The relationship between traditional metrics of research impact (e.g., number of citations) and alternative metrics (altmetrics) such as Twitter activity are of great interest, but remain imprecisely quantified. We used generalized linear mixed modeling to estimate the relative effects of Twitter activity, journal impact factor, and time since publication on Web of Science citation rates of 1,599 primary research articles from 20 ecology journals published from 2012-2014. We found a strong positive relationship between Twitter activity (i.e., the number of unique tweets about an article) and number of citations. Twitter activity was a more important predictor of citation rates than 5-year journal impact factor. Moreover, Twitter activity was not driven by journal impact factor; the 'highest-impact' journals were not necessarily the most discussed online. The effect of Twitter activity was only about a fifth as strong as time since publication; accounting for this confounding factor was critical for estimating the true effects of Twitter use. Articles in impactful journals can become heavily cited, but articles in journals with lower impact factors can generate considerable Twitter activity and also become heavily cited. Authors may benefit from establishing a strong social media presence, but should not expect research to become highly cited solely through social media promotion. Our research demonstrates that altmetrics and traditional metrics can be closely related, but not identical. We suggest that both altmetrics and traditional citation rates can be useful metrics of research impact.