Results for the episodic memory task, executive functions and PA are presented in Table 2. No effect of age group on IAL and IAS [t(42) = 1.47; p = 0.149 and t(42) = -0.28; p = 0.781 respectively] or on the overall PA index [t(42) = 0.03; p = 0.975].

The GLM conducted on episodic memory performance confirmed the age-group effect, F (1,40) = 90.85, p < 0.001, ηp2 = 0.69, with fewer words correctly recalled by older than younger adults. The results also showed an effect of PA, F (1,40) = 17.07, p < 0.001, ηp2 = 0.30. Correlational analyses indicated that PA was positively related to episodic memory performance (r = 0.32, p = 0.034). Finally, the interaction between age group and PA was significant, F (1,40) = 15.28, p < 0.001, ηp2 = 0.28. More precisely, to investigate this interaction, correlation analyses were conducted and indicated that the positive correlation between PA and memory performance was significant in older adults (r = 0.89, p < 0.001) but not in younger adults (r = -0.10, p = 0.695).

The GLM performed on the working-memory task revealed an effect of age group, F (1,40) = 35.43, p < 0.001, ηp2 = 0.47, with a higher percentage of errors by older than younger adults. This analysis also showed an effect of PA, F (1,40) = 10.14, p = 0.003, ηp2 = 0.20; participants with higher levels of PA made fewer errors on the working-memory task (r = -0.34, p = 0.024). This effect was similar in younger and older adults (respectively, r = -0.28, p = 0.244 and r = -0.57, p = 0.003), as there was no significant interaction between age and PA, F (1, 40) = 0.56, p = 0.458.

The GLM performed on the executive index revealed an age-group effect, F (1,40) = 44.52, p < 0.001, ηp2 = 0.53, with better executive functioning in younger adults. The analysis also showed an effect of PA, F (1,40) = 15.88, p < 0.001, ηp2 = 0.28, with higher levels of PA corresponding to a higher executive index (r = 0.39, p = 0.010). Finally, a significant interaction was found between PA and executive index, F (1, 40) = 4.57, p = 0.039, ηp2 = 0.10, indicating that this relationship was significant only in older adults (r = 0.63, p = 0.001) and not in younger adults (r = 0.24, p = 0.315).

Episodic memory performance and executive index were positively correlated (r = 0.60, p = 0.002) in older adults. Significant negative correlations were found between these two variables and the chronological age of older adults (r = -0.50, p = 0.01 for episodic memory, r = -0.67, p < 0.001 for executive index) and between PA and the chronological age of older adults (r = -0.56, p = 0.004 for PA). As these linear relationships were only found in older adults, regression analyses were performed only in this age group to better understand the underlying mechanisms of PA benefits on memory and executive functions in old age. The mediation model (including age, executive index and PA as predictors of memory performance) and the different pathways are presented in Fig. 2.

Mediation model and paths in older adults explaining episodic memory performance with age, PA and executive index as predictors. An arrow indicates that the effect of the first variable is mediated by the second variable (indicated by the arrowhead). Main findings: ABC indicates that the effect of age on memory could be predicted by executive functions. DEC indicates that the effect of age on memory could be predicted by PA. The significant indirect pathway (in black) indicates the effect of age on memory could be predicted by executive functions, which itself could be predicted by PA

First, the regression analysis revealed a significant direct association between age and episodic memory performance (i.e., percentage of correctly recalled words), F (1,23) = 7.84, p = 0.010, explaining 25.4% of the variance. Age was negatively associated with memory performance (path C, b = -0.56; 95% CI [-0.88, -0.19]).

The simple mediation model predicting memory performance from age and executive index (paths A, B and C) was significant, F (2,22) = 6.70, p = 0.005, explaining 38% of the variance in memory performance. To go further, age was negatively associated with executive index (path A, b = -0.19; 95% CI [-0.29, -0.010]), and executive index was positively associated with memory performance (path B, b = 2.33; 95% CI [0.81, 3.34]). After controlling for executive functioning (b = 1.85; 95% CI [0.15, 3.12]), the negative association between age and memory performance was no longer significant (b = -0.20; 95% CI [-0.64, 0.20]). Importantly, the indirect effect explaining the effect of age on memory performance through executive index was significant, 95% CI [-0.76, -0.11].

The other simple mediation model predicting memory performance from age and PA (paths D, E and C) was also significant, F (2,22) = 40.37, p < 0.001, explaining 78% of the variance in memory performance. To go further, age was negatively associated with PA (path D, b = -0.23; 95% CI [-0.34, -0.11]) and PA was positively associated with memory performance (path E, b = 2.36; 95% CI [1.81, 2.76]). As in the previous model, after controlling for PA (b = 2.33; 95% CI [1.77, 2.85]), the negative association between age and memory performance was no longer significant (b = -0.02; 95% CI [-0.26, 0.24]). For this model, the indirect effect explaining the age effect on memory performance through PA was significant, 95% CI [-0.81, -0.31].

The overall mediation model predicting memory performance from age, executive index and PA was significant, F (3,21) = 26.23, p < 0.001, explaining 79% of the variance in memory performance. To go further, the executive index was positively associated with PA (path F, b = 0.91; 95% CI [0.52, 1.32]). Most importantly, the effects of age and executive index on memory performance were no longer significant (respectively, b = 0.03; 95% CI [-0.28, 0.34] and b = 0.34; 95% CI [-0.92, 1.35]) when PA (b = 2.25; 95% CI [1.68, 2.80]) was entered in the regression analysis. These important results show that the effects of both age and executive index on episodic memory are mediated by PA. In this mediation model, the indirect effects explaining the effect of age on memory performance through executive index (paths A and B) and through PA (paths D and E) were no longer significant, 95% CI [-0.28, 0.17] and 95% CI [-0.46, 0.07] respectively. The serial indirect pathway explaining the effect of age on memory performance through executive index and then PA (corresponding to paths A, F and E) was significant, 95% CI [-0.68, -0.06], suggesting that the effect of age on memory could be predicted by executive index, which itself could be predicted by PA.

As PA was also positively associated with executive index (reverse path F, b = 0.43; 95% CI [0.23, 0.64]), we tested the serial indirect pathway explaining the effect of age on memory performance through PA and then executive index (corresponding to paths D, reverse F and B). This indirect pathway was non-significant, 95% CI [-0.10, 0.05].