The data matrix of this study is assembled on the dataset from our previous work [1] . Four fossil taxa ( Table 2 ) [5] [12] - [26] and ten extant taxa ( Table 3 ) [27] - [32] are added to that combined dataset of Wang and Li [1] . The four newly added fossils, morphologically attributed to Dryopteridaceae, include crown group fossils Elaphoglossum miocenicum from the Miocene and Polystichum pacltovae from the Oligocene, as well as stem group fossils Cretacifilix fungiformis and Dryopterites beishanensis from the Cretaceous. All fossils included in this study, along with their respective information, are presented in Table 2 [5] [12] [26] . The ten additional extant species, which were not included in the dataset of Wang and Li [1] , belong to Davalliaceae (two taxa), Didymochlaenaceae (three taxa), and Hypodematiaceae (five taxa). Their DNA sequences were obtained from GenBank, with accession numbers and references provided in Table 3 [27] - [32] . The data matrix consists of 15 morphological characters, and the DNA sequence data, totaling 3826 bp from three plastid genes (rbcL, atpA, and atpB), remains identical to that used by Wang and Li [1] .

*Fossils in pink are newly added this study. **The fossils are ascribed to Aspleniineae or Polypodiineae based on originally described.

Since the focus of this study is on the earliest divergence times of suborder Polypodiineae, or the total ages of Polypodiineae, we based our analysis on the dataset from Wang and Li [1] . The suborder Aspleniineae (eupolypods II) section of the dataset was kept unchanged, while we restructured the dataset by adding newly incorporated fossils belonging to suborder Polypodiineae. Each fossil or fossil group was combined with the constraint sets for family Dryopteridaceae or suborder Polypodiineae, resulting in 12 different analysis schemes ( Table 4 ). Meanwhile, we used stepping-stone analysis [34] [35] to estimate marginal likelihoods for each model ( Table 4 ). Our 12 tip dating analyses were performed in Mrbayes 3.2.7a [35] - [37] following the manuals downloaded from http://mrbayes.net . The FBD model was used as the tree prior, the ages of fossil terminals were provided as uniform or fixed priors with bounds equal to the limits of the estimated ages of their deposits ( Table 2 ). We used a “diversity” setting in the sampling strategy since we strived to include as many eupolypods terminals as possible, and set the sample probability prior to 0.0178; this was done because we included 214 terminals, while the diversity of the eupolypods lineage is currently of about 6000 species and we expected it contains about that same number of undescribed species. Our analyses were run for 20 million generations, sampling every 5000 generations. Bayesian posterior probabilities (PP) were calculated for the majority rule (>50%) consensus tree of all sampled trees after discarding the first 25% as burn-in. Visualized trees and all the nodes were checked in FigTree v.1.4 [38] .

*Three references are for three DNA accessions respectively. “/” No accessions were provided.

*All Bayesian analyses were conducted using relaxed clock model TK02 (autocorrelated lognormal; Thorne and Kishino [33] ) with an offset exponential tree age prior, as implemented in MrBayes3.2.7a [35] , ages of Total Suborder Polypodiineae in Jurassic were in bold. **The four newly added fossils—Cretacifilix fungiformis, Dryopterites beishanensis, Elaphoglossum miocenicum, and Polystichum pacltovae—are listed by genus name only in the table. ^$Fossils were set constraint to family Dryopteridaceae or suborder Polypodiineae. ^$$Marginal likelihood (in natural log units, ln) were estimated using stepping-stone sampling (Xie et al. [34] ).

The divergence times (median ages in Ma) for Eupolypods and its two subclades obtained from the 12 analytical schemes ( Table 4 , Figure 2 ) show significant variation. However, all results indicate that the diversification of total Eupolypods occurred in the Jurassic, ranging from 152.15 - 183.46 Ma. The diversification of total eupolypod II (suborder Aspleniineae) also took place in the Jurassic, between 145.29 - 174.77 Ma, while eupolypod I diversified later. Among the 12 analytical schemes ( Table 4 ), only four show that the earliest divergence time of suborder Polypodiineae occurred in the Jurassic, ranging from 158.88 - 168.02 Ma, and all four of these schemes include the earliest fossil of suborder Polypodiineae, Dryopterites beishanensis Ren et Sun from Early Cretaceous (Hauterivian-Barremian) of Northwest China. Our analysis suggests that the earliest divergence time of suborder Polypodiineae is determined by its earliest fossil record and the combinations that include this fossil, rather than being strongly influenced by whether the fossil or fossil combination is assigned to the constraint sets of family Dryopteridaceae or suborder Polypodiineae. However, the estimated divergence times are slightly higher when the fossil or fossil combination is assigned to the family Dryopteridaceae compared to suborder Polypodiineae.

Based on our 12 analytical schemes, the marginal likelihoods (in natural log units, ln) estimated using stepping-stone sampling [34] consistently show higher values for the six analytical schemes where the constraint set is family, compared to the six schemes where the constraint set is suborder ( Table 4 ). On the other hand, the values of marginal likelihoods decrease as the dataset size increases ( Table 4 ).

Figure 3. Chronogram of eupolypod ferns constructed using a tip-dating approach and the Fossilized Birth-Death model within a Bayesian framework. Clades of the Suborder Polypodiineae (Eupolypods I) are shown in green, while those of the Suborder Aspleniineae (Eupolypods II) are shown in blue. The different systematic positions of Hypodematiaceae on chronogram (a) and (b) are highlighted with red dashed frames. (a) The chronogram of Eupolypods, modified from Wang and Li [1] , includes only extant fern families and nine fossil taxa (in red), along with their relative extant genera. (b) The chronogram of Eupolypods I (Polypodiineae). Node bars represent 95% highest posterior density (HPD) intervals. Four newly added fossil taxa (in pink) are incorporated in this study. The three main lineages of eupolypods are indicated with their mean estimated ages, and the focal group of this study topic of this study, Suborder Polypodiineae, is highlighted with a red star.

Our tip-dating tree ( Figure 3(b) ) shows that the phylogenetic placements of fossil taxa are mostly in accordance with their previous taxonomic attributions. Among the four newly added Dryopteridaceae fossils, the crown group fossils Elaphoglossum miocenicum [20] and Polystichum pacltovae [23] , which are expected to belong to Dryopteridaceae, appear in the corresponding Dryopteridaceae lineage regardless of whether constraint sets are applied. Moreover, these two crown fossils have more concrete and accurate phylogenetic placements. For example, Elaphoglossum miocenicum [20] clusters with its extant Elaphoglossum relatives, and Polystichum pacltovae [23] clusters with its extant Cyrtomium-Polystichum relatives ( Figure 3(b) ). However, the situation is different for the stem group fossils Cretacifilix fungiformis [15] [16] and Dryopterites beishanensis [19] from the Cretaceous. The systematic positions of these stem group fossils in the tree depend on whether they are assigned to the constraint sets of family Dryopteridaceae or suborder Polypodiineae. If the two fossils are constrained to family Dryopteridaceae, they both occupy stem positions within Dryopteridaceae. If they are constrained to suborder Polypodiineae, they occupy stem positions within suborder Polypodiineae in our tip-dating tree ( Figure 3(b) ).

By incorporating ten additional extant taxa related to Hypodematiaceae ( Table 2 ), our tip-dating analyses identify Didymochlaenaceae as the sister group to all other lineages within Polypodiineae, with Hypodematiaceae as the next earliest diverging lineage ( Figure 3(b) ). This suggests that Didymochlaenaceae represents the earliest divergence within Polypodiineae, followed by Hypodematiaceae. These findings contrast with those of Wang and Li [1] , which placed Hypodematiaceae as the earliest diverging lineage within a clade of Polypodiineae, excluding Dryopteridaceae ( Figure 3(a) ).

Polypodiineae (Eupolypods I) is the most species-rich lineage of ferns at the subordinal level ( Figure 1 ), and analyses of its phylogenetic relationships and diversification times have been ongoing, resulting in considerable debate ( Table 1 ). We will refrain from commenting on previous studies; instead, we focus on our findings in conjunction with our earlier analysis in Wang and Li [1] to explore the discrepancies in the diversification times of Polypodiineae. Among the current 12 analytical schemes ( Table 4 ), only four indicate that the earliest divergence time of suborder Polypodiineae occurred in the Jurassic, ranging from 158.88 to 168.02 Ma ( Table 4 ), and all four include the earliest fossil of suborder Polypodiineae, Dryopterites beishanensis [19] . Our study highlights the significant role of fossil abundance and taxonomic composition in molecular dating analyses. The results of our tip-dating analysis align with a few divergence time estimates derived from different molecular dating methods (node-dating [2] [3] [6] and rate-dating [5] ). For the ages of crown Polypodiineae, all analytical schemes, except for 7/82S ( Table 4 , Figure 2 ), indicate that they are earlier than those of crown Aspleniineae, suggesting that crown Polypodiineae has a longer evolutionary history than crown Aspleniineae. This may explain its greater species richness compared to Aspleniineae and its more ecological opportunistic response to the establishment of complex, angiosperm-dominated ecosystems.

While our results in this study clarify the systematic position of Hypodematiaceae, indicating that it, along with Didymochlaenaceae, represents the basal lineages of Polypodiineae, this finding is only one of four analytical outcomes regarding its phylogenetic placement. Earlier studies have placed Hypodematiaceae nested with Didymochlaenaceae [8] [39] . Later, analyses of multiple chloroplast genes resolved Didymochlaenaceae as sister to the rest of Eupolypods I, Hypodematiaceae following [6] [28] [40] , a result consistent with our findings ( Figure 2(b) ). However, recent plastid phylogenomic [2] [3] and nuclear phylotranscriptomic [4] analyses, based on more extensive sampling, have identified Hypodematiaceae as the most basal family within Polypodiineae. It is quite uncommon for analyses by Wang and Li [1] and Regalado et al. [5] to show that Hypodematiaceae is not positioned at the base of Polypodiineae but rather at the base of a clade within Polypodiineae ( Figure 2(a) ). The primary cause of these topological discrepancies appears to be differences in dataset sizes. Further investigation with expanded datasets is necessary to assess how these topological differences influence divergence age estimates compared to previous studies.