery.
Or, to but it another way, the more branches a given parent species has, the higher the probability that that some of it's branches will have favorable mutations, whereas the parent species that doesn't branch as much will have fewer chances of producing favorable mutations.
This reminds me of the phenomona of self-exciting systems. It's a form of positive feedback that reinforces the initial process (speciation).