This has been a focus of linguists and biologists since systematic study of language and organisms began in the 19th Century.
It is difficult to conceive of a process of language change that is has not been considered in relationship to biological change, from language (or language family) to species (or genus) down to phonemes to codons.
This difficulty is apparent in the very nature of the discussion. The proposition that diverse languages were related to each other by a formerly existing language came as early as the late 16th century, when Europeans in India noticed resemblances among Sanskrit, Latin, and Greek. From the beginning, this was conceived of using biological terminology: the languages were part of a family, with parent languages giving birth to child languages through the same basic processes that would later become processes by which speciation was believed to occur. Primarily, geographical barriers to continued communication, linguistic or sexual, especially founder effects in previously uncolonized areas; and the development and/or exploitation of niches within a geographical area with no practical physical barriers to continued interchange of words or genes.
In addition to the language used, the graphical representations were very similar. Tree diagrams with an arrow representing time from trunk to branches to stems and leaves. Which of course were correspondent to family records of ancestry and inheritance. And, in turn, the oldest of these family records of ancestry and inheritance themselves provided the data regarding how the language used to record them and the names used within the population changed over time.
This was not unnoticed by scholars. Early linguistics innovators Jacob and Wilhelm Grimm devoted attention to the relationships. Early biology innovators such as Charles Darwin did the same from their side of the tree of knowledge.
Iceland is the ultimate example. There were nearly no inhabitants prior to the Norse colonization in the 10th century, and those who were there were Irish monks not prone to breeding. This resulted in a double founder effect.
The colonizers of Iceland were literate, and their naming system was directly dependent on ancestry - a child was given a personal name and a patronym, there were no family names as in many other cultures. Thus, our most famous living Icelander is named Björk Guðmundsdóttir. Her father, a prominent politician and author of textbooks on electrical engineering, is named Guðmundur Gunnarsson, whose father was named Gunnar Guðmundsson. This requires careful record keeping.
Iceland was also a very poor place in economic terms until the 20th century, with almost no immigration and a low population. This has resulted in having detailed records of the ancestry of nearly everyone who ever lived in Iceland, and texts recording this history that exemplify the changes in the language over the past 1000 years.
The questions that remain unanswered are the extent to which apparent similarity in structure, whether the language used to discuss two things, to graphically represent two things, or to mathematically represent two things, indicate that the phenomenon underlying these observations and representations by humans are in physical reality similar in such ways, or if they are a complex system of metaphor and analogy.
Note that no one really knows what "physical reality", "metaphor", or "analogy" refer to in such a way that they have successfully convinced other highly relevant parties that they that are correct.
So you have your relatively accepted analogies, such as comparisons of models of genetic drift to phoneme change in the form of glottochronology being used to date the divergence of two language populations in the same manner as changes in codons in areas of genetic material believed to be not under evolutionary selective pressure are used to date the divergence of biological populations.
You also have comparative analyses of islands as nature's experimental laboratories to study both language and genetic divergence (as well as use of mountains and rivers as similar barriers to exchange of information).
And there are serious investigations of historical records of language over time being calibrated with known or inferred population changes and movements. One prominent theory connects the spread of Indo-European languages from Anatolia into Europe and through western Asia into India with the spread of agriculture. On the other hand, another theory links the spread of Indo-European languages from the area north of the Black Sea in connection with the domestication of horses, which creates a huge change in military matters whenever cavalry are introduced to areas where no domesticated horses exist.
Note that both of these theories link the divergence of the Indo-European languages with changes in biological species, that of domestication. And it was analysis of the process of domestication that was one of the major sources of inspiration and argumentation for the theory of biological evolution.
A major question for the past several decades has been whether there is, in humans at least, another form of inheritance analogous in critical ways (i.e., a meaningful unit of information that can be replicated with less than perfect accuracy that is under selective pressure that impacts the likelihood of survival) that functions on a linguistic or cultural level. Also of major concern is whether this "second replicator" can act in ways that have a negative effect on likelihood of genetic replication and transmission.
Lucca Cavalli-Sforza, Robert Boyd, and Peter Richerson are prominent among those who provide more robust methods of investigation and evidentiary standards to support their theories that there is such a second replicator. There are others as well.
They tend to be trained in genetic and/or evolutionary biology or anthropology rather than linguistics or the life science areas that directly and traditionally focus on the brain, its contents, and the impact of those contents on behavior (the behavioral, cognitive, and neurosciences). Linguists and brain/behavior researchers are generally more skeptical of this process of analogy.
There is also a large population of academics and enthusiasts who more or less assume that this second replicator exists and engage in speculation about what that means for various aspects of human culture and thought.
So there is about 200 years of studies of various aspects of the relationship between language change and biological change, including much research on the language-species level of comparison.