Population growth of a powerful part of the population is often an indication of an increase of the language of that group. In historic times this was often related for male paternal lines. Discrete population growth of a significant percentage of the population can indicate the change of a language in a certain region in a certain timeperiod. Continuous population is unlikely to have strong impact on language changes.
Some reports on the major relations between languages and Y-DNA can be found on:
Island pattern: when populations were small they stayed on their location for a long period. This gives an "island-pattern". This results in long narrow Y-DNA branches, an isolated language, and a limited amount of violence between tribes. Exchange of ideas, knowledge, DNA was very limited. This pattern is present in the Americas, New Guinea, Andaman Islands, Khoisan languages, Ainu (in Japan), Negrito languages in Phillipines etc.
Tribal pattern: knowledge increased, population grows, diversity of roles in the community and an additional pressure on the powerfull people to conquer land from other peoples, so the own tribe can expand. This results often in a population jump, a migration and development of a language family. This is the case for Indo-Europeans (5000ybp), Bantu (4000ubp), Austronesian (4000ybp), Japonic (3000ybp), Korean (3000ybp). In later periods one can see characteristics in Berber, Arab, Finnic, Slavic.
Power increased with language distribution with limited Y-DNA characteristics. This is the case with the Hungarian language. Sino-Tibetan, Roman languages.
I don't knowI found insufficient data to make conclusions on these language families: Tai-Kadai, Austroasiatic.
Individual migrations: these happened in recent times when people migrated individually or in small groups without options to trace an individual line based on group migrations. These typically happened with people looking for a better chance to survive from Europe and other areas to the Americas, South-Africa, Australia, New-Zealand or as slave migrations. In these situations the language was chosen by the early arriving people (e.g. English, Spanish, Portuguese).
A review on the general concept of language change is given on the NativLang channel of youtube. An interesting article on the automated age determination of the languages is reported by Holman et al. (2011; doi:10.1086/662127)
Contact is a clear example of language change. Pidgin, Creolo are examples of mixing styles of languages. This is determined by the level of isolation. In case of contact it is expected that a less powerfull group adjusts his language on the aspects that is relevant for them. The Anglo-saxons in Britain maintained the Anglo-saxon words for the animals when producing meat, but when it was presented as a dish to the French elite, they used the French words.
In the NativLang presentation they report: Paya-Nyugan = 5000, Indo-European = 6000, Afro-Asiatic = 9000+ and Austronesion = 6000.
Several aspects in the time estimates are uncertain. In the Indo-European data, the moment of migration of R1b to Anatolia is the clearest strong migration. The Y-DNA yfull time estimates indicate 5300 ybp, which is about 20 percent larger than the glottochronology estimate of Holman et al. The time estimate of N in the Ural gives about 4000 ybp for the Uralic languages. This is about 25 percent larger than the estimate of Holman et al. The first Niger-Congo expansion that we see is 8900 ybp. The next expansion of this branch (followed by more expansions) was near 6100 ybp. If we use the first expansion it would be about 40 percent larger. If we use the E-L1250 (in E-V22; 7900 ybp) population growth (as suggested on E-M35 page) as the basic population jump for the Afroasiatic languages, it would result in a correction of 30 percent.
The time estimaes of Y-DNA are based on good statistics and fairly good normalization. The age determination from glottochronology gives a good general pattern, but the accuracy of the estimates is very limited. No good normalization exists, changes in small groups and in large groups are different, and cultural organization and mixtures also contribute to the speed of language change. A difference of 30 percent between a fairly accurate age estimate in Y-DNA and an inaccurate age estimate from glottochronology is no surprise.
Examples where in the easiest scenario a migration was not followed by a language change:
Examples where in the easiest scenario fits a substrate language
Notice the systematic effects of migrations as reported on the Time Maps page.
Below is an overview of languages on the map by wikipedia.