Sure! And, well, they're not necessarily old like I said, but it's actually two different papers:

"Beaked Whale Sexual Dimorphism, Mating Strategies, and Diversification" (Alves et al., 2023) and "A trade-off between precopulatory and postcopulatory trait investment in male cetaceans "(Dines et al., 2015).

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The first one takes into account recorded testes measurements, amount of tooth raking, beak reinforcement, tusk size, male association and known group size to investigate the possible strategies they use for reproduction. They suggested that more aggressive (typically heavily scarred) species tend to live in smaller pods with one dominant male, whose dominance is determined by precopulatory contests (i.e. fighting, headbutting).

For exmample, Blainville's BW pods are known to generally consist of one male and many females and immatures lasting from hours to months. They also gain some of the most scarring of any BW, and have small testes relative to body size, indicating strong competition for female access. They may search for females and mate with them and leave OR travel with them for a while to ensure their patternity.

Less-aggressive species are suggested to, at least sometimes, live in larger, mixed-sex groups and the females may mate with multiple males and indicate some sort of post-copulatory sperm contest, particularly in Berardius whales., since their testes are larger than in other beaked whales relative to body size!

The second paper pretty much details the same thing - precopulatory competition is likely the general rule amongst BW'S.