Are there any examples of how to apply evolutionary models?
Hypothesis testing in evolutionary biology

Pretty much any paper of empirical evolutionary biology tests hypothesis. If you go on google scholar and look for any empirical paper in the field of evolutionary biology such as "does sexual selection has antagonist effect to natural selection", "evolution of range limits", "evolution of mutational robustness" or "sensory drive speciation" you will find tons of papers that test hypotheses. Many of these hypotheses have been developed either in pure theory papers on in papers that mix some level of theory (no necessary need of complicated modelling) and empirical work. There is nothing in evolutionary biology that is different from the other field of biology or the other fields of science in our ability to test hypotheses.

A tiny bit of history

In the first half of the century most work in evolutionary biology was theoretic. Many hypotheses were left untested. Today, we perform lots of tests and the technics of molecular genetics (sequencing and stuff) help a lot to test hypotheses. Some papers, indeed uses metrics that are very hard to estimate, eventually too hard (too expensive) to be estimated today, it is true and it is an issue, an issue that all sciences know of. We sometimes have to wait for technical advancements before being able to test a hypothesis.

Concerning the paper you mention

From your description of the work they performed in the paper you linked (I haven't read this paper) it sounds like they are describing the concept of shifting balance theory, a process that has been first hypothesize by S. Wrigth in 1932. As said on the wiki article, there is little empirical evidence for shifting balance theory (but you may want to read this and that). The reason is that shifting balance theory is link to the concept of adaptive landscape. Adaptive landscape is what we call the relationship between fitness and phenotype or fitness and genotype. We have descriptions of fitness-phenotype relationship but we are only starting to offer good and complete descriptions fitness-phenotype-genotype relationship. Understanding the link between genotype and fitness is essential for testing shifting balance theory. Shifting balance theory is a logical consequence of the process of drift and selection, both of which are very well known (and well tested). Most of the issue is in the description of how rough is the fitness landscape to know whether shifting balance theory is indeed a thing that occurs in nature or whether it is very unlikely of such process to ever occur.