The Economic and Ecological Impact of Dairy Production in Alpine Prehistory: A Numerical Approach

1. Introduction

Cheese is a crucial element of the cultural identity of the Alps, and it represents one of the most valuable industries in the region (Grasseni 2011). The centrality of dairy products for Alpine communities has historical roots. The distinctive climate of the Alps (warm, dry summers and cold winters) and the ruggedness of the mountain landscapes limit the productivity of crop farming, while encouraging animal husbandry. The integration of agriculture and seasonal pastoralism in the Alps is known as ‘Alpine farming’ (Alpwirtschaft), and has analogues in other temperate mountain regions of Europe. The prominence of cheese making within this economic system has increased over the last few centuries, turning summer dairying and herders’ huts into symbols of Alpine rurality (Mathieu 2009). However, new archaeological evidence suggests that dairy produce might be associated with the evolution of farming economy in the Alps since Prehistory (Gilck & Poschlod 2019). Chemical analysis of pottery from upland archaeological sites in the Swiss Alps provided direct evidence of milk processing at high altitude during the Late Bronze Age, revealing a possible prehistoric origin of Alpwirtschaft (Carrer et al. 2016). Dry stone enclosures found in different upland areas of the Alps, dated to the Bronze Age, indicate a transformation of pastoral strategies in this period, possibly connected with the origin of summer dairying (Reitmaier, Carrer & Walsh 2021). The recent discovery of sophisticated ovens within a Bronze Age hut in the uplands of South Tyrol (Italian Alps) has been interpreted as strong evidence of large-scale cheese production (Putzer 2024). The intensification of pastoral occupation of the uplands during the 2^nd millennium BCE could imply an incipient dairy specialisation of Alpine societies in this phase, which suggests a change in the economic role of dairy products.

Although milk processing has been documented in the Alps since the Neolithic period (Spangenberg, Jacomet & Schibler 2006), there is general agreement among archaeologists that its relevance increases throughout the Bronze Age and during the Iron Age. A functional relationship between ore mining and dairy pastoralism, justified by the subsistence needs of miners and by the contiguity of mining sites and upland pastures, has been tentatively suggested (Pearce 2016). Robust support to this theory has recently been provided by biochemical analysis of human coprolites from the salt mine of Hallstatt (Austria), which showed that the diet of Iron-Age miners included blue cheese (Maixner et al. 2021). It is worth mentioning that only one coprolite revealed the presence of cheese fungus proteins, suggesting that cheese, albeit consumed, was not the staple food of the miners. This cheese was likely produced in the upland pastures of the Dachstein plateau (located in close proximity to the mining site), where archaeological research revealed an intensive pastoral occupation throughout the 2^nd and 1^st millennium BCE (Mandl 2009). This new data seems to indicate that the development of the mining industry went hand-in-hand with the specialisation of the dairy economy, between the Bronze and the Iron Age. But the importance of late-prehistoric dairy is not limited to the extraction of salt and ore. It is known from ancient literature that Alpine cheeses were a recognised delicacy during the Roman period and were exported from the Alps across the Empire (Segard 2009). These were, for the most part, hard cheeses, matured in dry and cold cellars, whose long preservation was essential for transportation and storage. It is quite likely that the roots of these Alpine cheeses are to be found in the late-prehistoric traditions discussed above. The development of the know-how required to produce durable dairy products (hard cheese) would have transformed cheese from an integral component of the local diet into a storable commodity, with significant implications for both subsistence and trade (Reitmaier & Möckli 2015) It can be argued that, between the Bronze and the Iron Age, cheese must have acquired a prominent role in the economic system of rural Alpine communities, which it retained and expanded during the Roman period, taking advantage of the new commercial opportunities provided by the vast internal market and contracts with the imperial army.

The intensification of archaeological research in the Alps is providing useful clues for understanding how significant cheese was for the subsistence and economic development of mountain communities during the 1^st and 2^nd millennia BCE. However, most of the inferences produced by archaeologists to date are based on informal comparisons with the ethnographic record and fail to establish a causal link between dairy specialisation and economic growth. Novel and rigorous approaches are required to test the contrasting hypotheses deriving from incomplete and biased archaeological evidence. A non-negligible contribution to the interpretation of the information currently in hand can be provided by computer modelling. In computer modelling, inferences and assumptions can be formally tested to investigate their consistency and verify if their theoretical foundations hold. Alternative scenarios (produced by weighting different model parameters) can be simulated to assess how variable starting conditions influence the development of the system and how each model output matches available data. Computer models have an enormous heuristic potential in archaeology, especially in the analysis of complex adaptive systems, like ancient economies and human-environment interactions (Brughmans & Wilson 2022; Robinson et al 2018).

In this paper, a mathematical model simulating alternative strategies of food production and land exploitation will be used to infer the consequences of dairy specialisation in a late-prehistoric rural community of the Alps. Although the main aim is to highlight the influence of the dairy economy on human subsistence and livelihood, the model will also assess the ecological impact of human activities, which is a big factor in the vulnerable mountain ecosystems of the region. More explicitly, this model addresses two key research questions: Does dairy specialisation increase the average product of labour in a small-scale prehistoric society of the Alps? Does dairy specialisation reduce the pressure of this small-scale prehistoric society on mountain environments? The labour efficiency and the amount of land dedicated to agriculture and pastoralism will be compared across subsistence scenarios with different proportions of crop and livestock farming and different reliance on dairy produce. A static equation-based model has been preferred to a more flexible and sophisticated computational simulation (see Lake 2014) for two main reasons: (1) The numerical approach is deemed more appropriate for the identification of basic functioning principles of prehistoric economy; (2) For the purpose of this study, the temporal dimension of the system and the decision-making strategies of the agents are not relevant. An agent-based approach could provide complementary insights to this research, and it will be the focus of a future study.

2. Methods

The methodology proposed in this paper is based on the equation-based model developed by Shukurov et al. (2015) to investigate the economy and subsistence of Late-Neolithic proto-urban communities in Ukraine. This model was then adapted by Carrer et al. (2020) to be applied to historical small-scale societies of the Alps. The original model had a single catchment area centred on the village, with crop, pasture and fodder areas distributed in annular zones at different distances from the village. The verticality of mountain ecosystems and the seasonal exploitation of the uplands required a profound revision of this spatial framework. The Alpine model combines an agricultural catchment around the village and a pastoral catchment, which includes mid-mountain meadows and upland pastures. The pastoral catchment is exploited for a fraction of the year (during the warm months), and it is not spatially contiguous to the agricultural catchment.

The model used for this publication is a revised and re-parametrised version of the dual catchment model (Figure 1). It represents a mathematical formalisation of the subsistence economy of a late-prehistoric community in the Alps. The key parameters used to investigate the subsistence system are the calories required to carry out the farming tasks and the calories provided by the farming products. For the sake of simplicity, the model disregards the effort of moving between and within agricultural and pastoral catchments, it ignores the calorie expenditure of those tasks not directly related to food production, and it does not consider additional resources acquired through trading and exchange. As the focus is on self-sustaining agricultural and pastoral practices, surplus in production is used to assess the overall performance of the system. Although research on subsistence strategies in the Alps during the Bronze Age has increased in the last few decades (Jacquat & Della Casa 2018; Schmidt & Oeggl 2005), very little is known about the economic structure of these productive systems. For example, the relative importance of crop farming and animal husbandry is still debated, as it is the role of dairy production, which is the main focus of this paper. To incorporate this uncertainty into the model, four alternative economic scenarios were produced:

• Scenario 1. In this scenario, 66% of the calories required by each member of the community are provided by agriculture (cereal and pulses), 26% are provided by pastoral products (meat and dairy), and 6% by wild animal products. This corresponds to the standard European prehistoric subsistence as approximated by other authors (Gregg 1988). Additional food products would be wild plants, nuts and fruits, but considering the low number of calories available in these products, their contribution to the diet was estimated around 2%, as a higher contribution would require an unrealistic amount of fruit and nuts. Dairy production is not maximised, and only the surplus of milk available after lactation is exploited.

• Scenario 2. The breakdown of calorie intake is the same as in Model 1 (66%, 26%, 6%, 2%), the only difference is that in this scenario more attention is given to dairy production. Through shorter weaning periods and selective culling of juvenile animals, the herders manage to maximise the amount of milk used for human consumption and dairy production, with consequences on herd/flock composition, labour redistribution, etc.

• Scenario 3. Agriculture and animal husbandry equally contribute to the overall calorie intake (46% each), complemented by game hunting (6%) and fruit/nuts gathering (2%). Pastoralism is specialised, with a high relevance of dairy produce (like in Model 2).

• Scenario 4. This scenario, instead, is primarily focused on agricultural production, which provides 80% of the calories for the community. Animal husbandry accounts for 12% of the calorie intake, whereas hunting and gathering are marginal, like in the other models (6% and 2%). Like in Model 1, the dairy economy exclusively exploits excess milk after lactation.

Figure 1

The first two scenarios represent two versions of the same economic system, where the main source of calories is crop farming while animal husbandry provides a significant contribution as well. The different emphasis on milk exploitation will reveal how important dairy products were for this system. The third and fourth scenarios will show what happens if the role of dairy pastoralism is enhanced or if agriculture becomes predominant. The equations defining the structure of the numerical model are provided in S1, and details and justification of the parameters used for each scenario are provided in S2. For each scenario, a population of 160 people distributed in 20 families (an average of 8 people per family, including elders and children) was estimated. These figures are tentative, based on comparable studies carried out elsewhere in the Alpine region (Reitmaier & Kruse 2019), and are primarily used to have a common realistic baseline for all the different scenarios. The scalability of the model ensures that adjustments of the population size (see Mathieu 2023; Wingenfelder 2024) would not affect the inferences drawn from the model outcomes. The outputs produced by the model for each scenario can be grouped into three main categories: the surface used for farming activities, the annual farming produce, and the labour required for each task. As outlined in the introduction, particular emphasis will be placed on comparing grazing and farming land surface (Outputs 1 to 5 in Table 1) and labour return (Output 24 in Table 1) across the four modelled scenarios. The former is a function of baseline livestock numbers and their fodder demand, of cereal/pulse yields per hectare (influenced by manuring intensity, which in turn depends on livestock numbers) and of the fallow system implemented by the agropastoral community. The latter represents the ratio of the total number of working days in a year (250) to the average number of days per adult dedicated to agropastoral labour. More details on these and other parameters can be found in S1.

The model was implemented using the R programming language. Parameters and equations were stored in separate scripts and sourced together via a third script. The code was used to simulate the four scenarios described above and to run sensitivity analysis for selected parameters. The R project is available on GitHub for full reproducibility (github.com/francescokar/PastMath).

3. Results

Table 1 presents the results of the equations described in S1 for each scenario, approximated to the second decimal digit.

The first part of the table focuses on land use. Row 1 returns the surface (in hectares) of cultivated fields (crops, legumes and other plants), whereas row 2 returns the surface of the fallow, the arable surface not cultivated to enable soil nutrients recovery. Rows 3, 4 and 5 return, respectively, the surface of grazing areas around the village, in intermediate areas and in the uplands. As explained before, these grazing areas are exploited in different periods of the year. Row 6 shows what fraction of fallow area around the village is used during the winter for animal grazing. The value of this output depends on the fallow area surface (row 2) and the grazing area required during the winter (row 3). Rows 7 and 8 correspond to the surface around the village and in intermediate grazing areas, necessary to produce fodder for livestock stabling during the winter. These values are used in rows 9 and 10 to estimate the fraction of fallow and intermediate grazing areas required for producing winter fodder for livestock.

Productivity and labour are addressed in the second part of the table. The timescale corresponds to a calendar year. Row 11 returns the yield of crops (mainly cereals and legumes) in kilograms per hectare. Since crop productivity is proportional to the availability of manure, row 12 reports the fraction of the field that can be manured, according to the number of animals and their grazing period around the village. Row 13–15 return the number of cattle, sheep and goats (considered as the same livestock category) and pigs. The following rows return the estimated time (person-day) for ploughing (row 16), cereal reaping and threshing (row 17), grass cutting for fodder (row 18), sheep shearing (row 19), milking (row 20) and cheese making (row 21). The bulk production of wool (row 22) and cheese (row 23) are included as well. Labour values depend on the land surface and on the number of available domesticates and are distributed equally among the adult population of the village. Row 24 estimates the labour return (in working days): the higher the number, the higher the ‘return’, the higher the efficiency of the economic system (i.e. the calories produced exceed the calories spent in production).

3.1 Sensitivity Tests

As pointed out above, some of the parameters used in the four scenarios have been tentatively approximated. To assess how parameter uncertainty influences the reliability of the model, sensitivity tests were performed by adjusting parameter values and observing changes in key model outputs. Particular attention was paid to parameters and outputs associated with the ecological and economic role of pastoral practices and dairy produce. These sensitivity tests, besides evaluating the robustness of the model, provide an important contribution to the interpretation of the role of cheese-making in Alpine Prehistory. Scenario 2 was chosen as a reference scenario for the tests, as it includes relevant parameters for both crop and animal farming. Full justification for the numerical ranges used in the tests can be found in the S2.

The usable meat weight per cattle was estimated at 200 kg in Scenario 2. According to ethnographic information, any meat weight between 100 and 550 kg could have been possible, with central values (150–300 kg) more realistic. Goat and sheep usable meat was averaged to 23 kg in Scenario 2, but it can span from a minimum of 10 kg to a maximum (probably overestimated) of 55 kg. Weight variation influences milk yield and fodder intake. Fodder requirement per head of cattle corresponds to 2.25% of their body mass, and 4% for sheep and goats. Considering a production of 2000 kg of dry matter per hectare and 304 days of grazing, the grazing surface per animal per year can be easily calibrated for different animal weights. There is no clear association between body mass and milk production, but based on ethnographic analogues, it was estimated that the amount of milk produced by traditional cows, goats or sheep tends to increase with their weight. On the other hand, if a proportional increase in the weight of the newborn is also assumed, the amount of milk used for lactation is expected to increase as well, since the milk consumed by calves, kids and lambs is a function of their body weight. To account for this variability and uncertainty, 100 random values were drawn from a normal distribution centred around a mean milk production value that increases linearly with animal weight (with standard deviation increasing at a similar rate). Based on the values in Scenario 2, the mean milk production (in litres) was estimated to be 2.5 times the live weight of cattle and 3 times the live weight of sheep/goats (the live weight is estimated here as twice the mass of usable meat). The amount of milk used for lactation, which also increases with animal weight, was then subtracted from the milk production value to estimate the milk surplus available for dairy production. This simulation was repeated for each value of animal weight, and an average milk yield was calculated for each simulation (Figure 2). Two different tests were run to investigate the influence of animal weight on model parameters. In the first test, body mass and fodder requirements were proportionally adjusted while milk yields were kept constant. In the second test, milk yields were also adjusted using the stochastic approach described above.

Figure 2

Figure 3 shows the effect of the variation of cattle and caprine weight on the size of the crop farming area and on the surface of upland pastures. If the milk yields are held constant, there is a negligible change in the crop farming area, but the result is different when milk yields are adjusted to animal weight. Higher milk yields reduce the number of animals necessary to sustain the community, as a larger proportion of the calories provided by animal farming comes from dairy products rather than meat. This, on the other hand, leads to a decrease in manure available for crop farming and a decline in soil fertility, which forces the community to expand its farmland. Nevertheless, the variability in the crop farming area is still modest, less than 1 hectare if we consider cattle weight (less than 0.5 hectare for sheep/goat weight). More interesting are the results for upland pastures. An increase in animal weight without a proportional increase in milk yields leads to a steep increment in the grazing surface required for bovines and caprines. This is expected, as fodder consumption is linearly dependent on animal weight. However, if milk yield is modelled as a function of animal weight, there is a significant contraction of the upland grazing area. As pointed out before, a higher milk yield leads to lower livestock numbers, which in turn results in a reduced pressure on upland pastures. Unlike the crop farming area, the range of variability in the surface of the upland grazing area is very significant (from 81 to 26 hectares considering cattle weight).

Figure 3

These initial tests suggest that milk production had a decisive influence on prehistoric land use. Milk production in cattle, sheep and goats can also vary independently from their body mass, as different breeds can have different milk yields. In order to incorporate this factor into the modelling framework, a range of milk production between 300 and 2000 L for cattle and between 50 and 350 L for sheep and goats was used for sensitivity tests. In this case, the weight of the animals was held constant, as it was the amount of milk used during lactation. This means that the surplus of milk available for cheese making increases with the animals’ milk productivity. The ranges of milk production used in these tests match those previously derived from animal weight, to facilitate the comparison of the results. Figure 4 indicates that milk yield alone explains all the land use variability observed in the previous tests. In particular, adjusting milk yield without changing animal weight leads to a much higher variability in the upland grazing area than the covariation of animal weight and milk yield. Milk surplus available after lactation is a much better predictor of farmland and pasture surface than the size of cattle, sheep and goats.

Figure 4

Another parameter that can have a significant impact on grazing areas is the productivity of meadows and pastures. Based on studies carried out in different parts of the Alps, an average value of 2000 kg of dry matter per hectare was used. However, these studies suggest that a great production variability, determined by local morphology, soil and micro-environmental conditions, should be assumed. The whole range found in the literature, from 500 to 5000 kg of dry matter per hectare, was evaluated in a sensitivity test, and its influence on upland grazing area was compared with the influence of milk yield (Figure 5). Unsurprisingly, fodder productivity turns out to be the most important parameter for estimating the scale of pastoral land use.

Figure 5

These tests show that a reliable estimation of fodder productivity and milk yield (especially for cattle) is essential to produce accurate models of prehistoric land use. The correlation of animal weight with milk yield, and their combined effects on the investigated socioecological system, suggests that a greater relevance of dairy products in the Bronze Age economy might have led Alpine communities to switch to larger cattle breeds. Dairy specialisation could then explain the different sizes of cattle in the Bronze and Iron Age of the Alps (Riedel & Tecchiati 2001). These speculative inferences require zooarchaeological validations that are beyond the scope of this paper, yet they provide interesting research questions that will be addressed in future studies. On the other hand, the importance of milk surplus (after lactation) emerges quite clearly from the tests, emphasising once again the primary role that dairy specialisation has for small-scale societies in mountain regions.

Another parameter that was tentatively estimated in the model is the fraction of the village employed in pastoral activities. Ethnographic analogues (Corti 2004; Šebesta 1991) do not provide decisive indications, as in some areas of the Alps a small number of villagers (or external labourers) were looking after the entire livestock of the village, whereas in others each family was taking care of their own animals. Since the time dedicated to pastoral activities influences labour return, it is possible to investigate how the percentage of people involved in pastoralism directly affects this value. Figure 6 (left) shows a steep increase in labour return as the fraction of the village involved in pastoral practices increases from 0 to around 20%; then the value flattens out, and it reaches 14 days with 100% of the population involved. This diminishing marginal return (see Dow & Reed 2023) is probably associated with the relatively high labour costs of pastoral tasks (see Table 1). It can be argued that the proportion of adults engaged in pastoral tasks was unlikely to exceed 20% of the total population, as a higher percentage would not significantly improve productivity. And this is particularly true for a community with a specialised dairy economy, like the one modelled in Scenario 2. Figure 6 (right) indicates that cheese making is by far the most time-consuming of the pastoral tasks, and that the number of working days dedicated to shearing and milking is very low even when a small proportion of the population is involved. In Figure 6 (left), the time required to produce 1 kg of cheese (which was tentatively gauged in Scenario 2 based on modern analogues) is plotted against labour return, showing a declining labour return as the production time increases. If cheese was economically important for prehistoric communities in the Alps, cheese making was also the main driver of diminishing marginal returns in pastoralism, and perhaps the reason why the dairy economy was integrated into an economic system largely based on crop farming. These tests confirm that the low proportion of people engaging in pastoral tasks estimated for Scenario 2 (10%) is realistic, but they also suggest that a more accurate estimation of cheese production time is required for a reliable approximation of labour return.

Figure 6

4. Discussion

The model returns the minimum amount of land required to sustain the community (160 people) and the time necessary to complete the key tasks of crop and animal farming for each economic scenario. These insights reveal which subsistence strategy can be considered the most sustainable in terms of land use and the most efficient in terms of labour. Number of animals and land productivity, available in Table 1, will not be discussed below: they are treated as numerical parameters that influence land use and labour, and therefore useful to display in the output lists but redundant for the discussion.

4.1 Land use

Unsurprisingly, Scenarios 1 and 2 show a similar cultivated area of approximately 50 ha. This is because the subsistence system formalised in the two scenarios relies primarily on crops. Scenario 3, where crops and animal products have the same importance, returns the smallest arable surface (35 ha), and Scenario 4, where crop farming is prominent, provides the largest arable surface (61 ha).

The most interesting differences can be observed in the grazing areas: winter grazing near the village, spring and autumn grazing in intermediate zones, and upland grazing during the summer. The total grazing surface in Scenario 1 is 256 ha, and it is half (125 ha) for Scenario 2. Considering that these two scenarios are structured around fairly similar subsistence strategies, the result seems surprising. But the main difference between Scenarios 1 and 2 is the importance of dairy produce, which is much higher in Scenario 2. Scenario 2 relies more on cattle, goat and sheep milk than on their meat, therefore fewer livestock is needed to feed the community, exactly half of Scenario 1: approximately 300 animals (bovine + caprine) in Scenario 1, 150 in Scenario 2. The grazing surface of Scenario 4, where pastoralism is marginal, is closer to Scenario 2 than Scenario 1 (97 ha), and the results of Scenario 3, where pastoralism and agriculture are balanced (but dairy production is important), are closer to Scenario 1 (207 ha). Obviously, as the contribution of pastoralism to the diet increases, the grazing surface increases. However, if the contribution of pastoralism to the diet increases together with the importance of cheese-making, the number of bovines and caprines is restricted and the expansion of the grazing areas is relatively modest. Another interesting aspect related to animal husbandry is the fraction of fallow area required for winter grazing. The fallow of Scenario 1 is barely enough to meet the requirements (95%), whereas less than half of the fallow is used in Scenario 2 (47%). This is additional evidence to support the higher efficiency of pastoralism in Scenario 2. Interestingly, 116% of fallow in Scenario 3 is necessary to graze the livestock during the winter, suggesting that Scenario 3, with pastoralism and agriculture equally contributing to the diet, is not balanced and, therefore, it might not be an economically sustainable strategy.

As expected, fodder production follows the same pattern as the grazing areas. 35 ha of meadows are required for producing winter fodder in Scenario 1 and Scenario 3, only 19 ha (nearly half) in Scenario 2, and 15 ha in Scenario 4. The fraction of fallow areas required to produce fodder is again comparable in Scenarios 1 and 3 (15% and 19% respectively), as well as in Scenarios 2 and 4 (7% and 5% respectively). As the intermediate grazing areas and fodder requirements are influenced by the same parameters in the equations, they are very similar in all the scenarios (and identical in Scenarios 1–2 and Scenarios 3–4).

Figure 7 (left) represents the correlation between cultivated land and upland grazing area for each scenario. Linear regression (dotted line in the plot) indicates a hypothetical trend from a purely pastoral (0 ha cereal area) to a purely agricultural (0 ha upland grazing area) economy. Unsurprisingly, Scenarios 3 and 4 are located respectively on the upper-left and lower-right sectors of the plot. Scenarios 1 and 2, despite their similarities, are quite far apart in the plot: the former is on the pastoral sector, not far from Scenario 3 (but with a much larger cereal area), the latter is on the agricultural sector, close to Scenario 4. Dairy specialisation enables a subsistence system focused on agriculture and animal farming to decrease its reliance on upland pastures without significantly increasing its farmland requirements.

Figure 7

If we combine the surface area of cultivated land and all grazing areas (village, intermediate and upland: see Table 1) for each scenario, we obtain the total surface required by each simulated subsistence system to produce enough food to sustain the local community. The largest surface belongs to Scenario 1 (296 ha), and it depends on the contribution of crop farming and on the high number of domestic animals. The second, by a large margin, is Scenario 3 (242 ha), where arable land is quite low, but the high number of animals requires a significant grazing surface. The model that uses the least amount of land is Scenario 4 (158 ha), mainly because crop farming has a higher productivity per hectare and needs less land than pastoralism. Scenario 2 requires a slightly larger surface than Scenario 4 (175 ha). However, if we consider that land exploitation for grazing is less intensive than for crop farming, Scenario 2 is expected to have a lower impact on mountain landscapes, as its cereal area is only 29% of the total (as opposed to the 39% of Scenario 4).

5. Conclusion

In this quantitative analysis of the Bronze Age subsistence economy of the Alps, four alternative scenarios were tested. The first two represent a typical late-prehistoric subsistence, widely used in other modelling efforts (Gregg 1988; Shukurov et al. 2015; Reitmaier & Kruse 2019). The only difference between the two scenarios is the exploitation of milk: negligible in the first, substantial in the second. Although the third and the fourth scenarios do not represent unrealistic economic systems, they can be considered ‘control models’: one where pastoralism is significant within the farming community, and the other where pastoralism is very marginal. Therefore, the main focus of these final remarks will be on Scenarios 1 and 2, with Scenarios 3 and 4 used as benchmark.

Scenario 2 utilises the second least amount of land: the second least for grazing land (after Scenario 4, where pastoralism is marginal) and the second least for arable land (after Scenario 3, where agriculture is less important). On the other hand, land use is the highest in Scenario 1: second lowest for arable land (like Scenario 2), but the highest for grazing land. This depends on the higher reliance of Scenario 2 on dairy produce, which significantly increases the productivity of pastoral land use. In terms of labour return, Scenario 2 is the most efficient. It is essentially as efficient as Scenario 3, but Scenario 3 uses much more land than Scenario 2. Scenario 1, instead, represents the least efficient scenario. If we ought to rank the four simulated subsistence systems, in terms of impact on the landscape (how many hectares of land they need to exploit) and labour efficiency (or labour return), the best would be the one formalised in Scenario 2, where crop farming is complemented by dairy-focused pastoralism. A crop-based system, with marginal pastoralism, as in Scenario 4, proved more parsimonious in terms of land use, but less efficient in terms of labour. The opposite can be said for a more balanced agriculture-pastoralism system (Scenario 3), with a significant constraint represented by the fodder provision for the winter. Correlations between land use and labour in the four scenarios are illustrated in the scatter plot of Figure 8. It can be deduced that a system favouring pastoralism might not be easily sustained if the animals need to be stabled during the harsh winter months. A system where crop farming is the primary source of calories, complemented by the products of seasonal pastoralism, seems to be more productive and resilient. Sensitivity tests indicate that a small percentage of pastoralists (10% to 20%) within a farming community guarantees a good labour return while minimising the inevitable decline in the marginal product of labour. This argument is also supported by the economic historian Jon Mathieu, who states that crop farming has always been the most important economic activity in many areas of the Alps, at least until the 19th century (Mathieu 2009). The four modelled scenarios show that, as the contribution of animal products to the diet increases, the subsistence system maintains moderate ecological pressure and remains labour efficient only with an increasing reliance on dairy produce. These inferences are corroborated by the sensitivity tests, which reveal an inverse proportional relationship between milk surplus and upland grazing areas. These insights provide a new perspective on the role of cheese in the economy of Bronze Age societies of the Alps.

Figure 8

The exploitation of milk and dairy products was believed to have developed after the emergence and spread of farming, as part of a Secondary Product Revolution that transformed the main economic focus of animal husbandry (Sherratt 1983). However, recent advancements in residue analysis confirmed that milk was already exploited in the Neolithic, suggesting an earlier origin of this practice (Evershed et al. 2008). Despite this hard evidence, the relevance of primaeval dairy strategies for the subsistence and economic development of Neolithic societies has been questioned. In fact, the exploitation of milk seems to intensify after the Neolithic and is associated with an increasing human occupation of marginal environments (Greenfield 2010). The scenarios modelled in this paper suggest that negligible and intensive use of milk have very different implications for prehistoric subsistence, and that dairy specialisation would benefit prehistoric communities living in areas less suited for crop farming, like the inner valleys of the Alps. Increasing dairy production reduces the number of livestock needed, increases labour return and enables an efficient exploitation of summer pastures (which cannot be used for crop farming) and winter fodder. Although Alpine societies possessed milk-processing know-how since the Neolithic (Spangenberg, Jacomet & Schibler 2006), specialised dairy appears to have emerged only during the Bronze Age (Carrer et al. 2016). The drivers of this economic shift are difficult to infer. Increasing population density in the inner valleys of the Alps could have made dairy specialisation more labour-efficient and more sustainable for the limited resources available, leading to the transformations observed in the archaeological record. The higher labour return generated by dairy production would have fostered demographic growth and led to a new population equilibrium (Wood 1998; Dow & Reed 2023). Although no long-term palaeodemographic reconstructions are currently available for the Alps, recent research in the Alpine foreland suggests a rapid population expansion during the Bronze Age (Hinz et al. 2022). Similar effects of innovation on population dynamics have been identified by economists, anthropologists and archaeologists in many small-scale societies of the present and the past (since Boserup 1965; see Freeman et al. 2024 for a recent archaeological example).

The processing of large quantities of milk requires techniques that ensure its long-term preservation. Most of the 1600 kg of cheese in Scenario 2 is produced during the summer to be consumed throughout the year (13.3 kg for each adult, 6.7 kg for each child or senile adult). This implies that the intensification of dairy production came with the development of hard or mature cheese. Long-lasting dairy products can mitigate the subsistence risks associated with crop failures, which are particularly severe in vulnerable mountain environments. Hard cheese turns perishable milk into a commodity, easier to exchange for other goods or supply to groups not involved in food production, like miners (Pearce 2016). The ripening process also significantly reduces the amount of lactose in the cheese, making it more digestible for lactose intolerant individuals (Rosenstock, Ebert & Scheibner 2021). The emergence of hard cheese in the Alps during the Bronze Age, which can be indirectly inferred from archaeological evidence (see Putzer 2024), could have provided the preconditions for the transformation of the subsistence economy described above. This innovation contributed to the Stored-Products Revolution, which Bevan (2019) attributes to the 1^st millennium BCE and that transformed food security and socio-economic development in Europe and the Mediterranean.

The use of mathematical modelling provided new insights into the economic and ecological role of dairy specialisation in the Alps, demonstrating the importance of intensive milk exploitation for the sustainability of prehistoric land use and the resilience of prehistoric subsistence systems. The interpretation of the results also suggests a correlation between this shift in food production, demographic pressure and the origin of hard cheese. These inferences are still largely speculative and require more archaeological data to be verified. Nevertheless, they represent a first attempt to analyse prehistoric subsistence and dairy production in the Alps from a microeconomic point of view.

Additional Files

The additional files for this article can be found as follows:

• S1. Supplementary Information 1: Equations. DOI: https://doi.org/10.5334/jcaa.209.s1

• S2. Supplementary Information 2: Description and justification of the parameters. DOI: https://doi.org/10.5334/jcaa.209.s2

• The code is available at www.github.com/francescokar/PastMath

Competing Interests

The author has no competing interests to declare.