 non-local individuals might therefore remain underestimated. This applies for the whole study, because the Carpathian Basin is broadly covered by Pleistocene loess, loam, and Quaternary fluvial sediments and may hence be considered geologically and isotopically homogeneous over wide areas [31][32][33]71]. In the late TLBK, new influxes from northern Croatia through the Sopot group and from Voivodina through the Vinča culture are archaeologically attested [16,22]. The interpretation of the strontium and oxygen stable isotope data indeed shows a particularly high proportion of site outliers in the Vinča samples: between 40 and 80% on the site scale (Fig 10A) and over 50% on the cultural group level (Fig 11). This tendency is also obvious concerning the Sopot culture, with more than 40% site outliers on the cultural group level (Fig 11). However, only one Sopot site provided a relatively large sample size (see ALE in Fig 10B and [40]). In the Alföld, two different patterns can be observed concerning the Tiszadob/Bükk and Esztár groups of the developed ALBK: on both the site scale (Fig 10) and the archaeological culture level (Fig 11), the Tiszadob/Bükk sample reveals particularly low proportions of site outliers (under 10% at HELI and POFE), while the Esztár sample shows increased proportions of site outliers. This may be an indication of the different ways in which these communities merged with ALBK [17,18,69,72], which will be discussed at greater length below. An increased proportion of site outliers can also be observed at two of the three Szakálhát sites (Fig 10A) and for the whole Szakálhát sample (Fig 11). This phenomenon is consistent with the archaeological record that shows that the Szakálhát groups are characterised by new features and extensive contacts [19,20].
At the end of the Neolithic, Transdanubia is first marked by a decrease in mobility and external inputs during the Lengyel period (under 30%, see Fig 11), as can be seen especially at the BAL and MORT sites (under 10%) [see also 26] and, to a lesser extent, at the CSAT site (under 30%) in Fig 10. This can perhaps be taken to indicate that the South-East European impacts observed in the material record of the Lengyel culture can probably be ascribed to trade rather than to the arrival of new population groups. In contrast, the increased proportion of site outliers during the Balaton-Lasinja period (nearly 40%) (Figs 10 and 11) correlates well with the archaeological record, according to which a new Balkanic influx can be attested [1][2][3][4].

PLOS ONE
Tracing mobility patterns in Neolithic Carpathian Basin through isotope analyses communities had thus spatially restricted daily activity areas. The assumed Balkan influx during the Tisza culture is not supported by this dataset.
The results of the strontium and oxygen stable isotope analyses and the interpretation of the data are generally consistent with the results of aDNA analyses conducted by Anna Szécsényi-Nagy and Victoria Keerl at the same sites, also within the framework of this project [6][7][8]. This project thus enables to retrace the fluctuations in mobility rates during the Neolithic in both Transdanubia and the Alföld. Another tendency illustrates that Transdanubian cultural groups usually have larger proportions of site outliers than the groups in the Alföld, even regarding the LBK groups (Figs 10 and 11). This can in all likelihood be explained by the geographical location of Transdanubia on the direct continental route of European Neolithisation that linked South and North in this part of Europe [7] and to the repeated Balkan inputs in Transdanubia [16,22,[73][74][75], or to more extended social and economic networks [see 26]. Moreover, Transdanubia is geologically more diverse, so non-locals or mobiles individuals are more likely to be detected [31][32][33]71]. The trend is therefore not necessarily cultural but could be triggered by the distinct environmental settings.

Different types of mobility
Three different types of mobility can be distinguished through the application of the abovementioned methods. First, it is possible to identify individuals who were born at the site but were particularly mobile during their life. These individuals either have a site-specific signal in their early mineralising and a site outlier signal in their late-forming tooth, or have a large offset regarding the isotope composition of their different teeth. This means that some locally born individuals were mobile during their lives and returned to the home site at some later time. Usually, only two teeth were sampled in this study, which enables the determination that an individual left after the mineralisation of the earliest sampled tooth (usually the M1, with site-specific signal) and before the formation of the latest sampled tooth (usually the M3, with site-outlier signal). At Veszprém-Jutasi-Munkácsy út (VEJ), however, two individuals were sampled for the first, the second and the third molar. The second permanent molar of an adult female (VEJ6) shows a site outlier 87 Sr/ 86 Sr ratio-which could correspond to a micro-regional value-and the first and third molars show a site-specific ratio (S6A Fig). This could mean either that she changed her place of residence or her dietary habits when she was five or seven years old. Moreover, another adult female (VEJ7) has a site-specific 87 Sr/ 86 Sr ratio in both the first and the second permanent molars, while the third molar exhibits a site-outlier-but probably micro-regional-signal. She could have left her place of birth or changed her dietary habits when she was about seven years old; however, information about her later place of residence or the time of her return remain unclear. Although this region is very heterogeneous and the results could be interpreted in different ways, these observations clearly indicate that sampling several teeth per individual offers a more accurate insight into mobility patterns. Moreover, they are consistent with demographic and social mobility patterns assumed for prehistoric communities, in which children assume essential social and economic responsibilities at an early age (e. g. [58,76]).
The second type of mobility corresponds to site outliers that probably originated from the immediate or (micro-)regional surroundings of the site. Given the determination of a microregional strontium isotope baseline [12], it is not only possible to distinguish individuals with site-specific from individuals with site-outlier isotope values, but also to divide site outliers into two categories: individuals with an isotope composition matching the micro-regional, and individuals that have neither site-specific nor micro-regional signals. Different or distant geographical areas can often have similar strontium and/or oxygen isotope compositions [12,46,70,77], meaning that individuals with micro-regional signals could have originated from a distant region. However, the interpretation in this study is based on the principle that the nearest region with a corresponding isotope composition is considered the most likely place of origin (e.g. [63,78]. The third type of mobility is represented by non-local individuals, who have neither a site-specific nor a micro-regional, but a non-local isotope composition in their teeth. They originated from a distant or geographically distinct region compared to the site and its surroundings and highlight spatially large-scale mobility patterns (e.g. by marriage or migration events).
The Starčevo and Körös archaeological groups show the overall highest number of mobile and site-outlier individuals (Fig 11). These communities were therefore demographically very dynamic. The high proportion of non-local individuals in the Körös and Starčevo cultural groups would be consistent with the archaeological "Neolithisation paradigm" positing that the first Hungarian Neolithic groups were predominantly "immigrants" [1][2][3][4] if the sample would correspond to the first generation of settlers. This would also fit in nicely with the results of aDNA analyses conducted on the same Neolithic sites, which highlighted the important role of immigrants in the composition of these communities [6]. However, it is not possible to identify the difference between initial settlers and later generations in the sample, so the interpretation of the non-local people in terms of large-scale migration and Neolithisation processes cannot be tracked with absolute certainty. According to the archaeological evidence, the first generation of Starčevo and Körös groups can be correlated with the expansion of the Anatolian-Balkanic agricultural civilisation in the 6 th millennium cal BC [1][2][3][4]. However, Borič and Price [79] and Voerkelius et al. [80] have demonstrated that the Balkans correspond to a wide area characterised by considerably differing 87 Sr/ 86 Sr ratios. Consequently, almost every non-local individual could theoretically be of Balkanic origin when considering only their human dental enamel 87 Sr/ 86 Sr data. In this context, oxygen isotopes work as a more suitable indicator (Fig 4), but the potential breastfeeding-effect that influences the oxygen isotope composition of deciduous teeth and first molars prevents the identification of the place of birth of non-local individuals [68]. Nevertheless, the oxygen data of non-local Starčevo and Körös individuals (BAM8, BAM10, BAM18, BAM20, M6-1164 and BENA3) do not match the expected Balkan values and would rather indicate a northern or alpine origin [37][38][39][