Bootstrapping R2 and adjusted R2 in regression analysis

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Forward selection of explanatory variables. (2008, methodology): “Using numerical simulations, Ohtani (2000) has shown that R2a is an unbiased estimator of the real contribution of a set of explanatory variables to the explanation of a response variable.”
From Classical to Canonical Ordination (2012, methodology): “Examples of the use of RDA to test ANOVA-like hypotheses are found in Sabatier et al. (1989), ter Braak and Wiertz (1994), Verdonschot and ter Braak (1994), Anderson and Legendre (1999), and Hooper et al.”
Bootstrapping and PLS-SEM: A step-by-step guide to get more out of your bootstrap results (2016, methodology): “Statistical significance of the coefficient of determination In a call for accompanying the coefficient of determination with a measure of precision, Ohtani (2000) drew attention to the virtues of bootstrapping.”
Socio-Economics and Vegetation Change in Urban Ecosystems: Patterns in Space and Time (2009, methodology): “This can be rectified to a degree by using an adjusted R2 value (Ohtani 2000), which corrects for the number of independent variables in the model, but Blanchet and others (2008) have shown that even this value can be inflated in forward selection regression.”