Our work studies the implications of transfer learning on model behavior beyond accuracy: how does the pre-training distribution affect the downstream robustness of a fine-tuned model? We analyze model robustness using the framework proposed by Taori et al. (2020), which demonstrates that in-distribution and out-of-distribution performances are highly correlated along a robustness linear trend. We explore various interventions that significantly alter the pre-training distribution, including label space, label semantics, and the pre-training dataset itself. In most cases, changes during pre-training have minimal impact on the original linear trend produced by models pre-trained on the full ImageNet dataset. We demonstrate these findings on pre-training distributions constructed from ImageNet and iNaturalist, and fine-tuning data from the iWildCams-WILDS benchmark.