The age–depth models of our four sediment records were based on a total of 56 210Pb-estimated ages, 41 calibrated 14C ages, and one tephra-based age (Fig. 2; Table S1). The chronology for Upper Capsule Lake follows Oswald et al. (2003). The 14C ages for the other three lakes are all in chronological order with the exception of the age at 107 cm in the Keche Lake core. This age was excluded from chronological modeling as it was considered too old based on surrounding dates; the dated material likely had resided in watershed soils before deposition in the lake, a common 14C-dating problem for arcto-boreal sediments (Oswald et al., 2005). The density of 14C dates varies across the four sites; for example, the Tungak Lake chronology is constrained by only five 14C ages for the past 35 500 years, whereas the Perch Lake chronology is constrained by 10 14C ages for the past 9500 years.

Sedimentation rates are relatively low across all four sites. Based on the age–depth model, the Perch Lake record spans the past ca. 9500 years, with an average sedimentation rate (±standard deviation) of 0.04 ± 0.08 cm yr-1 (Table 1). The Upper Capsule record spans the past ca. 12 100 years, with an average sedimentation rate of 0.03 ± 0.01 cm yr-1. The Keche Lake sediment core has a modeled basal age of 11.5  kcal BP and an average sedimentation rate of 0.03 ± 0.03 cm yr-1. Tungak Lake has the oldest sediment sequence in this study, spanning the past ca. 35 500 years. The sedimentation rate changes at 38 cm from 0.03 ± 0.04 cm yr-1 between 12.0 and 35.5 kcal BP to 0.01 ± 0.03 cm yr-1 after 12.0 kcal BP. These relatively low sedimentation rates did not present a problem for the identification of local fires because of the rarity of fires across all four sites (see below).

The two charcoal records from the North Slope both exhibit low background CHAR (mean is 0.008 pieces cm-2 yr-1 for Perch and Upper Capsule) (Fig. 3b), suggesting minimal biomass burned in the region over the past ca. 12 000 years. For comparison, background CHAR values have means of 0.340 pieces cm-2 yr-1 in boreal fire records from interior Alaska (Kelly et al., 2013) and 0.012 pieces cm-2 yr-1 in the tundra-fire records of the Noatak River Watershed (Higuera et al., 2011). Charcoal peak analysis identified only three local fires in the Perch Lake record, at 9.4 kcal BP, 6.5 kcal BP, and CE 2007 (Fig. 3c). This result confirms the published finding from this site that the ARF in CE 2007 was unprecedented in the past 5000 years (Hu et al., 2010), and extends the uniqueness of this fire event to the past 6500 years. Around Upper Capsule Lake, only one fire occurred during the past ca. 12 000 years. This fire is dated at ca. 6.45 kcal BP (Fig. 3c), coincident with the Perch Lake fire at ca. 6.48 kcal BP. Given the local origin of macroscopic charcoal peaks (0.5–1.0 km; Higuera et al., 2007) and the distance between the two lakes (∼ 50 km), it is unlikely that a fire event at one site resulted in a charcoal peak at the other site. Instead, the presence of a prominent charcoal peak at 6.5 kcal BP in both records likely represents a single large fire that burned across both sites. Because the magnitude of charcoal peaks reflects, in part, the amount of burned biomass (e.g., Whitlock et al., 2006; Higuera et al., 2009), the higher CHAR peak at 6.5 kcal BP at Perch Lake suggests that the amount of biomass consumed in the fire at 6.5 kcal BP was greater than that of the ARF. Alternatively, two separate but similarly-timed events may have occurred in the watersheds of these lakes. Because vegetation has changed little over the past ca. 7000 years (Oswald et al., 2003), this fire event suggests that climate and/or ignition constraints on burning were relaxed during this time, perhaps as least as warm and dry as the anomalous climatic conditions that facilitated the ARF (Hu et al., 2010). However, we cannot verify this interpretation because no suitable paleoclimate record with seasonal resolution is available from the region (Oswald et al., 2014).

The Keche Lake record spans several millennia during the early Holocene when tundra vegetation dominated the regional landscape and climate was generally cooler and drier than modern (Anderson and Brubaker, 1994; Kaufman et al., 2015; Clegg et al., 2011). Background CHAR is exceptionally low, with a mean of 0.0007 pieces cm-2 yr-1 from 11.4 to 8.8 kcal BP (Fig. 3b), suggesting little burning on the early-Holocene landscape of the region. No local fires occurred around Keche Lake during this period. Background CHAR increases to a mean of 0.02 pieces cm-2 yr-1 between 8.8 and 4.5 kcal BP (Fig. 3b), suggesting an increase in regional burning coincident with the development of a forest-tundra ecotone in the Alaskan interior with sparse stands of Picea glauca (white spruce) near Keche Lake by ca. 9.0 kcal BP (Anderson and Brubaker, 1994). Local fires were more frequent at Keche Lake between 8.8 and 4.5 kcal BP than during the early and late Holocene, with five events at 7.6, 7.4, 6.5, 5.1, and 4.6 kcal BP (Fig. 3c). This change implies that tundra burning was limited either by cooler summer temperatures in the early Holocene or by a lack of biomass, given that the early Holocene was drier than the middle Holocene in the Alaskan interior (Kaufman et al., 2015), which should have favored burning. It is possible that the lack of fire in the early Holocene resulted from locally moist conditions in summer, as suggested by peatland expansion that began ca. 11.2–10.7 kcal BP at a site ∼ 20 km to the northwest of Keche Lake (Jones and Yu, 2010). Background CHAR decreases to 0.004 pieces cm-2 yr-1 from 4.5 kcal BP to present, and only one fire event occurred during the past ca. 4500 years near Keche Lake (Fig. 3). In contrast, area burned and fire frequency increased after 4.0 kcal BP in the boreal forests of interior Alaska (Higuera et al., 2009; Hu et al., 2006; Kelly et al., 2013). This contrast can be attributed to the development of flammable forests dominated by P. mariana (black spruce) in the lowlands of interior Alaska (Higuera et al., 2009; Kelly et al., 2013), and the absence of this species in upland treeline areas around Keche Lake. The low fire frequency at Keche Lake after 4.5 kcal BP may have resulted from decreasing summer temperatures associated with late-Holocene neo-glaciation (e.g., Barclay et al., 2009; Clegg et al., 2011; Badding et al., 2013).

The Tungak Lake record is the longest fire-history reconstruction from Alaska. Throughout the past ca. 35 000 years, low background CHAR in this record (mean is 0.002 pieces cm-2 yr-1; Fig. 3b) suggests little burning, likely resulting from a combination of cold and sometimes arid conditions that limited biomass in the widespread graminoid-herb tundra of the region (Ager et al., 2003; Kurek et al., 2009). Only five local fires are identified over the past 35 000 years (Fig. 3c). Between 25.5 and 14.0 kcal BP, background CHAR is generally higher than the remainder of the record, and peak analysis shows four local fire events at 25.4, 17.8, 16.7, and 14.4 kcal BP. During this period, the modern-day coastal regions of Alaska experienced greater continentality because of lower sea levels, resulting in more arid conditions than today (e.g., Alfimov and Berman, 2001; Kurek et al., 2009). Such conditions may have relaxed the climatic constraints on tundra burning, leading to more frequent fire events between 25.5 and 14.0 kcal BP compared to the Holocene (i.e., after 11.7 kcal BP). During the Holocene, background CHAR is lower than during the glacial period, and peak analysis suggests only one fire event, at 7.0 kcal BP. Thus fire activity decreased during the Holocene, probably as a result of increased effective moisture in the region despite increased tundra biomass compared to the glacial period (Ager, 2003; Hu et al., 1995).

Overall, the most striking feature of our records is that these tundra regions have generally persisted as rare-fire systems for many millennia. With the exception of the ARF on the North Slope, the most recent fire events at these sites occurred from 882 to 7031 years ago (Table 2; Fig. 3c). These results stand in stark contrast with the paleofire data from the tundra ecosystems of the Noatak River Watershed. In that area, mean FRIs ranged from 135 to 309 years based on charcoal records of the past 2000 years from several lakes, comparable to mean FRIs from modern boreal forests in Alaska (Higuera et al., 2011). In northcentral Alaska, Higuera et al. (2008) documented frequent tundra fires during the late-glacial and early-Holocene period between 14 and 10 kcal BP, a finding supported by a microscopic charcoal record from central Alaska (Tinner et al., 2006). However, evaluating the spatial extent of this finding has not been possible because of the general lack of paleofire data from this period. Three of our four charcoal records span the entirety (Tungak Lake) or a portion of this period (Upper Capsule and Keche lakes). These new records show no enhanced fire activity during this period; only one local fire occurred near this time period (at 14.4 kcal BP at Tungak Lake), and regional biomass burning was consistently low across all three sites between 14 and 10 kcal BP (Fig. 3). Together with the previous fire-history reconstructions, our data suggest that the rate of tundra burning was spatially variable throughout the late Quaternary.

Our paleofire records can provide a context for comparison with modern tundra-fire regimes by invoking the statistical equivalency of the mean FRI and the modern fire rotation period (FRP; Johnson and Gutsell, 1994). We compared our paleo-based mean FRI estimates with the FRP values calculated from spatially explicit data of modern fire observations spanning the past 63 years. Across our four sites, modern FRPs within 100 km of each lake ranged from 771 years (Keche Lake) to 7560 years (Tungak Lake), with intermediate values at Perch (1909 years) and Upper Capsule (2070 years) lakes (Table 2). Although the rarity of tundra burning makes these estimates highly uncertain, the spatial patterns are similar to those in our paleofire records, suggesting that the differences in tundra burning across our study sites have been present over long timescales (Fig. 4). These variations are largely related to spatial heterogeneity in climate (Young et al., 2013), consistent with the finding that summer temperature and precipitation explained 95 % of the interannual variability in area burned in Alaskan tundra (Hu et al., 2010).

Our paleofire analyses underestimate the true mean FRI because the oldest and most recent fire events in each record only provide minimum FRI estimates (i.e., censored intervals; Fig. 4). Despite this underestimation, at three of our four study sites, the mean FRI estimates from the paleofire records are longer than the FRP estimates based on recent fires. Specifically, the mean FRI (range) estimates of 4730 (2924–6536) years at Perch Lake and 6045 (> 5590 to > 6500) years at Upper Capsule Lake are much longer than the FRP (95 % quantile range) estimates of 1909 (48–7042) and 2070 (52–7636) years for these lakes, respectively (Fig. 4; Table 2). Likewise, the mean FRI estimate of 1648 (144–3906) years at Keche Lake is longer than the modern FRP estimate of 771 (19–2844) years. The exception is Tungak Lake where the mean FRI of 5904 (1157 to > 9968) is shorter than the FRP of 7560 (191–27 888) years. This shorter mean FRI reflects more frequent burning between 25.5 and 14.0 kcal BP, when the region was probably more arid than during the Holocene. The FRP of 7560 years is similar to the most recent individual FRI of > 7031 years at that site (Table 2). Thus our analysis suggests that the frequency of tundra burning was higher over the past 63 years at three of our four sites compared to the late Quaternary. This inference suggests elevated fire activity in some tundra regions at present, possibly as a result of anthropogenic climate change.

However, the above comparison is inconclusive, because the range of individual FRIs at each site generally falls within the broad range of FRIs that can be expected to arise by chance, as defined by the 95 % quantile range around the FRP estimates (Fig. 4). Furthermore, the ranges of individual FRIs from the paleorecords are likely influenced by past climate and vegetation conditions that differed from modern conditions, and the estimates of both mean FRI and FRP are uncertain due to the rarity of tundra fires and thus high sensitivity to individual fire events. For example, without the ARF, the FRP in the tundra region of Perch and Upper Capsule lakes would be > 100 000 years, which is much longer than the FRP estimates of Perch (1909 years) and Upper Capsule (2070 years) lakes with the inclusion of the ARF. Thus quantitative comparisons between the mean FRI estimated from our paleorecords and the FRP estimates from historic observational records inherently contain a large amount of uncertainty.

Paleorecords provide critical information regarding natural variability and thus play an important role in assessing potential anthropogenic changes in climate and ecosystems. Our results comparing paleo-inferred mean FRI and observed modern FRP illustrate an important limitation of using paleofire records in systems that rarely burn to quantitatively assess whether recent burning is beyond the range of natural variability. This limitation is applicable to other situations where the events of interest have rarely occurred in the past. One way to circumvent this limitation is to increase the spatial density of paleorecords and pool the data of detected past events to improve statistical power (Whitlock et al., 2010). Several paleofire studies have demonstrated the value of increasing the spatial density of sampling for bolstering the confidence in inferences about recent changes (Marlon et al., 2012; Kelly et al., 2013).

The utility of paleorecords with rare events may improve if the frequency of such events increases markedly in the future. To examine how much burning would be required to shift the fire regime unequivocally beyond the range of past FRIs, we considered hypothetical scenarios of future burning around Perch Lake, which has two well-constrained (i.e., uncensored) FRIs in the Holocene paleofire record. We calculated the FRP for CE 2050, assuming the addition of one to four fires of the ARF size (∼ 1000 km2) within the 100 km radius around Perch Lake (Fig. 5). One additional ARF-sized fire would shift the Perch Lake FRP estimate to 1502 years. This FRP is much shorter than the mean FRI of 4730 years based on the paleofire record from Perch Lake, and the most recent FRI at the lake (6536 years) is well outside the 95 % quantile range indicated by this updated FRP estimate. Thus, the addition of a single ARF-sized fire within the 100 km region surrounding Perch Lake would offer compelling evidence that the modern fire regime represents a significant increase in fire activity. The occurrence of additional large fire events would further decrease the FRP and strengthen confidence in that estimate, making it increasingly difficult to accept the null hypothesis that the modern fire regime is consistent with past variability. Thus, although the rarity of fire events makes it uncertain as to whether modern fire regimes differ from the past, the uncertainty will be reduced as the observational record grows, especially if a dramatic fire-regime shift is indeed underway. Increasing the spatial density of paleorecords to refine our understanding of past variability would enhance the rigor of testing whether or not recent and future changes in fire regimes are truly unprecedented.