Philippa Kaur

The quality of global maps can be assessed in different ways. One way is global assessment where a single statistic is chosen to summarize the quality of the entire map: the map accuracy. For a categorical variable, this can be the probability that for a randomly chosen location on the map, the map value corresponds to the true value. For a continuous variable, it can be the RMSE, describing for a randomly chosen location on the map the expected difference between the mapped value and the true value. When a probability sample, such as a completely spatially random sample, is available for the area for which a global assessment is needed, then map accuracy can be estimated model-free (also called design-based, e.g., by using the unweighted sample mean in case of a completely spatially random sample). This circumvents modeling of spatial correlation because observations are independent by design6,9. This approach is called model-free because no model needs to be assumed about the distribution or correlation of the data: the only source of randomness is the random selection of sample units from a target population. If a probability sample is not available this approach cannot be used, and automatically the accuracy assessment approach becomes model-based10, which involves modeling a spatial process by assuming distributions and taking spatial correlations into account, and choosing estimation methods accordingly.Using naive random n-fold or leave-one-out cross-validation methods (or a simple random train-test split) to assess global model quality (usually equated with map accuracy) makes sense when the data are independent and identically distributed. When this is not the case, dependencies between nearby samples, e.g., in a spatial cluster, are ignored and result in biased, overly optimistic model assessment, as shown in, e.g., Ploton et al.5. Alternative cross-validation approaches such as spatial cross-validation5,11 that control for such dependencies are the only way to overcome this bias. Different spatial cross-validation strategies have been developed in the past few years, all aiming at creating independence between cross-validation folds5,11,12,13. Cross-validation creates prediction situations artificially by leaving out data points and predicting their value from the remaining points. If the aim is to assess the accuracy of a global map, the prediction situations created need to resemble those encountered while predicting the global map from the reference data (see Fig. 1 and discussions in Milà et al.14). This occurs naturally when reference data were obtained by (completely spatially random) probability sampling, but in other cases, this has to be forced for instance by controlling spatial distances (spatial cross-validation). Such forcing, however, is only possible when the distances in space that need to be resembled are available in the reference data. In the extreme case where all reference data come from a single cluster, this is impossible. When all reference data come from a small number of clusters, larger distances are available between clusters but do not provide substantial independent information about variation associated with these distances. Lack of information about larger distances means that we cannot assess the quality of predictions associated with such distances and cannot properly estimate global quality measures. Alternative approaches such as experiments with synthetic data15 or a validation using independent data at a higher level of integration16 would then be options to support confidence in the predictions.Another way of accuracy assessment is local assessment: for every location, a quality measure is reported, again as probability or prediction error. Such a local assessment predicts how close the map value is to newly observed values at particular locations. If the measurement error is quantified explicitly, a smoother, measurement-error-free value may be predicted10. If the model accounts for change of support10,17, predictions errors may refer to average values over larger areas such as 1 × 1, 5 × 5, or 10 × 10 km grid cells. Examples of local assessment in the context of global ecological mapping are modeled prediction errors using Quantile Regression Forests18 or mapped variance of predictions made by ensembles1,2. Neither of these examples quantifies spatial correlation or measurement error, or addresses change of support, as it is known from other modeling frameworks19. By omitting to model the spatial process, the local accuracy estimates as presented in the global studies that motivated this comment are disputable.The difference between global and local assessment is striking, in particular for global maps. A global, single number averages out all variability in prediction errors, and obscures any differences, e.g., between continents or climate zones. It is of little value for interpreting the quality of the map for particular regions. More

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In the version of this article initially published, there were mistakes in affiliations 1, 2 and 6. The corrected affiliations should read as follows: 1. Department of Earth System Science, Ministry of Education Key Laboratory for Earth System Modeling, Institute for Global Change Studies, Tsinghua University, Beijing, China; 2. Ministry of Education Ecological Field Station for East Asian Migratory Birds, Department of Earth System Science, Tsinghua University, Beijing, China; 6. Department of Geography, Department of Earth Sciences, and Institute for Climate and Carbon Neutrality, The University of Hong Kong, Hong Kong, China. The affiliations have been corrected in the HTML and PDF versions of the article. More

The data used here provides evidence that particular relationships may determine sex-specific patterns of witchcraft accusation. Cases where women were targeted frequently came from affinal kin, while those directed at men were often from unrelated individuals and blood relatives. Most previous research on factors that determine the sex of accused ‘witches’ has largely consisted of qualitative studies of a single society or a few societies48, or historical studies that have not tested for correlations49. Our findings, in support of the overarching hypothesis that accusations may be driven by various forms of competition, can be tentatively aligned with evolutionary literature on patterns of intrasexual and kin competition, intersexual conflict and polygamous mating30,31,50.Men were more often accused than women in our sample, although we did not have a prediction in relation to this. But the finding suggests how overall patterns of competition within relationships may contribute to societal ‘phenotypes’ of witches as male or female. The ethnography of the Ndembele perhaps indicates why women were less frequently targeted in Bantu societies: ‘in a case of witchcraft, the complainant is actuated by caprice, jealousy or pique; and the defendant is a person of wealth or popularity, and is always a man, for the women have neither wealth nor honor worth coveting’51.Our predictions about how the sex of accused ‘witches’ might be associated with particular relationship categories were supported. The majority of accusations targeting men came from unrelated individuals, which is unsurprising, as inclusive fitness52 would not mitigate the effects of competition between them. Blood relatives were the next most common relationship category directing accusations at men. This aligns with more recent studies indicating that witchcraft fears between family members are significant in parts of Africa, to the extent that they can be construed as ‘the dark side of kinship’53. In evolutionary terms, kin may compete with one another in environments where resources are limited30,31,50 and in societies with patrilineal inheritance related males, and particularly brothers, compete for resources in order to marry31. This aligns with an ethnographic observation that among the Banyoro witchcraft accusations often occurred between brothers over inheritance, but not between brothers and sisters, whose interests did not conflict21. The situations relating to accusations of men were also often connected to the acquisition of wealth and status, such as rivalry over village headmanships32, power struggles between a chief’s counsellors54 or disputes over inheritance55. These connections can be found in more recent contexts such as twentieth century Ghana, where notions of obtaining political power and wealth through occult means involving human sacrifice were pervasive56.Accusations of women were more likely to come from affines. Husbands were the largest category of affinal kin to accuse women (Supplementary Fig. 2). The higher rate of accusations from husbands to wives than wives to husbands aligns with evolutionary perspectives suggesting male coercion of females is a strategy to maximize male reproductive success39,41. Accusations of wives who were suspected of being unfaithful can be interpreted as a strategy for reducing investment in unrelated offspring35,41. In a case from the Shona a woman gave birth to a stillborn child. This was attributed to an affair before marriage, and was followed by divorce and the repayment of bridewealth to her husband, who commented she was ‘a witch, a woman who had killed her own child’48. Other ethnographic accounts suggest accusations of wives by husbands were an attempt to gain control within the marital relationship55.A significant number of accusations of women by affinal kin were from co-wives in polygynous marriages, and these were often notably associated with jealousy connected to a husband’s attention and investment32. Evolutionary models predict competition for reproductive resources would occur among co-resident breeding women57, as has been found to occur among the Mosuo of southwest China58. In the patrilocal social systems that are predominant in our sample, women disperse at marriage and are isolated from kin, so conflict may be more extreme30. This is consistent with ethnographic observations reporting that the relationship between co-wives in polygynous marriages was often (although not always) marked by conflict, and liable to produce witchcraft accusations38,59.There were accusations of women from other categories of their affinal kin (Supplementary Fig. 2). These again may result from competition for a husband’s time and resources between his kin and wife. New wives may be vulnerable in environments where they enter their husband’s families as unrelated strangers, and are potentially expendable, at least before the arrival of offspring. Some accounts of accusations indicate that accusations of wives by in-laws in patrilocal households are common29.Accusations directed at elderly individuals targeted women more often than men. This may form part of a broader pattern of geronticide: societies close to subsistence-level are documented as sometimes accepting the abandonment or killing of elderly people19,60. In modern Tanzania, ‘witches’ are mostly post-reproductive women, who are more likely to be murdered in periods of income shock19. This is also the case in contemporary Ghana, where accusations are frequently directed at middle-aged or elderly women, whose families may subsequently cease to provide them with financial or material assistance61. In our sample, elderly women may have been targeted more frequently as a result of longer female lifespans: in a polygynous society, men may marry younger women, so wives would be widowed at an earlier age than husbands. Among the Bantu, older men were accused, but some were possibly protected by their status.Accusers’ payoffs from accusations are not always explicit but they can be inferred. The most common outcome of accusations in our sample was that accused ‘witches’ were exiled from their communities or forced to move from where they were living. This would mean resources and cooperative assistance they would have used became available to their accusers or others nearby. Where the accused acquires a negative reputation, which was the second most common outcome, there may be a subtle removal of benefits, which may be preferred to direct ‘punishment’ as it is less costly62. Accusers’ gains need not be direct, as harming behaviours may reduce the overall pressure of competition in an environment28. 8% of accusations in the sample resulted in the acquisition of either resources or political positions from the accused, or in preventing the accused from acquiring them. Where the accused were penalised in other ways, such performing ceremonies to reconcile with accusers, this is perhaps akin to classic cooperation models involving the punishment of defectors (although the accused may not actually be uncooperative)11, providing accusers with subordinate partners who offer fitness benefits to avoid more serious allegations63. Where an accusation does not ‘stick’, ethnographic accounts sometimes indicate it was reversed through divination or ordeal54. In other cases, for various reasons accusations are short-lived and forgotten about4. Finally, although not tested in this dataset, accusers may gain informal prestige and dominance, an outcome analogous to competitive punishment63.Not all of the cases in our dataset support the hypothesis that witchcraft accusations are a mechanism for competition. There is a significant proportion where the accusation of a particular individual appears to be incidental, or dependent a on circumstantial association between the ‘witch’ and a negative event. Such accusations are unlikely to provide accusers with a competitive advantage. There are several possible explanations for such cases. They are in line with the hypothesis that witchcraft belief arises from attempts to identify the cause of an impactful misfortune3,4. Cultural evolutionary explanations of witchcraft beliefs suggest that they are a maladaptive attempt to explain misfortune. Although it is inaccurate, belief in witches is maintained through bias and selective inattention to evidence that would otherwise counter it64. Alternatively this could be viewed under the contention that superstitious beliefs (or errors in attributing cause and effect) are broadly adaptive if they occasionally lead individuals to acts which provide them with fitness benefits65.Although witchcraft accusations may be a mechanism for mitigating the damage to accusers’ reputations in harmful competitive acts, as with any behavioural strategy it is not without risks. Accusers may suffer costs in the form subsequent reputational damage or counter-accusations, as with punishment63, depending on factors such the level of support for an accusation by other members of the community.One limitation of our dataset is that it contains realized allegations of witchcraft, that cannot be tested against baseline population measures. We could not examine the risk that a particular individual, such as an elderly woman, would be accused. Instead, the analysis shows the odds, given an accusation occurred, that the ‘witch’ was male or female, given certain predictors. For example, if the accused was elderly, there are increased odds they were female rather than male.A dataset using historic witchcraft cases is almost certainly affected by selection bias. Cases with sensational outcomes are more likely to be reported, and cases that are dismissed or where the accused removes themselves from their accusers are liable to be overlooked19. Most incidents in our sample were reported anecdotally. Obtaining a random sample of witchcraft accusations within a population is challenging, if not impossible1,66. Attempts to systematically collect cases within a given location and timeframe cannot guarantee that all are brought to the attention of researchers19. Comparative studies of this kind usually use all the data that is available and control for confounding effects. Our sensitivity analyses suggest the large number of accusations of men in the dataset probably reflects patterns of accusations in these societies, rather than male-focused bias from ethnographers. There are many accounts of cultures where witches are predominantly male33,34,49. But the accuracy of historic ethnographic accounts cannot be verified, especially in relation to one-off events such as witchcraft accusations, just as it is unclear how much uncertainty there is in the ethnographic record overall67. Ethnographers may not always have noted the characteristics of the individuals involved, or there may be times where they were mistaken in reporting the circumstances surrounding an accusation. There are several explanations for cases where the identities of accusers or purported victims of witchcraft were not reported. Not all cases had identifiable ‘victims’, for example when the accused was thought to have used witchcraft to promote their own success, or ethnographers could not denote the relationship between the accused and their accusers when suspicions of witchcraft were communicated through general gossip. In a small number of cases, ethnographer perspectives on accusations (and possible inability to access further information) are salient, as they may ascribe more importance to one relationship over another in reporting a case, such as a witch’s envy of their victim, or a witch’s argument with an accuser.However, it is likely that ethnographers were for the most part accurate in documenting variables of interest such as the sex of an accused individual and their relationships with accusers. There is less certainty in relation to the situation connected to an accusation, especially taking into recent research that indicates the prevalence of phenomena such as the misperception of causation68,69. Our attempts to account for such possibilities with sensitivity analyses and meta-data on the production of ethnographies cannot conclusively provide reassurance that bias has not affected results, and so this section of the analysis should be treated with caution and regarded as exploratory. The situations documented in our study do however align with accounts of accusations from more contemporary observers and studies from different geographic locations, suggesting that similar causes of accusations arise convergently in different societies. For example in modern contexts accusations have led to accusers gaining land or property in India6 and cessation of the obligation to provide material and financial assistance to elderly relatives in Ghana61. One advantage of our cross-cultural data being drawn from numerous ethnographies is that it is not reliant on the perspective of one individual, meaning that random perceptual error or individual (as opposed to cultural) bias is more likely to be mitigated in the results than would be the case in the study of a single culture by one ethnographer.As a further limitation, we were reliant on accessible ethnographic records from the best-documented societies. Although selection bias in favour of better described societies is present in our sample, this should not impact the main aim of this research, which is to understand the determinants of witchcraft accusations being directed at male or female targets.Overall our findings may indicate allegations of witchcraft stem from diverse forms of competition between individuals. This aligns with evolutionary approaches to competition and conflict. Accusations may provide fitness benefits by allowing individuals to target competitors, but the exact form and direction of competition is determined by aspects of socio-ecology. This in turn influences which sex is most likely to be accused and the overall portrayal of witches in a society. Accusations may be more likely to occur in some relationships rather than others, when there is a gain for the accuser, as in disputes over inheritance and property, or where another individual may pose a threat, or by simply reducing numbers of competitors. The success of witchcraft accusations in removing competitors and their flexibility as an adaptive strategy may explain their widespread distribution. More

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A summary describing all plant architecture, flower, fruit, and yield, and phenological traits for each of the thirteen Phaseolus sp. and Vigna sp. landraces in the open field and the greenhouse conditions is provided in Supporting Tables S3, S4 and S5. Main effects Kruskal–Wallis tests are summarised in Table 1, and the interactions between treatment conditions (open field and greenhouse) and species, and landrace and climatic background are summarised in Table 2.Table 1 Main effects Kruskal–Wallis H tests for treatment (open field vs greenhouse conditions), species, landrace, and climatic background of the landraces.Full size tableTable 2 Kruskal–Wallis H tests for the interactions between treatment (open field and greenhouse) and species, landrace, or the climatic background.Full size tableI. Plant architecturePlants under high temperatures and low humidity in the greenhouse exhibited significant higher overall mean rank values than field plants for stem diameter, the degree of branch orientation, composite sheet length and width, and the terminal leaflet length. The size of the angle of the base of the terminal leaflet, however, was bigger in the field (Supporting Tables S3 and Table 1). There were overall significant differences for species and landrace for all studied characters (Table 1). The Kruskal–Wallis analyses of the interactions between treatment (open field vs greenhouse conditions) and species, climatic background, and landrace were significant for all the traits (p-value  More