Holocene bidirectional river system along the Kenya Rift and its influence on East African faunal exchange and diversity gradients

Significance Although biodiversity in East Africa is overall extremely high, species richness is not geographically uniform for fishes and mammals. We investigated the biogeographic relevance of past river activity in the Kenya Rift. We show that during a humid period 12,000 to 8,000 years ago, a river system connected currently isolated rift lakes and was partly connected to the Nile. While this river system formed pathways for the dispersal of fishes between lakes, it also acted as a barrier to the range expansion of forest mammals. This fairly recent hydrological connectivity between lakes has been a key driver of modern biodiversity patterns in East Africa. Climate-driven changes in drainage networks on multimillennial timescales are an important hypothesis in biodiversity research.


S1.1. Radiocarbon reservoir correction
Previous studies have noted significant disagreement in the timing of highstands in East African lakes during the African Humid Period (e.g., refs. 1,2,3,4). We note that it was only possible to establish the synchronicity of overflow lake levels and the connectivity between all major lake basins by applying 14 C reservoir corrections to the chronologies of Lakes Magadi-Natron, Siriata, Baringo-Bogoria and Suguta. Reservoir-affected 14 C dates have significantly older ages of the order of 2000 -4000 years than ages derived from reservoir-free 14 C dates, U/Th dates, or 137 Cs dates, which now constrain the reservoir effects for these basins (e.g., refs. 5,6). The source of depleted radiocarbon can be attributed to the continual release of mantle-derived CO2 along faults and from hot springs in the tectonically active rift-floor area (7). Whether or not Nakuru-Elmenteita, Naivasha and Menengai sediments also contain this source of chronological error (which is apparently negligible in Lake Turkana; 8) remains to be investigated.

Lake Suguta
A reservoir effect of Lake Suguta was first investigated by Junginger et al. (9), who derived a mean reservoir factor of 1900 14 C years based on age offsets of four pairs of charcoal and carbonate dates (1570,1940,1970 and 2240 14 C years). Garcin et al. (6) showed that the mean reservoir effect has a large error (1σ= 275 14 C years), indicating that the reservoir effect likely changed over time. These authors (6) therefore established a reservoir model and applied following reservoir factors: 1570±80 14 C years for dates ≥10930±50 14 C BP, 2240±65 14 C years for dates from 10795±50 to 10205±45 14 C BP, 1970±70 14 C years for dates from 10025±45 to 7850±50 14 C BP and 1940±65 14 C years for ages ≤6345±40 14 C BP. We followed this approach for correcting carbonate-derived radiocarbon dates from Lake Suguta.

Lakes Baringo Bogoria
Both Lake Baringo and Lake Bogoria receive groundwater from on-and offshore hydrothermal springs, partly from deep sources (10,11,12). CO2 is the dominating free-phase gas released by many of these springs that mixes with the lake water of Baringo. The CO2 from hot springs of the northern Kenya Rift (including Lake Baringo) has a mean δ 13 C-CO2 value of -9.2‰ (-5.4‰ --14.6‰; n= 7; ref. 10), which is very similar to the carbon isotope composition of CO2 of the Magadi-Natron springs (mean -8.0‰; ref. 7) and strongly indicates to be derived from the upper mantle (13). Hence a substantial 14 C reservoir effect for Lakes Baringo and Bogoria can be assumed and was already suspected by (1), (2) and (14) based on conspicuously old radiocarbon ages. An indication of a reservoir effect is given by two published 14 C dates obtained from the same interval (128-131 cm) of core Bogoria I for which bulk organic matter is dated to 4790±280 14 C yr BP but the carbonate fraction to 10400±470 14 C yr BP (difference of 5610 14 C years) (14). Because organic matter could also have been influenced by 14 C depleted carbon the age difference does not provide an unequivocal reservoir factor. De Cort et al. (5) estimated the modern reservoir effect for Lake Bogoria from a 14 C date of 4160±35 14 C yr BP at 40.5 cm depth and the 137 Cs activity (1964 peak at 35 cm) in core BOG01-1P. The 137 Cs-based extrapolated age at 40.5 cm is 1943 (or 182 14 C yr BP) and the deduced 14 C reservoir effect is 3980 14 C years (5), which we applied to all radiocarbon dates from Lakes Baringo and Bogoria (given the direct overflow of Lake Bogoria waters into Lake Baringo during the early Holocene).

Lake Siriata
We investigated the 14 C reservoir effect of Lake Siriata by comparing radiocarbon dates from three sample pairs consisting of charcoal and biogenic carbonates (i.e. Corbicula sp. shells); each pair collected from the same depth interval of lacustrine sediment deposits (Table S3). Two shell dates (Poz-78499, Poz-78500) collected 20 cm apart from the same outcrop (KOO15-6B) are chronologically reversed (13600±70 14 C BP vs. 13240±70 14 C BP), while the corresponding charcoal dates (9220±100 14 C BP vs. 9310±100 14 C BP) are in chronological order resulting in significantly different reservoir effects (4380±120 14 C years vs. 3930±120 14 C years). These differences indicate that the reservoir effect was fluctuating on short (centennial) timescales, but the temporal overlap of the two charcoal dates precludes us from resolving the time when the reservoir effect had changed. A third reservoir factor has a comparable duration (3980±120 14 C years) but was obtained from ca. 600-year younger sediments from a different outcrop (KOO15-3E). Given the consistent magnitudes of the age offsets we applied an average reservoir factor of 4095±180 14 C years, which was subtracted from all carbonate 14 C dates (Table S3). We also applied this reservoir effect to a 14 C date of fish bones (Poz-89660) from adjacent Lake Kwenia in the absence of a local reservoir factor (Table S3).

Magadi-Natron
Both Lakes Magadi and Natron are fed by numerous hot springs, aligned along normal faults, from which mantle-derived CO2 degasses (7). Given the deep and magmatic origin of this CO2 it can be safely assumed to be depleted in 14 C ('dead carbon'). The constant recharge of fluids rich in mantlederived CO2 into Lakes Magadi and Natron necessitates the correction of radiocarbon dates by a local reservoir factor. However, for these lakes no parallel radiocarbon dates on lacustrine and terrestrial matter are available to infer a reservoir effect in the standard way. To establish a 14 C reservoir effect for the Magadi-Natron Basin we compared U/Th and 14 C dates from core NF1 from Lake Magadi published by Taieb et al. (15) and Roberts et al. (16). Two U/Th dates were obtained from the depth interval 148-168 cm of core NF1: 1) 10970±750 yr BP (range: 10220-11720 yr BP) on organo-phosphates and 2) 8500±2000 yr BP on sodium-silicates (15). We discarded the second (younger) U/Th date because of its very large error, which would result in a highly uncertain temporal duration of the reservoir effect (~±2000 years).
The mean value of the 10970±750 yr BP U/Th date (= 10970 calendar years BP) is equivalent to 9560±16 14 C yr BP on the IntCal13 radiocarbon calibration curve (17). The lower bound U/Th date of 10220 BP equals 9031±14 14 C yr BP and the upper bound U/Th date of 11720 BP equals 10102±20 14 C yr BP on the IntCal13 curve. Incorporating all sigma ranges yields an equivalent radiocarbon age of 9560±550 14 C yr BP for this U/Th date (for error propagation we calculated the square root of the sum of squares of both the 14 C error and the reservoir error).
These three reservoir factors overlap from 1985 -2110 14 C years. The mean of this overlapping range is ~2050±63 14 C years. We adopt this approximation of 2050±63 14 C years for the reservoir correction of bulk and carbonate-based 14 C dates from Lake Magadi-Natron. We note that this reservoir factor is probably a conservative estimate as the second U/Th date from core NF1 would yield an average reservoir factor almost twice as large (~3870 14 C years), which is similar to the 4095±180 14 C year reservoir effect of the adjacent Lake Siriata.

S1.2. Selection of radiocarbon dates for deriving overflow ages
All published radiocarbon dates used in this study are listed in Table S2. In most cases, we reconstructed overflow conditions from radiocarbon samples that were deposited at overflow elevations. Our analysis therefore required good documentation of sample elevations of published radiocarbon dates. It is possible that nearly identical radiocarbon dates (overlapping sigma ranges) had been obtained from the same lake at both an overflow elevation (e.g. in a (near) shoreline setting) and an elevation below overflow level (indicating closed basin conditions). In such ambiguous case we gave priority to the higher-elevation sample as it is hard to explain how a sample could have been deposited above a paleo-lake surface, but conceivable that material could have concurrently been deposited below the lake surface (i.e. lake bottom) as well. We therefore attempted to restrict the selection of radiocarbon dated samples to those representing (near) shoreline conditions and wherever possible avoided samples collected from (thick) stratigraphic sections or sediment cores as these mostly stem from deposition under a deeper water column. However, if sediment proxies (e.g. diatoms) from such sections/cores clearly indicated open (overflow) conditions we considered them as well.
Lake Turkana Garcin et al. (8) provided a comprehensive and rigorous synthesis of published and new radiocarbon dates from the Lake Turkana Basin and established a robust lake level reconstruction with 105 14 C dates and their corresponding sample elevations. Here we used only those dates (n=37) listed in ref. (8) which were obtained from sample locations that were at or close to the former land-water-interface of Lake Turkana (i.e. near-shore, shoreline, and beach deposits), thus clearly indicating former lake levels. We excluded dated samples from benthic sediments and those with equivocal sample context (e.g. sands, sandy silt, lacustrine deposition, archeological excavation). The reported elevations for the selected radiocarbon dates were used to determine the timing of overflow above the outlet sill located at an elevation of 457-460 m. However, it should be noted that extensional tectonism and associated normal faulting resulted in subsidence of the central Turkana Basin floor and flexural uplift of the basin margins creating substantial relief differences during the Holocene and hence diverse elevations for the maximum highstand shorelines (MHS) across, at least, the southern Turkana Basin (8,18). Garcin et al. (8) corrected their sample elevations for subsidence, which are used here. Further radiocarbon dated stratigraphic sections and sediment cores from Lake Turkana are published by (19,20,21,22,23). Yet these studies do not add definite evidence for additional overflow periods than those based on the Garcin et al. (8) reconstruction and several of the dated samples remain uncertain in terms of their absolute elevations at the time of deposition due to the deformation of the Turkana Basin. Lake Suguta Lake level fluctuations of Lake Suguta were reconstructed by Bishop (24), Truckle (25), Casanova et al. (26), Garcin et al. (4,6) and Junginger et al. (9), together reporting 68 radiocarbon dates from the Suguta valley. The reconstruction of past lake levels in the Suguta valley is complicated by Holocene crustal deformation (subsidence due to extension, normal faulting, tilting of blocks and isostatic rebound) which resulted in different absolute elevations of the maximum highstand shoreline (MHS) across the Suguta valley and in lower elevations of all MHS (≤567 m) expressions than the present elevation of the outlet sill (581 m; ref. 18). For reconstructing overflow conditions, we selected only dates (n=14) from refs. (4) and (9) which indicated deposition close to the former land-water interface (shoreline). Various sample sites of the Suguta valley are steep-sided volcanic cones from which lake deposits could have been transported or eroded to lower elevations after deposition (especially with desiccation of the basin). We therefore followed a very conservative approach when selecting radiocarbon dated samples for this basin. We also did not include samples from (within) thick stratigraphic sections given the uncertainty of relating them to past lake surface elevations and avoided the use of published 14 C dates from older publications as these often lacked sufficient information regarding sample elevations. Yet, several 14 C dates from this earlier work (24,25,26) from stratigraphic sections with embedded fish fossils (Oreochromis, Lates etc.) were considered for the documentation of past fish dispersal.
Lakes Baringo and Bogoria Lake Bogoria is surrounded by a series of shorelines (including stromatolitic deposits) between 990.7 m and 999 m (2), which is 10 m above the modern lake level (989 m in 2003; ref. 5) and represents the overflow elevation of this lake (Loboi Sill: drainage divide between Bogoria and Baringo). Due to its narrow half-graben-shape Lake Bogoria can fluctuate by several meters over subdecadal timescales (5,27). For example, it rose to up to 996 m around 1900, ~997 m in 1928, 994 m in 1979 (2,27) and to over 992 m in 2012 (5). Therefore, stromatolithic paleo-shoreline indicators at these elevations could have been influenced by post-depositional alteration during the past few centuries. Stromatolites occur at 999 m (dated to 4140±60 14 C BP) and at 995 m (dated to 3880±60 and 3750±180 14 C BP; ref. 2,28). Given the substantial reservoir effect in Lake Bogoria the stromatolites could potentially have formed more recently than their Mid-Late Holocene ages suggest or, alternatively, could have diagenetically incorporated younger carbon during subaerial exposure (27). Because of these chronological uncertainties we avoided the use of radiocarbon dated stromatolites from Lake Bogoria. Although sediment cores from Lakes Bogoria and Baringo indicate freshwater conditions for the early Holocene (2,14), they either contain multiple age reversals likely related to the reservoir effect, lack sufficient age control or do not cover the entire Holocene (2,5,14). We therefore also omitted dated sediment cores from these lakes in this study. Consequently, we restricted the reconstruction of overflow to radiocarbon dated mollusk shells deposited on paleo-shorelines from Baringo, Bogoria and the intervening Loboi Plain.
Lake Menengai Lake sediments deposited up to an elevation of 1860 m and thus indicating overflow are present in the eastern part of the Menengai Caldera (29), but this outcrop remains to be dated. We therefore used the only available radiocarbon dates from other lacustrine deposits inside the Menengai Caldera (30). Lake Nakuru-Elmenteita We used radiocarbon dates from sediment cores of modern Lakes Nakuru and Elmenteita, for which detailed diatom records indicate the sequence of open (overflow conditions) and closed basin conditions (31,32). We integrated the core dates with radiocarbon dates on former shorelines and dates from sediment strata from various archeological investigations in the basin that both constrain past lake level fluctuations given their elevations with respect to the overflow level. Lake Naivasha Shorelines of the Lake Naivasha Basin have not been dated yet and only one onshore date is available that directly indicates a past lake level (33). We therefore relied on two dated sediment cores that cover the Holocene (32,34). Detailed diatom records are available from these core studies, from which closed and open (fresh) conditions were reconstructed by Richardson and Richardson (34) and Richardson and Dussinger (32).

Lake Siriata
We dated lake sediments of Lake Siriata that in one case overlay a dated paleosol, which indicates dry conditions prior to the onset of the Holocene. All sediment packages can be related to a single shoreline at the overflow elevation directly dated by 40 Ar/ 39 Ar of beach pumices to the early Holocene (see below). The lack of regressive shorelines indicates the rapid desiccation of the lake basin.
Lake Magadi-Natron Absolute lake levels were reconstructed by Hillaire-Marcel et al. (35) from dated stromatolites surrounding the entire Magadi-Natron Basin, which was fully adopted here. We did not consider sediment core studies (e.g., ref. 15,16) due to uncertainties in translating sediment proxy data into absolute lake levels for this endorheic basin. The local reservoir effect also necessitates a reassessment of original core data interpretations such as the proxy-based lake level reconstruction by Roberts et al. (16). Applying the reservoir effect of 2050 years to their reconstruction would place the onset of maximum lake levels to the early Holocene instead of the originally proposed Late Glacial period (a similar temporal adjustment was made for the Suguta record of Garcin et al. (4) after a 14 C reservoir-adjustment by (6) and (9)). This reservoir effectcorrected lake level reconstruction would then be synchronous with the highstand timing based on the dated Magadi-Natron stromatolites. We also incorporated radiocarbon dated layers of fossil fish from outcrop sections of the High Magadi Beds (e.g., ref. 36) for the reconstruction of the Holocene fish fauna of this basin.

S1.3. 40 Ar/ 39 Ar dating
Sanidine phenocrysts extracted from rhyolitic pumice clasts from two levels of the Siriata lake deposits were dated by the single-crystal incremental heating 40 Ar/ 39 Ar method. Sample OLOR16/SKG-1pB1 is a single large pumice clast from the uppermost levels of the diatomite deposits (1.961118°S, 36.367585°E), while sample OLOR16/SKG-2p1 (1.963817°S, 36.366806°E) is also a single large pumice clast from beach gravel deposits 310 m southwest of the previous location, where diatomaceous sediments shoal against the older trachyte rift flanks (Fig. S8). The stratigraphic relationship between the two samples is not known, but given the unusual occurrence of large floated pumice, and similar textural and compositional appearance of pumice from the two sites (white, satiny, stretched, crystal-poor rounded to sub-rounded lapilli to blocks), they may be derived from the same eruptive event. The methods used here are similar to those described in Deino et al. (37,38). Samples were processed at the Berkeley Geochronology Center in preparation for 40 Ar/ 39 Ar dating, using conventional separation techniques including disaggregation with a ceramic mortar and pestle, sieving, removal of magnetite with a hand magnet, distilled water rinses, magnetic separations with a Frantz Isodynamic Separator, heavy liquid separations, and rinses in dilute HF and distilled water. Finally, inclusion-free feldspar phenocrysts were hand-picked under a binocular microscope. The final crystal concentrates were irradiated in the Cd-lined CLICIT position of the Oregon State University TRIGA reactor for five minutes. Sanidine phenocrysts from the Alder Creek Rhyolite of California (orbitally referenced age = 1.1848 ± 0.0006 Ma; ref. 39) was employed as the neutron fluence monitor mineral. Standards and unknowns were co-irradiated in a circular configuration in wells in an aluminum disk, with standards at the cardinal positions, with two unknowns situated between standards. The appropriate neutron fluence factors (the 'J' parameter of 40 Ar/ 39 Ar dating calculations; ref. (40)) for the unknown positions were calculated from a planar fit of the standard calibrations, with 1σ errors derived by Monte Carlo simulation in the predicted J value ranging from 0.1-0.3%. Reactor-induced isotopic production ratios for these irradiations were: (36Ar/37Ar) Ca = 3.65 ± 0.02 × 10-4, ( 38 Ar/ 37 Ar) Ca = 1.96 ± 0.08 × 10-5, ( 39 Ar/ 37 Ar) Ca = 6.95 ± 0.09 × 10-4, ( 37 Ar/ 39 Ar) K = 3.24 ± 0.16 × 10-4, ( 38 Ar/ 39 Ar) K = 1.220 ± 0.003 × 10-2, ( 40 Ar/ 39 Ar) K = 3.5 ± 0.9 × 10-4. Atmospheric 40 Ar/ 36 Ar = 298.56 ± 0.31 (41) and decay constants follow (42). After a period of several months to permit radiological 'cooling' after irradiation, the individual sanidine phenocrysts were analyzed using incremental heating. Here, heating levels (laser output levels) were raised progressively from low temperature to fusion in a series of sequential independently measured steps (4-7 steps), termed the single-crystal incremental heating ('SCIH') approach. All argon measurements were carried out using an automated extraction line inlet to a Nu Instruments 5-collector Noblesse mass spectrometer, using ion-counting electronics. Completed incremental heating analyses were checked for apparent age plateaus, using a modified approach to that of Fleck et al. (43). Here, we search for a set of contiguous steps encompassing the greatest percent of 39 Ar release that exhibit an acceptable MSWD ('mean square of weighted deviates,' with a threshold probability >95% that the observed scatter is caused by analytical error alone and that geological scatter is not demonstrated). A plateau must comprise at least 50% of the total 39 Ar release and consist of at least three consecutive steps. We add here an additional threshold for inclusion of a plateau in further data analysis, in that the overall experiment must consist of more than three steps.
The incremental heating plateau age populations for each grain were then examined using 'inverse isochron' regressions ( 36 Ar/ 40 Ar vs. 39 Ar/ 40 Ar), and finally the age-probability distribution of the isochron ages was examined for each of the samples. We present two approaches to calculating the central tendency and error of the sample age populations. The first calculates a conventional weighted mean, with the error as a modified standard error ('mse,' the standard error multiplied by root MSWD where MSWD > 1). The second uses a Bayesian parameter estimation approach (38,44) that accommodates a tailing toward older ages commonly observed in East African feldspar phenocryst 40 Ar/ 39 Ar single-crystal data sets from tuffs (38).

S2.1. 40 Ar/ 39 Ar dating
We analyzed a total of 559 incremental heating steps on 11 grains of feldspar from sample OLOR16/SKG-1pB1, and 18 grains from OLOR16/SKG-2p1 (Table S4; Fig. S9). All but two grains (both from OLOR16/SKG-1p) yielded SCIH age plateaus (Table S5). Isotope correlation diagrams (isochrons) are shown for the plateau steps from each grain in Figure S10, and results tabulated in Table S5. None of the experiments demonstrated a 'trapped' 40 Ar/ 36 Ar significantly above atmospheric composition, suggesting that an 'excess argon' component is not present in these samples. The age-population density spectra of the isochron ages are shown in Figures S11 and S12. While sample OLOR16/SKG-2p1 displays a simple unimodal population with one marginally older result, sample OLOR16/SKG-1p exhibits a tail of older ages comprised of three experiments out of nine. Using a robust outlier detection method based on deviations from the median ('normalized median absolute deviation' >= 2; ref. 37,38), two grains in the older tail of OLOR16/SKG-1p are omitted, and none from OLOR16/SKG-2p1. The weighted-mean ages of the retained populations are 16.2 ± 1.2 ka (1σ mse, n = 7, MSWD = 1.3) for OLOR16/SKG-1p, and 11.9 ± 0.6 ka (n = 18, MSWD = 1.0) for OLOR16/SKG-2p1. However, given the tailing of ages present in OLOR16/SKG-1p, we prefer an alternative method to identifying the age of these samples, using Bayesian eruptive-age modeling (38,44). This approach, which allows use of the entire isochron data set without deletions, yields a markedly younger result for OLOR16/SKG-1p at 12.3 ± 2.7 ka, and a slightly younger result of 11.0 ± 1.0 ka for the more symmetrical sample OLOR16/SKG-2p1 (Fig. S12). The Bayesianmodeled ages are the preferred results for these dating experiments. With the above weightedmean approach, there is a significant difference between the two samples at the 95% confidence level, whereas with the Bayesian approach the age difference between the samples does not meet this confidence level criterion.

S3.1. Present and past rainfall in Kenya
The topography of East Africa strongly modulates the amount and distribution of rainfall ( Fig. S1C-S1D). Orographic precipitation is today prevalent across the central Kenya highlands (45), which receive mean annual rainfall of more than 2000 mm and have a positive moisture balance, in marked contrast to the adjacent semi-arid lowlands and the moisture-deficient rift valley (46) (Fig.  S1D). The high rainfall at the 3000 and 4000 m high rift shoulders of the Mau Escarpment and the Aberdare Range generates runoff that today feeds into Lakes Naivasha, Nakuru, and Natron (47). During the early Holocene a stronger monsoonal circulation produced about 20-30% more rainfall in East Africa than today in response to higher Northern Hemisphere summer insolation and increased greenhouse gas forcing (48,49,50). Orographic forcing by the central Kenyan highlands would therefore have generated even more precipitation and runoff over mountainous areas at this time. Moisture supply to the Aberdare Range was indeed higher during the early Holocene than at present (51). The abrupt increase in rainfall with the onset of the Holocene (52, 53) would have rapidly filled the headwater lake basins to their overflow levels, possibly within as little as 200 years according to lake-balance modeling (54). Enhanced dry season rainfall during the early Holocene (53) would have maintained river flow, in contrast to the present situation where flow in many Kenyan rivers is reduced or ceases during the biannual dry seasons (55,56). Earlier cessation of overflow from Lake Nakuru-Elmenteita (by about 8.6 ka) than that of Lake Naivasha can be explained by the small catchment area of this lake basin as compared to the latter (46) (Fig. S1C).       . Bayesian age models for Lake Siriata sediment outcrops generated with the rbacon package 2.3.8. A) age model for 290-0 cm of outcrop 1A. B) age model for the sediment package from 713-430 cm below surface of outcrop 3E, including an instantaneous deposit (tephra: 700-670 cm). C) age model for outcrop 3E extrapolated from 430 cm to 0 cm with same sedimentation rate as in between the uppermost two radiocarbon dates of B) and the same age uncertainties as in B), with the black line denoting the median age.    39 Ar/ 40 Ar isotope correlation diagrams) of the SCIH experiments. The isochron age is the x-axis intercept and is shown at 1s. ' 40 Ar/ 39 Ar Int.' refers to 'trapped' non-radiogenic 40 Ar/ 36 Ar ratio derived from y-axis intercept of the isochron. 'MSWD' refers to 'mean square of weighted deviates,' a measure of the observed scatter about the fit line, compared to the expected scatter. 'P' refers to the probability that the observed scatter can be explained by analytical errors alone. 'n' is the number of analyses.

Fig. S11.
Age-probability spectra of isochron ages, with weighted means. Sample legend is provided in lower-left. Top) Mean Ca/K atomic ratio of each aliquot derived as a by-product of the 40 Ar/ 39 Ar analysis. Middle) Rank order plot of the individual aliquots grouped by sample. Uncertainties in age are given at 1s standard error. Open symbols represent isochron ages omitted from the sample population based on the median outlier-detection criterion described in Methods. Bottom) Age-probability density spectra of each sample, with weighted-mean age and 1s error (including error in J, the neutron fluence parameter in 40 Ar/ 39 Ar dating). Dashed curves depict the probability density of the entire age population set, while the solid line represents the population after outlier deletion.      Fig. S4. 4 see photo 7 in Fig. S4. 5 see photo 8 in Fig. S4. 6 see photo 9 in Fig. S4. 7 see photo 10 in Fig. S4.  Prob.: Probability that the MSWD is fully explained by analytical scatter; if below 5%, plateau or isochron is not considered valid. 40 Ar/ 36 Ar trapped: 'Trapped' non-radiogenic argon ratio calculated from the isochron fit.

Isochron Results
Age (Ma ± 1s mse) 40 Ar/ 36 Ar trapped ± 1s mse Table S6. Cumulative probability distributions for the time and duration of overflow and closed basin conditions of Kenya Rift lakes.

River
Lake Basin Age ranges as Cumulative Probability Distributions (CPD) in years cal. BP (probability) 1 mid-late Holocene closedlake basin level early Holocene overflowlake level late Pleistocene closed-lake basin level