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The central‐marginal hypothesis (CMH) posits that range margins exhibit less genetic diversity and greater inter‐population genetic differentiation compared to range cores. CMH predictions are based on long‐held "abundant‐centre" assumptions of a decline in ecological conditions and abundances towards range margins. Although much empirical research has confirmed CMH, exceptions remain almost as common. We contend that mangroves provide a model system to test CMH that alleviates common confounding factors and may help clarify this lack of consensus. Here, we document changes in black mangrove (Avicennia germinans) population genetics with 12 nuclear microsatellite loci along three replicate coastlines in the United States (only two of three conform to underlying "abundant‐centre" assumptions). We then test an implicit prediction of CMH (reduced genetic diversity may constrain adaptation at range margins) by measuring functional traits of leaves associated with cold tolerance, the climatic factor that controls these mangrove distributional limits. CMH predictions were confirmed only along the coastlines that conform to "abundant‐centre" assumptions and, in contrast to theory, range margin A. germinans exhibited functional traits consistent with greater cold tolerance compared to range cores. These findings support previous accounts that CMH may not be a general rule across species and that reduced neutral genetic diversity at range margins may not be a constraint to shifts in functional trait variation along climatic gradients. [ABSTRACT FROM AUTHOR]