Abstract Understanding the emergence of the genus Homo is a pressing problem in the study of human origins. Australopithecus sediba has recently been proposed as the ancestral species of Homo, although it postdates earliest Homo by 800,000 years. Here, we use probability models to demonstrate that observing an ancestor’s fossil horizon that is at least 800,000 years younger than the descendant’s fossil horizon is unlikely (about 0.09% on average). We corroborate these results by searching the literature and finding that within pairs of purported hominin ancestor–descendant species, in only one case did the first-discovered fossil in the ancestor postdate that from the descendant, and the age difference between these fossils was much less than the difference observed between A. sediba and earliest Homo. Together, these results suggest it is highly unlikely that A. sediba is ancestral to Homo, and the most viable candidate ancestral species remains Australopithecus afarensis.

INTRODUCTION Understanding the origin of the genus Homo is one of paleoanthropology’s most enduring questions. A key element in resolving this question is determining which species may have been ancestral to our genus. Because Australopithecus sediba has recently been proposed as a candidate ancestral species (1–3), it is essential that we critically evaluate this claim. Fossil specimens from A. sediba are currently only known from Malapa, South Africa, which is dated to 1.977 million years (Ma) ago (2). These fossils postdate by 800,000 years (0.8 Ma) the only known specimen from the oldest, and currently unnamed, species of Homo (hereafter, “earliest Homo”), which is dated to 2.8 to 2.75 Ma ago at Ledi-Geraru, Ethiopia (4, 5). Most recently, the argument for A. sediba being ancestral to Homo was continued by Robinson et al. (6), who discussed how a fossil horizon from an ancestral species could be much younger than a horizon from the descendant and claimed, “On temporal grounds alone one cannot dismiss the possibility that A. sediba could be ancestral to the genus Homo” (p. 1). Two conditions must both be met for A. sediba to be ancestral to Homo and for the recovery of an A. sediba fossil horizon that is much younger than an earliest Homo horizon (barring severe postdepositional stratigraphic mixing or errors in taxonomic assignment or dating): (i) Because an ancestor’s fossil horizon can only postdate a descendant’s if there is some overlap in the species’ temporal ranges (Fig. 1A), the descendant must have speciated from the ancestor via budding cladogenesis (Fig. 1B). For our study, we assume that Homo cladogenetically budded from A. sediba because, otherwise, this analysis would be unnecessary, and the argument for A. sediba being ancestral to Homo would be illogical (because the A. sediba fossil horizon postdates the earliest Homo horizon). (ii) Given the large amount of time separating the fossil horizons of A. sediba and earliest Homo, there must have been substantial overlap between the two species’ temporal ranges, such that the end of the A. sediba range is able to postdate the beginning of the earliest Homo range by at least 0.8 Ma (Fig. 2). If range overlap is less than 0.8 Ma, then the A. sediba fossil horizon cannot be 0.8 Ma younger than the earliest Homo horizon (assuming A. sediba was ancestral to Homo) (Figs. 1A and 2). As range overlap increases, so does the probability of sampling the end and beginning of the A. sediba and earliest Homo ranges, respectively, such that their horizons are at least 0.8 Ma apart (Fig. 2A). This second condition forms the theoretical basis for our probability model. Fig. 1 Conditions where an ancestor’s fossil horizon can be younger than the descendant’s. For both figures, “A” represents the ancestral species, and “D” represents the descendant species. (A) When there is no overlap between the temporal ranges of an ancestor and a descendant, an ancestor’s fossil horizon can never be younger than the descendant’s. If ranges partially overlap (gray), then an ancestor’s fossil horizon can postdate the descendant’s (fossil horizons are represented by white circles). The maximum age difference between a younger horizon from an ancestor and an older horizon from a descendant is ultimately constrained by the amount of range overlap, such that the age difference can never be greater than the amount of overlap. (B) Three different ways a descendant can speciate from an ancestor. Budding cladogenesis is the only speciation mode that produces ancestors and descendants with overlapping temporal ranges and is therefore the only mode where an ancestor’s fossil horizon can postdate the descendant’s. “D1” and “D2” represent two sister lineages, which are both descendants of “A.” (B) is modified after Fig. 1 in (25). Fig. 2 Schematic used to derive the model for quantifying the probability that an ancestor’s fossil horizon postdates the descendant’s by at least 0.8 Ma. For both figures, “A” represents the ancestral species, and “D” represents the descendant species. (A). The probability of sampling an ancestor’s fossil horizon that is at least 0.8 Ma younger than the descendant’s is ultimately a function of the amount of overlap between both species’ temporal ranges relative to the age difference of interest (which here is 0.8 Ma). When range overlap is less than 0.8 Ma, the ancestor’s horizon cannot postdate the descendant’s by 0.8 Ma (represented by the Xs in the leftmost example). In the middle example, there is enough range overlap where 0.8 Ma separates the end and beginning of the ancestor’s and descendant’s ranges, respectively (black), and each species’ fossil horizon must be sampled from these black regions. As overlap increases (rightmost example), so does the size of the black regions and the probability of sampling an ancestor’s fossil horizon that is at least 0.8 Ma younger than the descendant’s horizon. The rightmost example is used to illustrate the three variables from our probability model (Eq. 5c): T d represents the age difference of interest (i.e., 0.8 Ma), T o represents the amount of range overlap, and T R represents the duration of the entire temporal range (i.e., 0.97 Ma). (B) Focusing on the black regions, a descendant’s fossil horizon (white circles) can sample some time near the species’ age of origination (leftmost example), which means that the ancestor’s horizon can be sampled anywhere in its own black region and still be at least 0.8 Ma younger than the descendant horizon (white-striped region). If the descendant’s horizon is found in the middle of the black region (middle example), the ancestor’s horizon must sample the younger half of its own black region. If the descendant horizon samples the end of its black region (rightmost example), the ancestor’s horizon must sample the end of its temporal range. The rightmost example is used to illustrate the X A and X D variables (Eq. 3), each of which represents the distance from the beginning of the black region to the temporal location of the fossil horizon in the ancestor’s and descendant’s range, respectively. For the ancestor’s horizon to postdate the descendant’s by at least 0.8 Ma, X A must be greater than X D , and two iterations of this are shown. While Robinson et al. (6) are correct that it is possible for an ancestor’s fossil horizon to be much younger than the descendant’s, a more informative question would be, “How likely is this chronological pattern?” We build upon previous work concerning the evolutionary relationships of A. sediba (1–3, 6) and construct a probability model, which serves as a null hypothesis test, to evaluate whether A. sediba is ancestral to Homo. We assume that (i) A. sediba and earliest Homo each had temporal ranges of 0.97 Ma (6), (ii) the probability of recovering fossils throughout each species’ range is uniform through time (7, 8), and (iii) the probability of sampling an A. sediba fossil horizon does not affect the probability of sampling an earliest Homo fossil horizon, i.e., these are independent events (see Materials and Methods). From these assumptions, we quantify the probability of finding one fossil horizon from A. sediba that is at least 0.8 Ma younger than one horizon from earliest Homo (i.e., the observed data), assuming A. sediba is ancestral to Homo (i.e., the null hypothesis). The computed probabilities are equivalent to P values, and if they are exceptionally low, this would suggest that A. sediba is unlikely to be the ancestor of Homo (i.e., the null hypothesis is falsified). We calculate multiple P values as a function of the overlap between the two species’ true temporal ranges, which is currently unknown. We analyze temporal evidence only (6) and do not consider morphological data concerning the evolutionary relationship between A. sediba and Homo (1, 9–11). We also analyze the historical record of hominin discovery and calculate the geological age difference between initial fossil discoveries in purported ancestor and descendant species. The aim here is to corroborate our theoretical probability results and to empirically assess how likely it is for an ancestor’s fossil horizon to postdate a descendant’s by at least 0.8 Ma.

RESULTS The probability of finding an ancestor’s fossil horizon that is at least 0.8 Ma younger than the descendant’s is, by definition, zero when temporal range overlap is less than or equal to 0.8 Ma (Figs. 2A and 3 and Eq. 5c). This probability monotonically increases with range overlap when overlap is greater than 0.8 Ma (Fig. 3 and Eq. 5c) for reasons discussed above (Fig. 2A). However, even when the two species’ ranges completely overlap, which is impossible for ancestor-descendant species and is only presented as a theoretical upper bound, the computed P value is only 0.016 (Fig. 3 and Eq. 5c). If we treat all possible values of range overlap as equally likely, the mean P value over all overlap values is 0.0009 (Eq. 6c). We have confirmed our probability model results with simulations (fig. S1 and data file S5). Fig. 3 Probability of finding an ancestor’s fossil horizon that is at least 0.8 Ma younger than the descendant’s fossil horizon (P value). P values are plotted as a function of the overlap between the two species’ true, unknown temporal ranges, each of which is assumed to be 0.97 Ma in duration (6). Reviewing the paleoanthropology literature, we recorded 28 hypothesized ancestor-descendant species pairs (table S1). There is only one instance where an ancestor’s first-discovered fossil postdated the descendant’s: ancestor Homo erectus sensu lato (Kedung Brubus 1) dated to 0.8 to 0.7 Ma ago (12) and descendant Homo antecessor (ATD6-1) dated to 0.9 to 0.8 Ma ago (13). The age difference between these specimens (i.e., 0.1 Ma) is far less than the age difference observed between A. sediba and earliest Homo (i.e., 0.8 Ma) (Fig. 4). When the mean and SD of the 28 observed age differences are used to generate a normal distribution model (bell curve in Fig. 4), 0.8 Ma falls in the >99.9th percentile, which translates to a P value less than 0.001. Fig. 4 Histogram of the geological age differences between first-discovered fossils in purported hominin ancestor-descendant species pairs (n = 28). Negative age differences represent those species pairs where the ancestor’s first-discovered fossil is older than the descendant’s, and positive age differences indicate the opposite. The black arrow represents the observed age difference between A. sediba (hypothesized ancestor) and earliest Homo at Ledi-Geraru (hypothesized descendant). The bell curve represents a normal distribution model, generated using the sample mean and SD of the 28 observed age differences.

DISCUSSION We have demonstrated using probability models that the null hypothesis of A. sediba being ancestral to Homo can be falsified. That is, it is very unlikely (about 0.09% on average) to find an A. sediba fossil horizon that is at least 0.8 Ma younger than an earliest Homo horizon, if the former species is actually ancestral to the latter. The prior record of paleoanthropological discoveries also reflects the rarity of cases in which this chronological pattern is observed, further supporting that A. sediba is unlikely to be ancestral to Homo. We can explore how strongly our assumptions influenced our modeling results. We calculated our P values, assuming the 2.8-Ma-old Ledi-Geraru mandible actually belongs to Homo (5). Some researchers dispute this (14), so we also ran our analyses assuming A.L. 666-1 (2.33 Ma-old)—a specimen widely regarded as Homo—represents the oldest Homo specimen (15). Although a handful of researchers argue that all pre–1.9-Ma-old specimens assigned to Homo are invalidly named or are poorly dated (2, 3), we view this assertion as unlikely [as does Robinson et al. (6)]. By selecting a younger fossil to represent the oldest Homo specimen, we are decreasing the observed age difference between A. sediba and earliest Homo, which should increase the P values overall (Eq. 5c). We also explored whether our choice of 0.97 Ma to represent hominin temporal durations might affect our results because using a longer duration will increase the amount of time associated with a given percentage of range overlap between two species, and this should increase P values as well (Eq. 5c). We therefore reran our analyses assuming hominin temporal durations of 2 Ma, which is at the larger end of estimated mean species durations in African large mammals [all African large mammals: 2.3 Ma (16); eastern African bovids: 1.4 Ma (17); large mammals in the Omo-Turkana Basin, Ethiopia/Kenya: 1.4 Ma (17); Australopithecus anamensis-afarensis: 1.2 Ma (7, 8)]. Results show that calculated P values are still small even when relaxing the age of earliest Homo to 2.33 Ma ago or hominin temporal durations to 2 Ma. For example, P values exceed 0.05 only when range overlap is at least 70%, and the mean and maximum P values over all possible overlap values are only 0.04 and 0.20, respectively (Eqs. 5c and 6c, and fig. S2, A and B). When both assumptions are simultaneously relaxed, P values exceed 0.05 when overlap is at least 50%, and the mean and maximum P values are 0.093 and 0.34, respectively (Eqs. 5c and 6c, and fig. S2C). For our model, we assumed that the probability of recovering a fossil horizon from each of the A. sediba and earliest Homo temporal ranges is uniform through time. This assumption is a parsimonious one given that only one horizon each has been sampled from A. sediba (1, 2) and earliest Homo (5), and a uniform fossil recovery potential (FRP) (i.e., the probability of finding a fossil horizon) is a good approximation for the one hominin lineage where FRP has been explored, i.e., A. anamensis-afarensis (7, 8). However, we also have to consider the possibility that FRP is not uniform through time in the A. sediba and earliest Homo temporal ranges. Our P values would only be biased downward if FRP is greater in South Africa and eastern Africa during the geological time periods when A. sediba and earliest Homo are found, respectively. This is because if FRP is actually higher toward the end and beginning of the A. sediba and earliest Homo temporal ranges, respectively, then it is more likely that one will recover an A. sediba horizon that is much younger than an earliest Homo horizon, even if the former species is ancestral to the latter. Using the number of hominin fossil horizons—defined as midpoint ages of hominin-bearing members with age duplicates removed (see data file S3) (7, 8)—as a proxy for FRP, we find that FRP is not appreciably higher during the times when A. sediba and earliest Homo are found in their respective geographic regions (fig. S3). There is the possibility that FRP might be slightly higher in South Africa around the time of A. sediba (fig. S3), but even if we double the probability of recovering a fossil horizon in the last 25% of the ancestor’s (i.e., A. sediba) temporal range, the maximum P value is only 0.025 (fig. S4). Regarding our analysis of the historical record of first-discovered hominin fossils, ancestor-descendant hypotheses might implicitly or explicitly incorporate temporal information, which would potentially render our analysis circular. That is, if ancestor-descendant relationships are proposed at least partly based on the fact that the ancestor’s fossil predates the descendant’s, it should be no surprise that ancestors’ fossil horizons rarely postdate descendants’ horizons. However, incorporating temporal data into ancestor-descendant hypotheses does not necessarily mean that the ancestor’s first-discovered fossil must predate the descendant’s first-discovered fossil (fig. S5). For example, a newly discovered fossil from the ancestral species may sample the end of its temporal range, and the rest of the range is revealed only after subsequent sampling. A second, more recently found fossil may be proposed as the ancestor’s descendant based on the new fossil postdating the ancestor’s first appearance, but the new descendant fossil can still predate the younger, first-discovered fossil from the ancestor (see fig. S5 for a discussion about the more complicated scenario when the descendant fossil is found first). Regardless of whether the ancestor or descendant was found first, none of the ancestor’s first-discovered fossils ever postdated the descendants by more than 0.8 Ma (i.e., the observed age difference between A. sediba and earliest Homo) in our literature review (Fig. 4 and table S1). Robinson et al. (6) write, “Until such time as additional data on its temporal range are available for A. sediba, any inferences about the evolutionary relationship between it and Homo should be based primarily on morphological data” (p. 6). More fossils will always strengthen any inference, but we have demonstrated here that even with the scant data relevant to the question at hand (i.e., only one fossil horizon each from A. sediba and earliest Homo), we can still use temporal evidence to rigorously assess the proposed ancestor-descendant relationship between these two species. This is accomplished by modeling the process/question of interest to generate the probability of obtaining the observed pattern (i.e., an ancestor’s fossil horizon that is 0.8 Ma younger than the descendant’s), analogous to a null hypothesis test. Our analyses demonstrate that strong inferences can be made even with an incomplete fossil record, so chronological data and tests should not be so quickly discarded. The issue of the origin of Homo is one of the thorniest questions in paleoanthropology and one that has led to myriad proposals and, sometimes, speculations (2, 3, 18, 19). Answers to the questions of how, when, and where the earliest representatives of the genus emerged are still in flux, owing especially to the dearth of fossil data from the relevant temporal range (3.0 to 2.5 Ma ago). It is therefore important to use all available lines of evidence when addressing a question as data poor as this one. While fossil remains from the 3.0- to 2.5-Ma-old interval are necessary to reasonably document the morphological patterns surrounding the origin of Homo, probabilistic methods such as the one used here are also critical for assessing the chronological evidence for proposed relationships between Homo and candidate ancestors. Hypothesized ancestor-descendant relationships must satisfy both temporal and morphological criteria (7, 20). We tested the first criterion here, and the second one has been tested elsewhere (11). A. sediba fails both benchmarks, and the most viable ancestral candidate for the genus Homo remains Australopithecus afarensis both on morphological (5) and temporal grounds (7, 8).

MATERIALS AND METHODS Probability model We are interested in the probability that an ancestor’s fossil horizon postdates the descendant’s by at least some amount, T d . Let us denote this probability as P(H A − H D > T d ), where H A and H D represent the ages of the ancestor’s and descendant’s fossil horizons, respectively. To have an ancestor’s horizon postdate the descendant’s, the fossils must come from the period of temporal range overlap (Fig. 1A). To get an ancestor’s horizon that postdates the descendant’s by at least T d , the ancestor’s fossil must sample the younger end of the overlap region, and the descendant’s fossil must sample the older end (Fig. 2A); let us designate these respective regions as end A and end D (i.e., black regions in Fig. 2A), and the probability of sampling these regions is P(end A ) and P(end D ). Because we assume that the ancestor and descendant species have equal temporal ranges, P(end A ) = P(end D ) (Fig. 2A). Assuming sampling probability is uniform throughout a species’ temporal range, the probability of sampling a fossil horizon from this region is P ( end A ) = P ( end D ) = T o − T d T R (1)where T o is the amount of range overlap and T R is the duration of the entire temporal range (Fig. 2A). We assume here that the probability of selecting a fossil horizon from the ancestor’s range is independent from selecting a fossil horizon from the descendant’s range. This is a sensible assumption given that the earliest Homo specimen is from eastern Africa (5), whereas the A. sediba specimens are from South Africa (1). Therefore, the probability of sampling one fossil horizon each from end A and end D is P(end A ) × P(end D ) or P ( end A ∩ end D ) = ( T o − T d ) 2 T R 2 (2)where “∩” denotes the intersection, i.e., when two events both occur. Once end A and end D are both sampled, Fig. 2B illustrates the necessary conditions that must occur for the ages of the ancestor’s and descendant’s fossil horizons (i.e., H A and H D , respectively) to be separated by at least T d . Let X D represent the age difference between the beginning of end D and H D (X A represents the same but for the ancestor) (Fig. 2B). For a given value of X D , which we will call t, X A must be greater than X D , so H A falls within the white-striped regions in Fig. 2B. The probability of this occurring for all possible values of t (i.e., from zero to infinity) is P ( X A > X D ) = ∫ t = 0 ∞ P ( X A > X D | X D = t ) P ( X D = t ) d t (3a) Note that this is the law of total probability (21), which states P ( A ) = ∑ n P ( A | B n ) P ( B n ) , i.e., the probability of event A occurring is equal to the probability of A given event B n multiplied by the probability of B n , and all these are summed (or integrated) over all possible instances of B n in the sample space to get the total probability of A. Because we assume X A and X D are independent (i.e., the probability of X D taking on some value, t, does not affect the value of X A and whether it is greater than t), the first probability on the right-hand side in Eq. 3a can be simplified, so P ( X A > X D ) = ∫ t = 0 ∞ P ( X A > t ) P ( X D = t ) d t (3b) Because we assume that FRP is uniform throughout a species’ temporal range, the probability of sampling a fossil can be modeled as a Poisson process, where X A and X D are exponentially distributed (22, 23). The first probability in the integral (i.e., P[X A > t]; Eq. 3b) can be thought of as the probability that H A is not found within the interval (0, t) (or one minus the probability that H A is sampled in this interval). Using the exponential cumulative distribution function, this probability is P ( X A > t ) = 1 − ( 1 − e − λ t ) = e − λ t (3c) The second probability in the integral (P[X D = t]; Eq. 3b) can be calculated using the exponential probability density function (i.e., the probability that X D takes on some value, t), so P ( X D = t ) = λ e − λ t (3d) Substituting Eqs. 3c and 3d into Eq. 3b, we get P ( X A > X D ) = ∫ t = 0 ∞ e − λ t λ e − λ t d t (3e) Note that because we are only concerned with sampling one fossil horizon each from the ancestor’s and descendant’s range, both of which are of equal duration, the sampling rate, λ, for each species is the same. Solving Eq. 3e P ( X A > X D ) = λ ∫ t = 0 ∞ e − 2 λ t d t = λ ⋅ − e − 2 λ t 2 λ | t = 0 ∞ = λ ( − e − 2 λ ∞ 2 λ + 1 2 λ ) (3f) The exponential term equals zero given that λ is positive, so P ( X A > X D ) = λ 2 λ = 1 2 (3g) The same logic and result hold if the roles of X D and X A are reversed, i.e., if we instead solve P ( X D < X A ) = ∫ t = 0 ∞ P ( X D < X A | X A = t ) P ( X A = t ) d t . Therefore, the probability of getting H A and H D separated by at least T d given that H A and H D come from end A and end D , respectively, is one-half, or using probability notation P ( H A − H D > T d | end A ∩ end D ) = 1 2 (4) Putting all the above equations together using the law of total probability (21) P ( H A − H D > T d ) = P ( H A − H D > T d | end A ∩ end D ) P ( end A ∩ end D ) + P ( H A − H D > T d | [ end A ∩ end D ] c ) P ( [ end A ∩ end D ] c ) (5a)where the superscript “c” denotes the complement, i.e., when an event does not happen. We have already established that end A and end D need to both be sampled for an ancestor’s horizon to postdate a descendant’s by at least T d (Fig. 2A), so P(H A − H D > T d | [end A ∩ end D ]c) = 0. Therefore, the second product in Eq. 5a equals zero and can be dropped. We have already solved the two probabilities in the first product of Eq. 5a with Eqs. 4 and 2, so P ( H A − H D > T d ) = P ( H A − H D > T d | end A ∩ end D ) P ( end A ∩ end D ) = 1 2 × ( T o − T d ) 2 T R 2 = ( T o − T d ) 2 2 T R 2 (5b) And because P(H A − H D > T d ) must be zero when the age difference of interest (T d ) is greater than the amount of range overlap (T o ) (Figs. 1A and 2A), the final model is P ( H A − H D > T d ) = { 0 T d > T o ( T o − T d ) 2 2 T R 2 T d ≤ T o (5c) For our main analysis (Fig. 3), T d = 0.8 Ma, we assume T R to be 0.97 Ma (6), and we explored multiple values for T o , which is currently unknown. Because T o (i.e., how much the A. sediba and earliest Homo temporal ranges overlap) is currently unknown, we also applied uniform prior probabilities over all possible values of T o to distill the P value function (Eq. 5c) into its mean value (i.e., the expected value) (24). To get the expected P value, we integrate Eq. 5c with respect to T o over all possible values of T o (i.e., from zero to T R ) against the probability density function of our T o uniform prior, which is defined as 1/T R between zero and T R . Therefore, the expected value is E [ P ( H A − H D > T d ) ] = 1 T R ( ∫ T o = 0 T d 0 d T o + ∫ T o = T d T R ( T o − T d ) 2 2 T R 2 d T o ) (6a) Note that because P(H A − H D > T d ) is a piecewise function (Eq. 5c), we break the integral into the sum of two integrals separated by T d (i.e., the value that separates the piecewise function in Eq. 5c). The first integral in Eq. 6a equals zero, and pulling out the 1/2T R 2 constant in the second integral gives E [ P ( H A − H D > T d ) ] = 1 2 T R 3 ∫ T o = T d T R ( T o − T d ) 2 d T o (6b) Solving Eq. 6b E [ P ( H A − H D > T d ) ] = 1 2 T R 3 × ( T o − T d ) 3 3 | T o = T d T R = 1 2 T R 3 [ ( T R − T d ) 3 3 − ( T d − T d ) 3 3 ] = ( T R − T d ) 3 6 T R 3 (6c)which is the expected P value from Eq. 5c, treating all possible values of T o as equally likely. Analysis of published fossil ages We reviewed the literature and recorded the geological ages (lower and upper bracketing ages) and year of discovery of the first fossil found in each species in a hypothesized hominin ancestor–descendant pair [this mirrors the situation in A. sediba and earliest Homo, both of which currently have only one fossil horizon each (2, 5)]. Because we were only interested in by how much the ancestor’s first-discovered fossil postdated the descendant’s first-discovered fossil, we were more inclusive than not in our selection (i.e., the accuracy or widespread acceptance of an ancestor-descendant relationship should have no bearing on the age difference between first-discovered fossils). To calculate the age difference, we subtracted the midpoint age of the ancestor’s first-discovered fossil from the midpoint age of the descendant’s first-discovered fossil, where the midpoint age is defined as (lower bracketing age + upper bracketing age)/2. Negative age differences indicate that the ancestor’s first-discovered fossil is older than the descendant’s, and vice versa, for positive differences.

SUPPLEMENTARY MATERIALS Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/5/eaav9038/DC1 Fig. S1. Confirming our probability model results (Fig. 3) with simulations. Fig. S2. Same analysis as in Fig. 3 but assuming hominin temporal durations of 2 Ma, A.L. 666-1 (2.33 Ma old) represents the oldest Homo fossil, or both. Fig. S3. Uniform probability plots for 4- to 1-Ma-old hominin fossil horizons in South Africa and eastern Africa. Fig. S4. Same analysis as in Fig. 3, but the probability of sampling a fossil horizon (i.e., FRP) from the last 25% of the ancestor’s range is doubled. Fig. S5. Schematic illustrating how proposing an ancestor-descendant relationship based on temporal evidence does not necessarily constrain the first-discovered fossil in each species to be in the “correct” order (i.e., where the ancestor’s first-discovered fossil predates the descendant’s). Table S1. Previously proposed ancestor-descendant hominin species pairs (n = 28), and the year discovered and geological ages of the first-discovered specimen in each species. Data file S1. Hypothesized hominin ancestor–descendant species pairs. Data file S2. Geological ages for first-discovered specimens of hominin species. Data file S3. Four- to 1-Ma-old South African and eastern African hominin-bearing members and their geological ages. Data file S4. Dataset references. Data file S5. R code for analyses and creating figures. References (26, 27)

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REFERENCES AND NOTES ↵ L. R. Berger , D. J. de Ruiter , S. E. Churchill , P. Schmid , K. J. Carlson , P. H. G. M. Dirks , J. M. Kibii , Australopithecus sediba: A new species of Homo-like australopith from South Africa . Science 328 , 195 – 204 ( ). OpenUrl ↵ R. Pickering , P. H. G. M. Dirks , Z. Jinnah , D. J. de Ruiter , S. E. Churchill , A. I. R. Herries , J. D. Woodhead , J. C. Hellstrom , L. R. Berger , Australopithecus sediba at 1.977 Ma and implications for the origins of the genus Homo . Science 333 , 1421 – 1423 ( ). OpenUrl ↵ L. Berger , Australopithecus sediba and the earliest origins of the genus Homo . J. Anthropol. Sci. 90 , 117 – 131 ( ). OpenUrl PubMed ↵ E. N. DiMaggio , C. J. Campisano , J. Rowan , G. Dupont-Nivet , A. L. Deino , F. Bibi , M. E. Lewis , A. Souron , D. Garello , L. Werdelin , K. E. Reed , J. Ramón Arrowsmith , Late Pliocene fossiliferous sedimentary record and the environmental context of early Homo from Afar, Ethiopia . Science 347 , 1355 – 1359 ( ). OpenUrl ↵ B. Villmoare , W. H. Kimbel , C. Seyoum , C. J. Campisano , E. N. DiMaggio , J. Rowan , D. R. Braun , J. Ramón Arrowsmith , K. E. Reed , Early Homo at 2.8 Ma from Ledi-Geraru, Afar, Ethiopia . Science 347 , 1352 – 1355 ( ). OpenUrl ↵ C. Robinson , T. L. Campbell , S. Cote , D. J. de Ruiter , Temporal ranges and ancestry in the hominin fossil record: The case of Australopithecus sediba . S. Afr. J. Sci. 114 , 7 ( ). OpenUrl ↵ A. Du , J. Rowan , S. C. Wang , B. A. Wood , Z. Alemseged , Statistical estimates of hominin origination and extinction dates: a case study examining the Australopithecus anamensis-afarensis lineage . J. Hum. Evol. . ↵ Z. Alemseged, A. Du, J. Rowan, B. A. Wood, “Estimating the timing of and placing confidence intervals on the origination and extinction of the Australopithecus anamensis-afarensis lineage,” Abstr. 2018 Paleoanthropology Soc. Meet. PaleoAnthropology 2018, A1 (2018). ↵ J. D. Irish , D. Guatelli-Steinberg , S. S. Legge , D. J. de Ruiter , L. R. Berger , Dental morphology and the phylogenetic “place” of Australopithecus sediba . Science 340 , 1233062 ( ). OpenUrl M. Dembo , N. J. Matzke , A. Ø. Mooers , M. Collard , Bayesian analysis of a morphological supermatrix sheds light on controversial fossil hominin relationships . Proc. Biol. Sci. 282 , 20150943 ( ). OpenUrl CrossRef PubMed ↵ W. H. Kimbel , Y. Rak , Australopithecus sediba and the emergence of Homo: Questionable evidence from the cranium of the juvenile holotype MH 1 . J. Hum. Evol. 107 , 94 – 106 ( ). OpenUrl ↵ G. D. van den Bergh , J. de Vos , P. Y. Sondaar , The Late Quaternary palaeogeography of mammal evolution in the Indonesian Archipelago . Palaeogeogr. Palaeoclimatol. Palaeoecol. 171 , 385 – 408 ( ). OpenUrl CrossRef Web of Science ↵ D. Moreno , C. Falguères , A. Pérez-González , P. Voinchet , B. Ghaleb , J. Despriée , J.-J. Bahain , R. Sala , E. Carbonell , J. M. B. de Castro , J. L. Arsuaga , New radiometric dates on the lowest stratigraphical section (TD1 to TD6) of Gran Dolina site (Atapuerca, Spain) . Quat. Geochronol. 30 , 535 – 540 ( ). OpenUrl ↵ J. Hawks , D. J. de Ruiter , L. R. Berger , Comment on “Early Homo at 2.8 Ma from Ledi-Geraru, Afar, Ethiopia” . Science 348 , 1326 ( ). OpenUrl ↵ W. H. Kimbel , D. C. Johanson , Y. Rak , Systematic assessment of a maxilla of Homo from Hadar, Ethiopia . Am. J. Phys. Anthropol. 103 , 235 – 262 ( ). OpenUrl CrossRef PubMed Web of Science ↵ E. Vrba, in Cenozoic Geology of Southern Africa, T. C. Partridge, R. Maud, Eds. (Oxford Univ. Press, 2000), pp. 277–304. ↵ F. Bibi , W. Kiessling , Continuous evolutionary change in Plio-Pleistocene mammals of eastern Africa . Proc. Natl. Acad. Sci. 112 , 10623 – 10628 ( ). OpenUrl ↵ B. Wood , M. Collard , The human genus . Science 284 , 65 – 71 ( ). OpenUrl ↵ B. Villmoare , Early Homo and the role of the genus in paleoanthropology . Am. J. Phys. Anthropol. 165 , 72 – 89 ( ). OpenUrl CrossRef PubMed ↵ C. R. C. Paul , The recognition of ancestors . Hist. Biol. 6 , 239 – 250 ( ). OpenUrl ↵ W. Mendenhall, R. J. Beaver, B. M. Beaver, Introduction to Probability and Statistics (Brooks/Cole, Cengage Learning, ed. 14/Student edition, 2013). ↵ D. Strauss , P. M. Sadler , Classical confidence intervals and Bayesian probability estimates for ends of local taxon ranges . Math. Geol. 21 , 411 – 427 ( ). OpenUrl CrossRef ↵ J. F. C. Kingman, Poisson Processes (Oxford Studies in Probability Series, Clarendon Press, 1993). ↵ G. Casella, R. L. Berger, Statistical Inference (Thomson Learning, ed. 2, 2002). ↵ M. Foote , On the probability of ancestors in the fossil record . Paleobiology 22 , 141 – 151 ( ). OpenUrl ↵ B. Wood , E. K. Boyle , Hominin taxic diversity: Fact or fantasy? Am. J. Phys. Anthropol. 159 , S37 – S78 ( ). OpenUrl ↵ J.-J. Hublin , A. Ben-Ncer , S. E. Bailey , S. E. Freidline , S. Neubauer , M. M. Skinner , I. Bergmann , A. L. Cabec , S. Benazzi , K. Harvati , P. Gunz , New fossils from Jebel Irhoud, Morocco and the pan-African origin of Homo sapiens . Nature 546 , 289 – 292 ( ). OpenUrl CrossRef PubMed

Acknowledgments: For discussions about probability models, we thank A. Gordon (who recommended substantive improvements), M. Foote, and E. Friedlander. We thank S. Wang, M. Foote, and K. Hatala for comments on an earlier version of the manuscript. We also thank The University of Chicago Anthropology Journal Club for their helpful comments on the manuscript. Funding: No funding was received for this project. Author contributions: A.D. and Z.A. designed the research. A.D. and Z.A. collected the data. A.D. created the probability model and analyzed the data. A.D. wrote the paper with contributions from Z.A. Competing interests: The authors declare that they have no competing interests. Data and materials availability: All analyzed datasets and R code can be found in the Supplementary Materials. Additional data related to this paper may be requested from the authors.