Niche construction and theory of agricultural origins. Case studies in punctuated equilibrium

In contemporary archaeological and anthropological research, the domestication of plants and animals in the Near East during the Early Holocene is alternatively interpreted as an overall slow and gradual, or as a rapid process. The present reanalysis of published archaeobotanical and archaeozoological data shows that the wild-domesticate-transition (WDT) was indeed initially slow (millennial scale), but terminated at 10.2 ± 0.2 ka cal BP with an abrupt switch to herding and agriculture. The abruptness of WDT can be understood as due to amplification under positive feedback conditions (resonance) of some few biological and social factors, primarily the short and longdistance transport of domesticates, in conjunction with a synchronous, abrupt climatic switch to higher precipitation. IZVLE∞EK – Sodobne arheolo∏ke in antropolo∏ke raziskave razlagajo pojav kultiviranih rastlin in udoma≠enih ∫ivali na Bli∫njem vzhodu v ≠asu zgodnjega holocena bodisi kot po≠asen in postopen bodisi kot hiter proces. Pri≠ujo≠a ponovna analiza objavljenih arheobotani≠nih in arheozoolo∏kih podatkov ka∫e, da je bil prehod med divjimi in doma≠imi vrstami (ang. kr. WDT) sprva po≠asen (na nivoju tiso≠letij), ki pa se je kon≠al v ≠asu ok. 10.2 ± 0.2 ka cal BP z nenadnim preklopom na ∫ivinorejo in poljedelstvo. Nenadnost tega prehoda lahko razumemo kot posledico oja≠enja pri nekaterih biolo∏kih in dru∫benih dejavnikih, predvsem pri transportu udoma≠enih vrst na kratkih in dolgih razdaljah, do katerih je pri∏lo zaradi pozitivnih povratnih razmer (resonanca) skupaj z nenadno klimatsko spremembo, povezano z intenzivnimi padavinskimi obdobji.


Introduction
A central challenge to the theory of agricultural origins (TAO) concerns the integration and joint interpretation of the increasingly large amounts of numeric empirical data made available by participating scientific disciplines, for example, cultural studies, archaeobotany, archaeozoology, plant and animal genetics, radiometric dating, palaeogeography, palaeoclimatology, and others.In a recently published study, Kristen Gremillion et al. (2014) have argued that it may be possible to unify the scientific results pertaining to TAO under the umbrella of neo-Darwinian evolutionary theory.To the same topic, Kim of plants and animals, both microscopic and macroscopic, including humans (Gould, Eldredge 1977;1993;Gould 1989;Jones et al. 1994;Laland et al. 2016;Saltz et al. 2016;Zeder 2016).NCT is equally promising for applications in archaeology, for which purpose even the elementary (unpretentious) renaming of the Neolithic Package as a mobile eco-system that is capable of environmental or climatic habitattracking may help students and researchers alike to achieve a qualitatively better understanding of the complex processes underlying Neolithisation.In the long run, however, quantitative modelling of archaeological NCT appears to be necessary.

Punctuated Equilibrium (PE)
In the following, let us explore what might happen in archaeological NCT discourse if concepts derived from the neo-darwinian theory of punctuated equilibrium (Gould, Eldredge 1977;1993;Gould 2007) are taken into consideration.In contrast to classical Darwinian forecasting, the geological record shows not a slow and continuous fossil development (graduation), but instead long periods of stasis with no observable change.Then follows an abrupt switch from one species to the next (punctuation), with no apparent transition.According to Darwin's (and others'), explanation, the geological observation of a seemingly abrupt and quasi-instantaneous origination of new palaeontological species is caused by the notoriously imperfect character of the fossil record due to stratigraphic disturbance, incomplete preservation, and fragmentary research (Gould, Eldredge 1993.223).For PE theory, in contrast, the abrupt origination of species is the result neither of noisy or missing data, nor of an unobserved geographic switch in habitat, but the expected and meaningful consequence of a rapid genetic switch from one species to the next, following the law of natural selection.In a nutshell, most species originate in such brief moments of time, that expected 'transitions' have no apparent manifestation in the geological stratigraphy (Gould 2007).
But how does PE work?As indicated above, many PE related processes are (today) subsumed under what is more commonly called the Theory of Complex Systems (or similar), but I propose we continue to use the term PE.An example from physics would be coulomb excitation, whereby a subatomic particle passes so close to an atomic nucleus that the local disturbance of the electromagnetic field triggers the production of a new particle (Alder, Winther 1958).
The key word in this example is disturbance, al- Sterelny and Trevor Watkins (2015.673)propose that it would be advantageous to extend the application of niche construction theory (NCT) in archaeological research if it were extended to accommodate the more complex social worlds of human societies in the form of a cognitive-cultural (or informational) niche.Moving in the same direction, in the present paper it is suggested that a particular extension of NCT, namely Punctuated Equilibrium (Gould, Eldredge 1993), can be observed in the archaeological record for Early Neolithic plant cultivation and animal domestication, despite its high degree of 14 C-related chronological noise.
Parallel to the rapid expansion of empirical data and knowledge pertaining to the archaeological, palaeogenetic, and socioecological context of Early Neolithic plant cultivation and animal domestication in the Near East, what we observe in the archaeological theory of agricultural origins (TAO) -according to Gremillion et al. (2014) -is an increase in particularism and a major retreat from generalising anthropological theory.The authors propose that this change in research traditions may be due to the wealth of archaeological records, the very richness of which appears to "dampen the appeal of general explanations for the transition to agriculture" (Gremillion et al. 2014.6171), and which has the effect of producing an "increasingly critical attitude of archaeologists towards hypothetico-deductive science".According to the authors, this scientific disposition would lead to a proliferation of research in favour of "historical narratives that highlight local events and processes and downplay general principles" (ibid.).They propose unifying the different approaches to human agricultural origins under the umbrella of neo-Darwinian evolutionary theory (Gremillion et al. 2014.6176).
Interestingly, a similar repositioning of agricultural theory is envisioned by Sterelny and Watkins (2015), who contend that concepts underlying now widely applied biological niche construction theory (NCT) would also fit the description of the Neolithisation process, if only NCT were extended to encompass the more complex social worlds of human societies in the form of a cognitive-cultural (or informational) niche (Sterelny, Watkins 2015.673).We may abbreviate discussion of these issues by confirming directly that NCT has increasing importance in a variety of disciplines, ranging from anthropology, biology, evolutionary theory, genetics, palaeontology and biological physics, all the way through the alphabet to zoology, and thereby, naturally, for different species though other scientific disciplines might replace it by words such as amplification, bifurcation, psychological or mechanical stress, break in symmetry, genetic bottleneck, or genetic isolation.Hence, in TAO, disturbed equilibrium would be a useful alternative to punctuated equilibrium.In general terms, when a long-stable running system is disturbed, interesting things may happen, and if the change does happen, it will typically happen suddenly (e.g., particle production, formation of ice crystals, Neolithic founder crops (Heun et al. 1997;2012), Rapid Climate Change, the French Revolution, particle freeze out in cosmology, Neolithisation (this paper), switch in pottery style, North Atlantic thermohaline circulation (Rahmstorf 2002), division-by-zero, and genetic bottleneck (Lucas et al. 2012).If all disturbances were put together in a box (modelled) and compared (quantified) it is quite likely that the strongest disturbance will turn out to be: human agency.This is our first accomplished PE forecasting.

Archaeological examples of punctuated equilibrium
To continue the (now initialised) archaeological PE thought experiment we must next be unscrupulous enough to replace geological with historical timescales, whereby millions of palaeontological yearsas in the original case studies by Stephen J. Gould and Niles Eldredge (1993) -are reduced to the few generations (or less) required for prehistoric societal change, even down to the few nanoseconds needed for the molecular reactions of DNA-molecules.But as a reward, the following case studies render some first indication that punctuated equilibrium may also be identifiable in the Neolithisation process, even if initially the concept is seemingly contradictory.But there are many other archaeological studies with PE application (e.g., Kolodny et al. 2015;with references).
In contemporary Neolithisation research, the spread of farming/herding lifestyles from the Near East to Europe is most often described as a slow and continuous process, steered mainly by demographic considerations, which need focus on limitations on otherwise explosive exponential population growth, and whereby many thousands of years are considered necessary for the long-distance transfer of the new lifestyle from the Fertile Crescent through Anatolia to Central Europe.Average speeds are estimated to be in the order of 1 km/yr, with small variations, max ± 30% (e.g., Ammerman, Cavalli-Sforza 1971;Pinhasi et al. 2005).Observed deviations from such slow and gradual Neolithisation are understood to be noteworthy exceptions, which therefore require exceptional explanation.This is evident in the formulation of research questions such as "why did the expansion of the Körös-Star≠evo culture stop in the centre of the Carpathian Basin?" (Kertész, Sümegi 2001).
A further whispering of the possible existence of a very different, namely rapid, PE-type of Neolithisation is manifest in the names chosen for a number of farming dispersion models, such as leapfrog Neolithisation (Arnaud 1982), late escape (Schoop 2005), floodplain hopping (van Andel, Runnels 1995), and -most clearly -in arrhythmic dispersal (Guilaine 2001;2013).Admittedly, nomen est omen is not an entirely convincing argument.Perchance a better example would be the Neolithisation of the British Isles, which was established around 4000 cal BC, within less than 200 years (Bayliss et al. 2007;Whittle et al. 2008;Collard et al. 2010).In this case, it is the transition from the Mesolithic to the Neolithic that would appear punctuated (P), and the punctuation P is both preceded and followed by extended periods of cultural equilibrium (E); first, a long Mesolithic-E, then a long Neolithic-E, but with only a little time in between for changes in culture and economy, perhaps a few human generations.The occurrence of rapid cultural PE on the British Isles around 4000 cal BC is well-supported by vast numbers of 14 C-dates.Although rapid Neolithic demographic expansion does not only follow from the size of the 14 C-database, both are in perfect agreement with PE extension of NCT.We note with interest that the long-term success of Neolithic stasis on the British Isles has been called into question by Chris J. Stevens and Dorian Q. Fuller (2012), who postulate a failure of plant cultivation and temporary switch to pastoralism, if only based on missing data in the radiocarbon record.There is critical response by Rosie R. Bishop (2015).
Neither would the postulated overlap of European Neolithic 'cultures' based on arguments to replace the old pottery-style definitions with new 14 C-derived concepts (Manning et al. 2014), provide convincing anti-PE arguments.According to Katie Manning et al. (2014Manning et al. ( .1065)), the "...resulting [ 14 C-statistical] analysis gives a new and more accurate description of the duration and intensity of European Neolithic cultures".In my view, the opposite is the case; namely, the traditional sequence of European Neolithic cultures, with its (true) abrupt and geographically widespread, indeed often block-wise switch from one pottery style to the next (e.g., LBK -> Stichbandkeramik -> Rössen -> Michelsberg), complies entirely with PE-forecasting.Furthermore, the 14 C-overlap used by Manning et al. (2014) to motivate the introduction of a new, statistical definition of culture has little relation, if any, to any previous discourse on how to define archaeological culture (e.g., Lüning 1972).It is due to the inherent noisiness of underlying archaeological 14 C-data (e.g., Breunig 1987).This readily explains the observed, largely Gaussianshape (white noise) of calibrated summed 14 C-distributions.Indeed, the noisiness of archaeological data is so overwhelming that the calibrated distributions (Manning et al. 2014.Figs. 4-6) show little of the otherwise regularly observable distortion due to the non-linear shape of the 14 C-age calibration curve.In comparison, the punctuated peak production (basically a division-by-zero problem) that is induced by theoretically motivated but experimentally invalidated Bayesian normalisation (Weninger et al. 2011;2015) remains all the more visible in the calibrated age distributions.Together with their wide Gaussian shape, these two observations imply that the graphs show (largely) noise.What does deserve further attention is the question why the abrupt changes in Neolithic pottery style observed so often in finds are so clearly compatible with PE rules.
A much larger scale PE-NCT application is demonstrated for the spread of farming from the Near East into the Aegean along established Epipalaeothic coastal networks in the eastern Mediterranean (cf.Çilingiroglu 2010;Reingruber 2011;Brami, Heyd 2011;Horejs et al. 2015).The radiocarbon dates indicate a simultaneous (decadel-scale) Neolithisation of the Turkish west coast and of the Peloponnese, which my colleague Lee Clare and I have attributed to climatic habitat-tracking due to widespread cold winter Rapid Climate Change (RCC) conditions, with a similar incentive presumably underlying the long-distance movement from the Near East along the Turkish south coast into the Aegean (Weninger et al. 2014;Clare, Weninger 2014;2016;Clare 2016).Recently, bio-climatically optimised choice of landscapes by Neolithic farming communities is also reported for the Balkans, both for the start and end of the RCC-synchronous Neolithisation of the circum-Aegean landscapes (8.6-8.0 ka cal BP), and this we may consider evidence of Neolithic climatic engineering, in any case of careful (simultaneous) ecological and cultural niche selection (Krauß et al. 2014;2017).High dispersion speeds are also reported for the land-based spread of farming out of the Aegean into the Pannonian Basin (Weninger et al. 2014), as well as for coa-stal movements in the Western Mediterranean (Isern et al. 2017) as far as Morocco (Linstädter et al. 2012;2016).Again, it is primarily the timing of these transitions that indicate PE-type Neolithisation.Conversely, beyond confirming PE-type Neolithisation, these findings immediately challenge the conclusion of Neus Isern et al. (2017.897),that speeds of ~2500km in 300yrs can be achieved only by sea travel, and not overland.This perception clearly relies on the validity of slow and continuous wave-of-advance-type dispersion, such that (slow) overland routes would be the predictable norm and (fast) sea travel the specific exception.Neolithic wave-of-advance dispersion is clearly at odds with PE-type modelling, for which both routes are equally fast.Hence, although yet further confirmation of the quite astonishing speeds of Neolithic dispersion would be welcome, these examples demonstrate the potential of PE-forecasting.In general terms, from the viewpoint of NCT, we may expect only a few exceptions from the otherwise general rule that, to be successful (in a Darwinian sense), major changes in both economic and cultural resources should be as rapid as possible.Now turning to the theory of agricultural origins (TAO), it would follow from PE that the time required for the Near-Eastern transition from wild to domesticated (plants and animals) is likely to be short (i.e.punctuated), and unlikely to be extended (i.e.protracted).What complicates matters is the large number of participating units (cereals, legumes, sheep, goat, cattle, humans etc.), as they are intricately interconnected within a complex eco-system (e.g., Gopher et al. 2001;Jones et al. 1994;Laland et al. 2016).Nevertheless, based on observed complexity alone, we should not automatically concede that the WDT was necessarily protracted (e.g., Purugganan, Fuller 2011;Fuller et al. 2012;Maeda et al. 2016; cf.significant critique by Heun et al. 2012).An open question is, do we really observe the postulated protracted adaptation of domesticated plants and animals?Namely, given that corresponding timescales are essentially all based on 14 C-data, and knowing of the extreme noisiness of such data, we might instead become immediately (very) suspicious as to the quality of the observations.Some large (but difficult to isolate) part of the observed slowness in the archaeological record is surely to be caused by the artificial spread of 14 C-data, e.g., due to stratigraphic disturbance, sample contamination, chance statistical reasons, age-distortion due to the non-commutative character of the calibration curve etc. Strictly speaking, with much of the 14 C-data under study now half a century old, we would like to disregard the data altogether.At first glance, the best procedure to separate the signal from the noise would indeed be to apply some strong taphonomic and statistical filter to the 14 C-data.This was the analytical method applied to the 14 C-data by Pascal Flohr et al. (2015) in search of the potential impact of the 8.2 and 9.2 ka cal BP cold winter climatic events on the Near Eastern Neolithic.Unfortunately, and as Flohr et al. (2015) correctly observe, even the strongest filtering of available 14 C-data does not itself provide a straightforward 'yes/no' answer to the research question in hand, concerning potential social climate impact.It is also unfortunate that the postulated social resilience to climate change does not even theoretically follow from its non-identification (Flohr et al. 2015).A more promising approach lies in dedicated climate-archaeological fieldwork (e.g., Zielhofer et al. 2012).
In the following, we continue our previous WDTstudies with subordinate further consideration of the available 14 C-data, which have already undergone sufficient analysis (e.g., Weninger et al. 2009;Asouti, Fuller 2013;Borrell et al. 2015).Instead, let us have a fresh look at the remarkable coincidence of the WDT with the previously identified major increase in precipitation levels in large parts of the Near East at around 10.2 ka cal BP.This is now possible in the context of newly available climate records, particularly, the Lake Neor Titanium (dust) record (Sharafi et al. 2015).As previously noted (Weninger et al. 2009), within dating errors of approx.±100yrs (68%), the earliest use of genetically changed cereals coincides perfectly with both an abrupt 50-metre rise in Dead Sea levels, as well as the onset of Sapropel S1.On the archaeobotanical side, the synchronism is based on cereal data from a reasonable number of archaeological sites (N = 44), with cereal inventories classified as 'wild' (N = 8), 'domesticated' (N = 31) and 'unclear' (N = 5) by Mark Nesbitt (2002).In the meantime, and based on significantly extended archaeobotanical and 14 C-radiometric datasets, Eleni Asouti and Dorian Q. Fuller (2013) have come to an entirely different conclusion, which is that the transition from the use of wild to domesticated plants was an extended (protracted) process, with a time-span in the order of thousands of years.This is curious, since statistical theory would normally predict a shortening of any time-span based on a refined set of 14 C-data, and not a lengthening (and least not by a factor ~10 according to Asouti, Fuller 2013in comparison to Nesbitt 2002and Weninger et al. 2009).

Methods and data
We will return below to the arguments supporting rapid (decadel-scale) WDT versus slow and gradual (millenial scale) development.To run this comparison required the expansion of available CalPal-software, and in particular the development of a new CalPal-dialog (called Multiclimate Composer), as described in detail in the Appendix, available online at http://dx.doi.org/10.4312/dp.44.1.

Results
Utilising for the first time the new CalPal Multiclimate Composer, Figure 1 and Figure 2 provide a graphic representation of published archaeobotanical (here: barley), archaeozoological (here: cattle) and climatic data (selected regions).In my view, although non-expert in the analysis of archaeobiological data, the records would support the statements listed below (Points 1-8).Note that these results are based on (further) critical interpretation of the large amounts of archaeological 14 C-data that were already critically assembled and statistically analysed by the authors of the respective botanical and zoological data (Asouti, Fuller 2013;Arbuckle et al. 2016).Additionally, I am applying here an extended mode of record interpretation, whereby it is deemed necessary to read the given (68% confidence) chronological time-spans of the archaeological settlements in a specific manner: (A) The time-spans provided for sites that contain domesticated cereals (here exemplified for domesticated barley) are interpreted as termini post quem for the earliest use of cereals.Hence, in Figure 1C, the true dates for the introduction of domesticated barley must range on the left (older) side of the (blue) set of site intervals.
(B) The time-spans provided for sites that contain wild cereals (here exemplified for wild barley) are interpreted as termini ante quem for the earliest (possible) use of domesticated cereals.Hence, in Figure 1E, the true dates for the introduction of domesticated barley must range on the right (younger) side of the (green) set of site intervals.
(C) The time-spans provided for sites that contain 'partially domesticated' cereals (here exemplified for barley) are indecisive in terms of further refining the already given age and length of the WDT (Weninger et al. 2009-using data of Nesbitt 2002).The archaeobotanical refinement by Asouti and Fuller (2013) of introducing 'partially domesticated' cereals is  nonetheless helpful in identifying promising archaeological sites for further studies.

Fig. 2. Selection of climatic records and comparison with LSI (Logarithmic size indices) for cattle bone from Early Holocene archaeological sites; graph drawn with CalPal Multiclimate Dialog (Fig. 5) and edited with Adobe Illustrator©. A Greenland GISP2 ice-core stable oxygen isotopes δ δ 18 O (Grootes et al. 1993) shown to illustrate the long timespan (i.e. stasis) between Younger Dryas (end ~11.6 ka cal BP) and WDtransition at 10.2 ± 0.2 ka cal BP (vertical line); B Dead Sea Lake
Accepting that available 14 C-data are mostly too imprecise to support further modelling, in reward, we gain freedom in our ability to make generalising statements about the theory of agricultural origins, as advised by Gremillion et al. (2014).In the present paper, these generalising statements are as follows: ❶ The introduction of domesticated cereals in the Near East was a rapid and abrupt process for which a maximum time-span of ~1000yrs (p = 95%) is presently recognisable in the 14 C-data.Due to the wellknown highly distributive properties of historical 14 C-data, the process itself is likely to be significantly shorter, in the order of 20-30 years (max.200 years) as experimentally demonstrated for wild wheat and barley (Hillman, Davies 1990).Since the precise date and time-span of the WDT remain unknown, and also to emphasise their derivation from punctuated equilbrium (i.e.utiliding a specific theory of evolution), in the following we use the term 'punctuated' to denote a value of 0-200 years.
❸ The punctuated transition from wild to domesticated animals occurred at 10.2 ± 0.2 ka cal BP (cattle: Fig. 2; other species cf.data in Arbuckle et al. 2016).
❹ Following an extended period of cultural and biological stasis during and following the Younger Dryas (Bar-Yosef 1989;1998;Haldorsen 2011), the WDT is coincident with a major climatic switch to higher levels of precipitation (winter rain).This quite remarkable climatic background to the WDT is observable as a sharp transition to higher levels of precipitation around 10.2 ± 0.2 ka cal BP in a large number of terrestrial records, including Lake Neor (Iran), Aammiq (Lebanon), at high resolution (U/Th) in Jeita Cave (Lebanon), as well as in many Eastern Mediterranean marine records (Schmiedl et al. 2010).
❺ The age-value of 10.2 ± 0.2 ka cal BP common to these archaeobiological and climatic events and processes is itself synchonous (within given dating limits) with earliest farming communities in Central Anatolia, such as at Asikli Hüyük (Stiner et al. 2014), as well as in Iran, in particular at Ganj Dareh (Zeder, Hesse 2000).Additional evidence of a punctuated beginning of farming/herding at around 10.2 ± 0.2 ka in Iran can be seen in the remarkable increase in the number of radiocarbon dates that are classified as 'Neolithic' in the CalPal-database (cf.Appendix, available online at http://dx.doi.org/10.4312/dp.44.1).The temporal development of Iranian Neolithic 14 Cdata runs closely parallel with Sapropel S1 as well as with the dust record from Lake Neor (Fig. 5, lowest record), for reasons yet to be deciphered.The Iran/Neolithic 14 C-data (N = 362) is imported here with no filter applied from the CalPal 14 C-database.The 14 C-data in the database of Flohr et al. (2015) shows essentially the same structure, with or without filtering (e.g., long/short-lived samples, high/low measuring precision, modern/old excavations etc.).This motivates further hydroclimatic-archaeological studies of the Iranian Neolithic, but is not our immediate topic.
In conclusion, the system disturbance necessary to understand PE-type Neolithisation is presumably to be found in (A) the self-pollinating properties of the Near Eastern founder cereals.This property makes the movement of domesticated plants beyond ~50m dependent on human agency (Honne, Heun 2011;Heun et al. 2012), and/or (B) in genetic isolation of mixed W/D-cereals due to the colonisation of Cyprus and (amplifying) back-transport of domesticated cereals to the mainland (Lucas et al. 2012), and/or (C) abrupt changes in precipitation that occurred around 10.2 ± 0.2 ka cal BP (Fig. 1); and/or (D) the occurrence of a brief (decadel-scale) cold-winter RCCextreme event at around 10.2 ± 0.2 ka calBP (Bar-Yosef 1986;Weninger et al. 2009;Borrell et al. 2015), but with presumably a different impact in the northern and southern Levant (Cheng et al. 2015), and/or (E) the major geographic dispersal of the Neolithic at around 10.2 ± 0.2 ka calBP into Central Anatolia and Iran that would itself have presumably caused the (further) genetic isolation of WD-transitional plants and animals (cf.Brandolini et al. 2016); as well as, most importantly, (F) short-and long-distance exchange/trade in domesticates, as proposed by Heun et al. 2012), and finally, (G) an amplifying combination of factors (A-F).

Outlook for quantitative modelling
My personal preference for modelling the WDT is (G): the PE auto-amplification description.This is because, if confirmed, any attempted larger-scale mathematical study would presumably have a good start already by application of the well-known and widely applicable harmonic resonance equations (for different frequencies and dampening).In agreement with proposals by Sterelny and Watkins (2015), surely the most important causal parameter in the rapid WDT is human agency, which could be modelled as a central driving factor acting under resonance conditions within a wider network of natural (bioclimatic) processes.The factors leading to WD-resonance might have to be attenuated (dampened) to some extent, e.g., to allow for continued human selection of wild cereals during and followed the WDT.This would introduce an additional temporal spread of the rapid transition, yet to be quantified (presumably multi-decadel scale), on top of the (conservative) 200-year estimate by Gordon C. Hillman and M. Stuart Davies (1990), but even then the width of transition would be well-covered by the statistical interval of ± 0.2 ka (68%), i.e. length 1000 years (>95%) as shown (graphically) in Fig. 1 for the WDT.Presumably, there exist other cultural and biological niche-related phenomena yet to be discovered that show resonance amplification.I could also imagine that the application of resonance equations would be an interesting alternative to the use of stepwise truncated exponential or logistic growth functions in archaeological (or other) applications of punctuated equilibrium, but this surely depends very much on application (e.g., Kolodny et al. 2015).

Conclusions
In this paper the suggestion is made that Punctuated Equilibrium (Gould, Eldredge 1993) can be observed in the archaeological and archaeobiological record for the Early Holocene WDT in the Near East, despite its high degree of chronological noise.This idea is derived from a combined graphic visualisation of large quantities of palaeobiological, climatological, and archaeological data.From the viewpoint of Nonlinear System Theory, it appears possible to describe (as well as understand) the extreme rapidity of the WDT as due to amplification with positive feedback for a small number of reasonably explicit causal factors.With such an approach, it might be possible to decide whether the WDT-transition follows deterministic (strictly forecastable) or chaotic (non-predictable) laws.A more general application of PE-type Neolithisation in the Theory of Agricultural Origins is indicated by case studies relating to later phases of Neolithic Dispersion.
My special thanks go to Harvey Weiss, who made me aware, as so often, of fascinating research I would have otherwise presumably not encountered, in this case by Stephen Jay Gould and Niles Eldredge.