coalescent methods

Basic idea: build a phylogenetic (gene) tree based on (ideally) neutral genomic samples. The shape of the tree (rate of branching per unit time) tells us whether the population is decreasing, increasing, or stable.

See Elliot and Mooers (n.d.) (intro, a little mathy, but very clear); Kuhner (2009) (intro journal article); Volz et al. (2009) (using coalescents for epidemics); Stadler et al. (2013) (ditto)

Elliot, Mick, and Arne Mooers. n.d. “Introduction to Coalescent Theory.” https://web.archive.org/web/20170919050032/http://www.sfu.ca/biology/courses/bisc869/869_lectures/MHP_Coalescent.pdf.
Kuhner, Mary K. 2009. “Coalescent Genealogy Samplers: Windows into Population History.” Trends in Ecology & Evolution 24 (2): 86–93. https://doi.org/10.1016/j.tree.2008.09.007.
Stadler, Tanja, Denise Kühnert, Sebastian Bonhoeffer, and Alexei J. Drummond. 2013. “Birth–Death Skyline Plot Reveals Temporal Changes of Epidemic Spread in HIV and Hepatitis C Virus (HCV).” Proceedings of the National Academy of Sciences 110 (1): 228–33. https://doi.org/10.1073/pnas.1207965110.
Volz, Erik M, Sergei L Kosakovsky Pond, Melissa J Ward, Andrew J Leigh Brown, and Simon D W Frost. 2009. “Phylodynamics of Infectious Disease Epidemics.” Genetics 183 (4): 1421–30. https://doi.org/10.1534/genetics.109.106021.