Assessing whether the best land is cultivated first: A quantile analysis.

Classical land rent theories imply that the best land is cultivated first. This principle forms the basis of many land-use studies, but empirical evidence remains limited, especially on a global scale. In this paper, we estimate the effects of agricultural suitability and market accessibility on the spatial allocation of cultivated areas at a 30 arc-min resolution in 15 world regions. Our results show that both determinants often have a significant positive effect on the cropland fraction, but with large variations in strength across regions. Based on a quantile analysis, we find that agricultural suitability is the dominant driver of cropland allocation in North America, Middle East and North Africa and Eastern Europe, whereas market accessibility shows a stronger effect in other regions, such as Western Africa. In some regions, such as South and Central America, both determinants have a limited effect on cropland fraction. Comparison of high versus low quantile regression coefficients shows that, in most regions, densely cropped areas are more sensitive to agricultural suitability and market accessibility than sparsely cropped areas.

Introduction

Cultivated land covers around 1,500 million hectares (Mha), representing nearly 12% of the Earth's land area [1, 2]. Besides their key role in food, feed and bioenergy supplies, cultivated areas have major impacts on the environment, including climate change, water pollution, and biodiversity loss [3-7]. Agricultural projections anticipate that, by 2050, up to 330 Mha of land will be required at the global scale for food and feed production [8, 9]. On the other hand, climate mitigation scenarios stress the importance of freeing up land to regrow forest or to produce bioenergy crops [10]. Faced with this dilemma, optimizing the use of cultivated land represents a major challenge: increasing the supply of biomass for food and non-food purposes while limiting negative impacts on climate and biodiversity [11, 12].

To this end, we need a better understanding of the factors driving the spatial distribution of cropland. It is commonly accepted that the suitability of land for cultivation, which itself depends on climatic conditions during the growing season and soil characteristics (e.g. soil moisture, pH, slope and soil carbon content), influences the location of cultivated areas [13]. Market accessibility is also viewed as a key driver of the spatial distribution of cropland, as it is essential for trading in agricultural products and purchasing key inputs (e.g. seeds and fertilizers) [14].

These factors are captured in the economic concept of rent (surplus), which is the basis of economic theories of land allocation [15]. According to these theories, land is used in such a way as to maximize the rent generated by its use. Market accessibility and agricultural suitability have been recognized as key determinants of land rents since the 19th century in Ricardo’s and von Thünen’s classic theories [16, 17]. According to these theories, land is assumed to be cultivated gradually in descending order according to its quality and its distance from the market, to quote Ricardo: "The most fertile, and most favorably situated, land will be first cultivated" [16]. In this paper, we refer to the highest grades of land in terms of potential productivity, location suitability or both as “best land”. Today, these theories are still directly applied in some land use assessments [18, 19]. Many global land use models are rooted in classical rent theories by allocating land according to a profit function that depends on the intrinsic qualities of land provided by vegetation models (usually in terms of climatic potential yields) [20-22] or based on index of agricultural suitability [23]. Land supply elasticities are also generally used to determine land conversion rates in a given location. In this case, the elasticity is estimated based on assumptions derived from rent theories [24].

Several empirical studies at the local scale have investigated responses to agricultural suitability and market accessibility [25]. Although strong relationships have been observed between cultivated area and agricultural suitability and market accessibility in several European regions [26, 27], some croplands in China were recently moved to less fertile areas in response to urbanization dynamics [28]. At the land system level, several assessments reported ambiguous effects of some spatial determinants on land use, like for example a negative effect of market accessibility on agricultural land use [25].

In this paper, we provide a comprehensive empirical analysis of the effects of agricultural suitability and market accessibility on the allocation of cultivated areas in 15 world regions (see region map in Fig 3). Our analysis is based on global datasets including suitability values and accessibility indices and cropland fractions on a 30 arc-minute grid. Agricultural suitability is proxied by an index synthetizing the climatic, pedologic and topographic properties of land [29]. Market accessibility is represented by an index reflecting the travel time using different types of infrastructure to medium (>50khab) and large (>750khab) cities and large maritime ports [14]. In this paper, we refer to the areas with the highest suitability and/or accessibility indices as "best land". Using these indices, we display cropland distributions over quartiles of agricultural suitability and market accessibility in each of the 15 regions. This representation has the advantage of displaying the quality of cropland allocation in relation to the region's potential in terms of agricultural suitability and market accessibility, since each region has its own specific conditions for cropland settlement. We then estimate the response of cultivated land to change in agricultural suitability and market accessibility, using quantile regression models [30] fitted to global datasets. This econometric approach was chosen here to make as few assumptions as possible about the distribution of data.

Fig 3

Map of the 15 world regions.

Patterns of cropland allocation

The spatially explicit datasets that are currently available provide information on the cultivated fraction at the grid cell scale. However, we cannot directly infer from the formulation of rent theories their implications on this variable. To clarify this point, we show four contrasted patterns of cropland allocation on Fig 1. Four hypothetical regions are considered including four land classes covering an increasing gradient of land quality (Q1 = lowest quality, Q4 = highest quality). Here, the quality of land can correspond to either agricultural suitability or market accessibility (see Method for details). Each of the four land classes is further divided into four parcels of homogenous quality on which cropland can be allocated and cover from 0 to 100% of the areas (red areas). The resulting distribution of cropland over land classes is shown on the histograms displayed in Fig 1 (center left). Depending on the proportion of cropland in the total land area, it may not be possible to allocate the entire area of cropland to the best land (i.e. in land class Q4). For this reason, the histograms compare the cropland distribution (in red) against a theoretical distribution (in blue) assuming that all cultivated land is allocated over the best parcels of land first. The boxplots (center right) describe the distribution of the cultivated fractions within land classes (i.e. the fraction of the parcel areas colored in red). The line charts (right) show the regression lines on the 25% least cultivated areas and the 75% most cultivated areas.

Fig 1

Illustrative patterns of cropland allocation over a land quality gradient indicated by four land classes Q1, Q2, Q3, Q4 (Q1 = lowest quality, Q4 = highest quality) defined from the 1st quartile, median, and 3rd quartile of the considered quality index (suitability or accessibility).

Four hypothetical regions are distinguished, with low (case 1) to high (case 4) cultivated areas. Each region includes 16 parcels (white squares). A fraction ranging from 0 to 100% of each parcel can be cultivated (red squares in the graphics on the left). The histograms (center left) describe the corresponding cropland distributions expressed in % of agricultural land allocated to each land class (in red) in comparison to theoretically optimal land allocations (in blue). The boxplots (center right) describe the distributions of the cultivated fractions within land classes. The line charts (right) show the regression lines on the 25% least cultivated areas and the 75% most cultivated areas. Case 1 corresponds to a random and homogeneous distribution of the cultivated areas over the parcels. Case 4 illustrates a strong preference for an allocation of cultivated land in high quality parcels. Cases 2 and 3 are intermediate.

In the first hypothetical region (case 1), the cropland area (shown in red) is homogenously distributed over land classes, yielding a uniform distribution of cropland area over land types as well as a uniform distribution of crop fractions (25% in the four land classes). In the next two regions (cases 2 and 3), cropland is preferentially distributed to the highest classes of land quality either by increasing the number of cultivated plots (case 2) or by increasing the fraction of cultivated area within a given parcel (case 3). These two cases yield the same distribution of cropland area but with distinct distributions of crop fraction. In case 2, the crop fraction increases on the least densely cultivated parcels, making the lower range of the boxplot increase with land quality, while in case 3, the crop fraction increases on the most densely cultivated areas, making the higher range of the boxplot increase with land quality. In case 4, cropland is preferentially distributed on the best land class both by increasing the crop fraction and the number of cultivated plots. In this case, both the higher and lower ends of the boxplot increase with land quality. Note that, in case 4, we set the area of cropland of our hypothetical region to 40% of the total land area, which is larger than the area covered by the parcels of the last land class (25%). Consequently, the theoretical distribution (in blue) spans the two last classes.

This schematic representation shows that the same distribution of cultivated areas can result from different spatial allocation strategies. Cropland can be preferentially distributed on the best land either by allocating crops to the least densely cultivated areas (better allocation) or by concentrating more crops on already densely cultivated areas (higher intensity) or both. These strategies lead to different graphical patterns in the boxplots of cultivated fractions. With the first strategy, we observe a steeper response at the lower end of the boxplot to land quality level whereas, with the second strategy, the response is steeper at the upper end of the boxplot (see right-hand charts on Fig 1).

Fig 1 summarizes the general approach adopted in this paper: we start from gridded data from which we derive crop distributions over land qualities (Q1-Q4). We then express these distributions as boxplots of cultivated fractions, and estimate the effect of land qualities for different quantiles of fractional crop coverage.

Materials and methods

The analysis is carried out at global scale using datasets describing cropland fractions, agricultural suitability and market accessibility at the beginning of the 20th century at a 30 arc-min resolution. Data are scaled to values ranging between 0 and 1 where this is not already their native format. The fraction of cropland, infrastructure and other areas (including grassland and forest) in each grid cell comes from historical data based on HYDE version 3.2.1 [1] for the year 2017 without any distinction between crop types. HYDE 3.2.1 combines country statistics for different land use categories from FAO for the period 1960–2015, subnational levels statistics and spatially explicit depiction of land cover from the ESA Land Cover consortium maps for the year 2010. Data can be found athttps://easy.dans.knaw.nl/ui/datasets/id/easy-dataset:74467/tab/2. Global agricultural suitability is measured using an index reflecting the climatic, soil and topographical conditions necessary to grow the 16 most important food and energy crops [29]. This index represents for each pixel the maximum suitability value across the 16 crop species. This index is strongly correlated with the Global Agro-Ecological Zones index [31]. As the Zabel’s index is more recent, this index was chosen in our study. Data can be found at https://zenodo.org/record/3748350#.XzpPjegzbIU. Market accessibility of land is measured on the basis of the travel time using different types of infrastructure to medium-sized (>50khab) and large (>750khab) cities and large maritime ports integrated into a single index accounting for travel behavior [14]. Data can be found at http://www.ivm.vu.nl/en/Organisation/departments/spatial-analysis-decision-support/Market_Influence_Data/index.aspx. Maps of cropland fraction, agricultural suitability and market accessibility are shown on Fig 2 as well as zoomed-in maps for North America and Brazil on S15 Fig of S1 File. Results are aggregated for 15 agroclimatic regions (see Fig 3).

Fig 2

Cropland fraction in the year 2017 in percentage of grid cells from Goldewijk et et al. (Panel A). Index of agricultural suitability (min = 0, max = 100) from Zabel et al. (Panel B). Index of market accessibility (min = 0, max = 100) from Verburg et al. (Panel C).

In order to assess the robustness of our conclusions as to the origin of the data, we compare our results to those obtained using cropland fraction from the Erb et al. land-use dataset [32]. We also use the market influence index, which incorporates population density data as well as national level per capita GDP values in addition to travel time to cities and ports [14]. Results, shown on S11-S14 Figs of S1 File, are consistent with those obtained with the default datasets.

Building cropland distribution over suitability and accessibility quartiles

Quartiles of agricultural suitability and accessibility are calculated using the quantile function of R (v. 3.5.1). Quartiles are calculated for land where the suitability and accessibility index is not equal to 0 to avoid skewing the distributions in regions with large proportions of desert or remote areas. The largest proportion of unsuitable land (index = 0) is found in Middle East and North Africa (14%) and Eastern Europe (9%), and the largest proportion of inaccessible land (index = 0) is found in Oceania and South-Eastern Asia (23%) and Southern Africa (11%).

Due to the relatively low resolution of the maps and the granularity of the indices (in terms of decimal place), the quartiles obtained do not exactly yield a homogeneous distribution of 25% land by quartiles. This is particularly the case for the suitability index, whose granularity is limited to two digits after the decimal point (compared to seven for the accessibility index). The quartiles of agricultural suitability obtained using the quantile function default setting were compared to quartiles empirically calculated by iterative processes. The latter quartiles were used when they provided a more uniform distribution of 25% per quartile. The resulting distribution of total land area over quartiles of suitability and accessibility is provided in S1 and S2 Tables of S1 File.

The theoretical distribution of land shown in blue bars in Figs 1 and 4 is calculated by allocating an area equivalent to the cultivated area in a given region to the four land categories defined from the quartiles of suitability and accessibility. All types of land are included in the calculation–cropland, pasture, forest or wilderness areas–with the exception of areas occupied by infrastructure.

Fig 4

Percentages of cropland area allocated to four different classes (Q1, Q2, Q3, Q4) of suitability (red) and theoretically possible distribution (blue) for six regions. Shade levels indicate land classes of accessibility, the darkest colors showing the most accessible land. The four land suitability classes were defined from the 1st quartile, median, and 3rd quartile of the considered suitability index.

Quantile regression

We use quantile regression to measure the effect of agricultural suitability and accessibility on cropland fraction [30]. This semi-parametric approach provides a more detailed picture than classical least square regression methods, as it focuses on the entire conditional distribution of the dependent variable, not only on its mean. It allows us to assess how cropland fractions are distributed over different types of land characterized by different quantiles (high quantiles correspond to more intensively cultivated land than low quantiles). Successively, for two quantile levels τ (1st and 3rd quartiles), we estimate the coefficients β0, β1, β2, β3 of the following quantile regression model:

The regression coefficients were estimated using the procedure described by Koenker [35] with the rq function of the R quantreg package.

Standard errors are obtained by bootstrap methods with 1,000 replications. The quality of fit of the quantile regression models is assessed using a pseudo R2 noted R1 for each specified quantile (here the first and third quartiles). This quality of fit criterion (in the range 0–1) was specifically designed for regression quantile models [33] and is expressed as a weighted sum of the values of the residues of the fitted quantile regression. R1 is a natural analog to the R2 for quantile regression and measures the local quality of fit at each fitted quantile.

Results for the 1st and 3rd quartiles are shown on Fig 6. Additionally, quantile regression models were fitted for each of the 15 relevant regions at a 5-percentile interval between the 10th and 95th percentiles. Results for all quantiles are shown on S5-S7 Figs of S1 File.

Fig 6

Estimated effects of agricultural suitability (Panel A), market accessibility (Panel B), and the interaction between suitability and accessibility (Panel C) for the first and third quartiles of cropland fractions in 15 regions. Estimates were produced by quantile regression. The first and third quartiles represent the 25% least- and most-cultivated land. Colors indicate the levels of statistical significance for each region. RAS: RestAsia, BRA: Brazil, NoAM: North America, CeAM:Central America, CHI: China, EAFR: Eastern Africa, EEUR:Eastern Europe, IND: India, MENA: Middle East and North Africa, OECDPa: OECD pacific, OEA: Oceania Southeastern Asia, SoAM: South America, SAFR:Southern Africa, EU27: European Union, WAFR: Western Africa.

Heteroscedasticity, multicollinearity and spatial autocorrelation

By fitting linear regressions to different conditional quantiles of the range of a response variable, quantile regression overcomes the problem of heterogeneity of variance [34] and is thus well suited in the presence of heteroscedastic error (the Breusch-Pagan test fitted to a linear regression model is highly significant).

To test for possible multicollinearity issues, we calculate the Spearman coefficient of correlation between independent variables (see S3 Table of S1 File). The resulting values are in most cases below 0.6. Regression coefficients have been estimated both through univariate and multivariate regressions: we did not find any noticeable difference in the values of the coefficients except for North America. In this region, we obtained a value for the accessibility coefficient of the multivariate regression about four times lower than that of the univariate regression. As there is only a moderate correlation between the independent variables in North America (Spearman = 0.49), we decided to use the value of the multivariate regression coefficient because of its lower Bayesian Information Criterion (BIC) values.

The Moran test for spatial auto-correlation confirms that both our dependent and independent variables are spatially autocorrelated. Thus, the spatial autocorrelation of our response variable (crop fraction) is probably caused by our autocorrelated predictors (suitability and accessibility). In this case, it is not relevant to remove this effect from our predictors because our objective is precisely to estimate the effects of suitability and accessibility on the crop fraction. However, in order to avoid any unintended effect resulting from a residual autocorrelation, all p-values and confidence intervals of our estimates were computed using a non-parametric bootstrap procedure with 1,000 replications. The corresponding confidence intervals are shown in S8-S10 Figs of S1 File and do not indicate any spurious effect.

Results

Cropland is preferentially distributed in areas with high levels of agricultural suitability and market accessibility in most regions

The cropland distributions over classes of agricultural suitability for a selection of world regions is shown in Fig 4. The four land classes are defined from the 1st quartile, median, and 3rd quartile of the considered suitability index. The distributions in all of the 15 regions studied, as well as distributions over classes of land accessibility, are provided in the Supplementary Information (see S1 and S2 Figs of S1 File). As in Fig 1, we compare the actual cropland distribution (in red) against a theoretical distribution (in blue) assuming that all cultivated land is distributed over the class of the most suitable land unoccupied by infrastructure (see Method). It should be noted that the theoretical distribution does not necessarily represent an optimum to be achieved and is simply intended to show possible limitations in land availability.

The shape of the cropland distributions reveals that cultivated areas are in most cases allocated preferentially to the most suitable land, although there are substantial variations between regions. With 50% of its cropland area located on the most suitable class of land and only 8% on the least suitable land class, North America is the only region where the difference in cultivated land allocation between the lower and upper classes (noted Q4-Q1 in the following, for convenience) is greater than 30 percentage points. This Q4-Q1 difference is lower in India (16 percentage points), EU27 and Brazil (21 percentage points in each case). In India and EU27, the total cropland area is such that it is not possible to allocate all cropland beyond the 3rd (in EU27) or the 2nd quartiles (in India) of agricultural suitability. In Brazil, on the other hand, all crops could theoretically be located beyond the 3rd quartile, also on land with relatively good accessibility (see blue bars on Fig 4). Out of the 15 regions studied, 10 have a Q4-Q1 difference between 20 and 30 percentage points. The lowest Q4-Q1 differences are found in Oceania and South-Eastern Asia and Central America where the cropland distributions are almost uniform (see Fig 4 and S1 Fig of S1 File).

Compared to agricultural suitability, the concentration of crops on the most accessible land is greater: out of the 15 regions studied, seven have more than 40% cropland above the third class (see S2 Fig of S1 File), a value found only in North America with respect to agricultural suitability. The largest Q4-Q1 differences in terms of land accessibility are found in Middle East and North Africa, Rest of Asia, Eastern Europe and Western Africa, and the lowest in Oceania and South-Eastern Asia and OECD Pacific.

The crop fraction (%) in areas of 30 arc-minute grid cells are shown in Fig 5 for the same selection of regions and in S3 Fig of S1 File for the whole set of regions. The crop fraction tends to increase with agricultural suitability in most regions and the trends are consistent with the cropland distributions shown in Fig 4. The response is particularly strong in North America but is much weaker in Oceania and South-Eastern Asia. Fig 5 shows that, in most regions, the increase in crop fraction is stronger at the upper end of the boxplots than at the lower ends. India is a notable exception as the effect of agricultural suitability on the crop fraction is stronger in the least cultivated areas. This can be explained by the particularly dense crop cover in India, which implies that the effect of suitability is mainly obtained through a better allocation in the least cultivated areas rather than an increased intensity in the most cultivated areas. A similar upward trend was observed for crop fraction with respect to the accessibility index, with a steeper increase in the most cultivated areas in all regions except India and Oceania and South-Eastern Asia (see S4 Fig of S1 File).

Fig 5

Distribution of crop fractions (%) in areas of 30 arc-minute grid cells for four classes of suitability (Q1, Q2, Q3, Q4) in six regions.

The four land suitability classes were defined from the 1st quartile, median, and 3rd quartile of the considered suitability index.

Quantification of the effects of agricultural suitability and market accessibility on cropland fraction

Quantile regression models were fitted for each of the 15 relevant regions to estimate the effects of a one-unit increase in suitability and accessibility on the cropland fraction. For each region, two models were fitted separately: one for the 25% most cultivated land, i.e. areas with crop fraction above the third quartile of the grid cells in our dataset, representing densely cropped areas; and one for the 25% least cultivated areas, i.e. areas with crop fractions lower than the first quartile of the grid cells, representing sparsely cropped areas (see details in Method). The estimated coefficients obtained for these two quantiles are plotted in Fig 6. Their comparison makes it possible to analyze the response of the fraction of cultivated land to a one-unit increase in suitability and accessibility, taking into account the intensity of agricultural land-use.

The results of the quantile regression on the 25% most cultivated land (3rd quartile) show that increasing suitability has a positive effect on the fraction of cultivated land for all regions (Fig 6A). This effect is always significant (p<0.01) with one exception in OECD Pacific. The suitability effect is higher than 0.5 in four regions, namely North America, EU27, Eastern Europe and Middle East and North Africa. According to these estimates, a 10% increase in suitability would increase the cropland fraction by more than 5% in these regions. However, in Eastern Europe, India, Rest of Asia and Brazil, this positive effect can be partially offset by a strong negative and significant interaction between suitability and accessibility (Fig 6C).

For the 25% least cultivated land (1st quartile), the estimated effects of suitability are almost always significantly above zero (p<0.01) with only two exceptions: Oceania and South-Eastern Asia and OECD Pacific (Fig 6A). The estimates are systematically lower on the 1st quartile, except in India which is the only region where the estimated coefficient is higher than 0.4. Thus, the response to agricultural suitability is achieved in most regions through a higher intensity in already densely cultivated areas (Case 3 in Fig 1) rather than through a better allocation of cropland in the least densely cropped areas (Case 2).

With respect to the accessibility index, the estimated effects of a one-unit increase in accessibility on cropland fractions in the 25% most cultivated land are higher than 0.75 in five regions: Rest of Asia, Western Africa, Eastern Europe, OECD Pacific and Eastern Africa (Fig 6B). Estimates are significantly higher than zero for all regions (p<0.01). As shown for suitability, the estimated coefficients are lower when considering the 25% least cultivated land, except in India and Oceania and South-Eastern Asia, which is consistent with the boxplots of crop fractions (see S4 Fig of S1 File).

Coefficients of interaction are significant at both the 1st and 3rd quartiles in only seven regions (Fig 6C). They are positive in most regions at the 1st quartile of crop fractions and negative in most cases at the 3rd quartile. Thus, in the most densely cropped areas, the effect of one of the two explicative variables becomes less important as the value of the other variable increases, while it becomes more important in areas with low crop density. The interaction between suitability and accessibility is particularly acute in Eastern Europe, Rest of Asia, India and Brazil.

Ricardian and Von Thünen paths of cropland allocation

To assess the relative importance of suitability over accessibility, we use a standard criterion, called R1, frequently used with quantile regressions [33] to measure the quality of the model at a given quantile (see Method). High R1 values indicate a better explanatory power of the estimated model. This criterion is close to zero when the response is nearly flat and close to 1 when the quality of fit of the model is almost perfect for the relevant quantile. Here, we calculate R1 at the 1st and 3rd quartiles for two univariate models with agricultural suitability and market accessibility respectively as independent variables. The higher of the two R1 values in the two quartiles is reported in Fig 7.

Fig 7

R1 values of quantile regression of two univariate models linking crop fraction to agricultural suitability (y-axis) and market accessibility (x-axis). The higher of the R1 values in the first and third quartiles of crop fraction distribution is reported. Values are computed at the third quartile for the regions labelled in black, at the first quartile for the regions labelled in blue, and at the third quartile regarding suitability (suit.) and the first quartile regarding accessibility (access.) for the region labelled in red.

R1 values are higher at the third quartile in all regions, except India, EU27, and Oceania and South-Eastern Asia (for accessibility only in the last case). The best fits are found in North America, Middle East and North Africa, Eastern Europe and China for both the suitability and accessibility indices. In these regions, the R1 values are equal to 0.3 or higher, meaning that the fit is improved by more than 30% compared to a model with the intercept only. R1 values of less than 0.2 confirm that agricultural suitability and market accessibility have a small effect on cropland fractions in South and Central America, OECD Pacific, Oceania and South-Eastern Asia and Southern Africa.

The 1:1 line shown in Fig 7 separates regions where the highest degree of explanation is provided by agricultural suitability from those where it is provided by market accessibility. Referring to the underlying economic theories, the former regions can be labelled as Ricardian regions and the latter as Von Thünen regions. A number of regions–India, South America, Eastern Africa and China–lie near the 1:1 frontier, indicating a certain balance between accessibility and suitability criteria. At the top right of the R1 plot, North America shows a Ricardian-oriented allocation, with crop allocation highly concentrated in the highly suitable areas of the Corn Belt. At the bottom right, Rest of Asia and Western Africa, where crops are mostly located close to major rivers (Niger and Mekong) characterized by high levels of accessibility, can be described as Von Thünen regions.

The prevailing influence of one variable over the other might be related to the relative level of heterogeneity found in suitability and accessibility. Thus, if suitability levels are more heterogenous than accessibility, one might expect a stronger effect of suitability on cropland fractions. Conversely, in regions where agricultural suitability is relatively homogeneous, as for example in Brazil (see S15 Fig of S1 File), there will be little benefit in improving land allocation on this criterion. To test this assumption, we analyzed the relationship between the ratio of the estimated effects of suitability vs accessibility and the ratio of coefficients of variation (relative standard deviation) of suitability vs accessibility (see S4 Table of S1 File). Results show a significant relationship (p value < 0.01 and adjusted R-square = 0.39), thus confirming our assumption.

Discussion

Our results show that the validity of the assumption that the best land is used first–arising from classical land rent theories–varies across the regions of the world. In most regions, agricultural suitability and market accessibility have a significant positive effect on the fractional crop coverage, but their influence may be limited in some cases such as in Central and South America. Moreover, the prevailing driver of cropland allocation differs between regions. Agricultural suitability and market accessibility have a similar influence on crop fractions in several regions, in particular in China, India, and EU27. However, in North America, Middle East and North Africa and Eastern Europe, agricultural suitability appears to be a stronger driver of cropland allocation than accessibility.

Comparison of high vs. low quantile regression coefficients shows that, in most regions, cropland systems with high fractional crop coverage are more responsive to higher land grades than extensive or mosaic cropland systems characterized by sparser cultivated areas. This suggests that large-scale commercial farms are more likely to use the best land than smallholders and mixed crop-livestock agriculture. India and Oceania and South-Eastern Asia are two notable exceptions that can be explained by a higher proportion of smallholders engaged in commercial farming, especially in oil palm and rice production [35-37].

It is noteworthy that the best fits are found in regions with a long history of intensive agricultural settlement—North America, Middle East, Eastern Europe, China, India and European Union—while the poorest fits are found in regions where the agricultural frontier remains active—especially Brazil and Oceania and South Eastern Asia. This finding is consistent with the hypothesis of a process of gradual optimization of land allocation through learning described by Mather and Needle in the forest transition theory [38]. The United States is a “textbook” case of gradual optimization of land allocation. In the US, crop allocation were originally cultivated in relatively unsuitable land on the East Coast and in the Appalachian foothills [15, 39, 40]. The reduction in transport costs resulting from the development of the railways, combined with the reduction in transatlantic freight rates, made it possible to cultivate the fertile lands of the Midwest and export part of the agricultural production to Western Europe [39]. Our results are also consistent with the findings of several authors regarding the presence of increasing marginal returns in areas of agricultural expansion [41, 42] and support Di Tella's abnormal rent theory distinguishing between frontiers in equilibrium, where the price equals the average cost (zero profit) with a possibility of differential rent formation as one moves away from the frontier, and frontiers in disequilibrium with a possibility of positive profit and increasing returns [43].

This paper provides a number of insights that could help to improve the efficiency of land-use allocation and limit the pressure of agricultural activities on natural areas. Our results highlight substantial potential for improving the allocation of cropland in some major agricultural regions, particularly in South America and West Africa, where large amounts of the most suitable and accessible land are used for other purposes than crop production. Our results also suggest that the relative importance of agricultural suitability to market accessibility as a driver of cropland allocation in a given region is related to the relative level of variability of each determinant in that region. Thus, reducing the variability of market accessibility conditions through better transport infrastructure may foster the effect of agricultural suitability on cropland allocation and allow for more efficient use of the agronomic potential in a given region.

Coordination between public institutions and the private sector will be key to improving land-use patterns through, for example, the dissemination of information, fiscal incentives and facilitated provision of production factors [44]. Most importantly, promoting more equal access to land is essential to enable all types of agriculture, including smallholdings, to use the most suitable and accessible land. The environmental impact of such reorientation should also be taken into account in order to ensure that it benefits the conservation of natural areas.

Making land allocation more efficient also implies that it is possible to substitute different types of land uses, such as croplands, pastures and forest areas. However, the level of substitutability between different types of land uses depends on the interplay of many parameters, including cultural factors, the type of actors involved and local agricultural and environmental regulations [44-46]. For example, important complementarities between land use types (e.g., forest vs. cropland) in mosaic system can impede the transition towards more efficient cropland allocation.

Better representation of land-use changes is essential to decision-making. Here, we show that classical rent theories, which are still influential in land-use studies, cannot be applied independently of the regional context. They need to be used as contextualized generalizations rather than as “grand theories” [47] to account for the varying effects of spatial determinants of land allocation in the different regions of the world. Finally, it is important to emphasize that in many parts of the world market accessibility, which is sometimes overlooked in land-use studies, is a more important driver of cropland allocation than agricultural suitability.

There are several limitations to our work. First, we use a static dataset that does not provide an analysis of land-use transitions. This implies that our analysis spans the entire history of agricultural settlement in a given region, and may not detect recent changes in the spatial allocation of crops. Moreover, we consider total cultivated area without distinguishing the different crop types and their associated agronomic constraints. This could be a source of inaccuracy in certain regions, for example Oceania and South-Eastern Asia where the dominant crop is oil palm for which suitability is mainly dependent upon regular rainfall. In this study, we assume that the actual crop mix is close to the optimal one (i.e., the crop mix showing the highest suitability in a given grid cell). This seems a reasonable assumption because farmers generally tend to grow the species that are best adapted to their environment, i.e., to local climatic, soil and topographical conditions. In some cases, humans have nevertheless been able to shape their environment, through irrigation, drainage or terracing, to make it more suitable for agriculture. This may explain deviations from a perfectly efficient distribution (i.e., where all crops would be on the best land). Also, climate change may make the choice of crops more complex, leading possibly to larger discrepancies between the actual and optimal crop mix. Finally, this analysis does not account for cropping intensity (i.e., the fraction of the cultivated area that is harvested). In doing so, we cannot conclude about Ester Boserup's critique of rent theories. This critique states that rent theories are based on an “oversimplified conception” of the agricultural system distinguishing between cultivated and uncultivated land, while landscapes are actually shaped by a continuum of land types that differ in their frequency of cropping [48]. The two views may be however not entirely divergent from a land use perspective. One can certainly think that there is a link between density of cultivated areas and cropping intensity. Low densities may be a signal of long fallows, while high densities are usually associated with annual or multiple cropping. This hypothesis, which remains to be confirmed, would be a way of reconciling the two sides.

(DOCX)

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27 Jul 2020

PONE-D-20-17711

Assessing whether the best land is cultivated first: A quantile analysis

PLOS ONE

Dear Dr. BRUNELLE,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

Reviewers have raised concerns about the data used and the need to provide a bit more description and justification for their use. There is also the need to improve the explanation for the selection and composition of the agricultural suitability index, and a justification for its choice over others. The discussion section will need a bit more effort to enable readers better appreciate the implications of the study as well as its limitations. Please, kindly review the figures in line with suggestions made by the reviewers.

Please submit your revised manuscript by Sep 10 2020 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

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Gerald Forkuor

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PLOS ONE

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Reviewers' comments:

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Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Partly

**********

2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: I Don't Know

Reviewer #2: Yes

**********

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Reviewer #1: Yes

Reviewer #2: No

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Reviewer #2: Yes

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5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: PLOS One review of “Assessing whether the best land is cultivated first: A quantile analysis”

This paper explores the question of whether the best (i.e. most suitable and accessible) land is cultivated first, using quantile regressions on cropland fraction, agricultural suitability and accessibility at the global scale. The paper provides a very valuable and well-articulated contribution that I believe will be of interest to people studying issues related to land use. I therefore think that it would be a good paper for this journal if it addresses a few concerns. I am describing these below. I should note that I am not familiar with quantile regression as a method, and as such, my ability to comment on that aspect of the manuscript is limited, though the methods do seem sound.

Choice of data: In general I think the paper could better justify and describe the data, including how it is produced and what resolution it’s at – if space restrictions make it impossible in the paper, then a brief description in the SI would be fine. Specifically:

- I am not entirely clear why the authors chose to use the HYDE database as a source for cropland areas, even though the fact that they come to similar results when using another dataset (Erb 2007) is reassuring. HYDE’s purpose being to reconstitute broad trends of land use over thousands of years, I am not sure its baseline map is as accurate as others that are available, such as for example the LUGE lab’s maps of cropland and pasture areas (available at http://www.earthstat.org/cropland-pasture-area-2000/), which is available at 5 minutes resolution. If the authors think that HYDE is the best choice of data in this case, perhaps a short justification would be in order. Also, the authors say the map is for 2017 but HYDE website says the current map is for 2000 and the HYDE 3.2.1. release note says that the maps go up to 2015. It would be good to clarify this (and confirm that it is indeed a map of cover and not a simulation that is being used in this analysis).

- Related to this, a more recent and possibly more accurate accessibility dataset might be worth considering: https://malariaatlas.org/research-project/accessibility_to_cities/ (published as doi:10.1038/nature25181). This also has a high resolution, of 1x1km2.

- Finally, the paper could explain better the selection and composition of the agricultural suitability index, considering the importance of that variable for the analysis. The authors say that “Global agricultural suitability is measured using an index reflecting the climatic, soil and topographical conditions necessary to grow the 16 most important food and energy crops” (l.153-155). The mention of 16 crops suggest that an index was built somehow from 16 suitability maps, begging the question of how. After looking up the source (https://zenodo.org/record/3748350) I realize that “The agricultural suitability represents for each pixel the maximum suitability value of the considered 16 plants”, but clarifying this in the paper would be better. As well, a few words about why this index is superior to others (e.g. the FAO GAEZ) would be welcome.

Spatial resolution: What is the rationale for the use of a 30 arc-min resolution? Unless I misunderstood, all datasets are available at a higher resolution (HYDE AND Verburg et al. at 5 arc-min, Zabel et al. at 30 arcsec), so I’m not sure why the analyses are run at 30 arc-min especially since it seems to cause some minor issues (l. 179 and following). Related to that, lines 181-2, it would be easier to understand if the granularity were expressed in terms of resolution (what do “two digits after the decimal point” represent?).

Theoretical crop distribution and crop composition: The authors use an index representing the max suitability for any crop in order to represent suitability. So, when mapping the potential crop distribution, we don’t actually know the composition of crops that would be possible in that distribution: maybe it is theoretically possible to cultivate the same area of crops in that area; but is it possible to cultivate the same crop mix? The lumping of all crops together masks the fact that reaching the potential distribution would likely imply a significant restructuring of agricultural production. I don’t think that is a fatal flaw but I think it warrants some discussion in the paper.

Implications of the results: I find that the authors jump a little too quickly to the conclusion that areas where the explanatory power of accessibility and suitability is low or allocation doesn’t seem to follow the best land are areas of suboptimal land allocation (lines 431 and following). It would be interesting to have a bit more discussion of what might explain that low explanatory power, first. For example, there may be political reasons that prevent the cultivation of some areas. Or, importantly, other uses that are not taken into account here (e.g., livestock herding, forestry) are competing with croplands. I think that the question of land competition is important to discuss here as cropland allocation doesn’t occur in a vacuum, so optimal cropland allocation may not mean optimal land allocation. Without such a contextualization, recommendations like those on lines 437-446 seem to come out of the blue.

Figure 1:

- In the left-hand side of the diagram, it wasn’t immediately clear to me that the divisions within each quantile were different parcels. While this becomes clear by reading the text, I think that adding a visual legend showing quantile, parcel, and cultivated areas (with arrows and text) would help make it more intuitive.

- I wonder if there would be a way to shade or hash that left part in such a way as to represent the theoretical distribution? That would provide another visual point of comparison. Just a suggestion, not a request.

- One alternative way to present that information would be having the cases arranged horizontally instead of vertically and aligning the four quantiles across different plots for each case. This would require compressing the left-hand plots a bit but might help readers link the plots mentally. Also just a suggestion.

- Finally, I wonder if the regression curves are useful here. That plot is not used in the rest of the paper, so it feels a bit like we’re putting effort into understanding a plot for nothing.

From Figure 1 and in the discussion referring to it, case 3 seems to reflect a situation in which there are important agglomeration economies – it is more interesting to develop agriculture close to where there is already some. I wonder if you could comment a bit on the role of agglomeration economies (…)

Figure 3: The shadings are a little confusing. I would suggest displaying both series of plots instead (accessibility and suitability).

Figure 4: Do the colours have a meaning? If not it might be good to either include these same colours in the theoretical example in figure 1, or to revert to black and white.

Figure 5: the labels are a bit cluttered, especially in panel A. Is there a way to avoid that the lines go over the labels?

Map: I think it would be good to have a zoomed-in map showing an example of how accessibility and suitability quantiles are distributed in a real-life territory. This would help grasp the concept better.

Minor remarks:

l.124: Typo: should be “a given parcel”.

l. 175 and throughout: I would suggest saying “Middle East and North Africa”, “Oceania and South-Eastern Asia”

l. 336-338: “However, in Eastern Europe, this positive effect can be at least partially offset by a strong negative and significant interaction between suitability and accessibility”: The plot indicates that India, Brazil, and RestAsia also have strong negative interactions. Why are they not included here?

l. 453: “market accessibility, which is sometimes overlooked in land-use studies”: that is a surprising statement to me, as it seems that accessibility is the one thing that most land use scholars all agree is important. There may be some studies that don’t take it into account but this suggests that it’s being ignored more systematically which I don’t think is accurate.

Reviewer #2: Dear Editors of PLOS ONE,

Thank you for the opportunity to review the manuscript ‘Assessing whether the best land is cultivated first: A quantile analysis.’ I find the effort to be an interesting and innovative approach to land use modeling and assessment, and I very much encourage it’s publication.

I did, however, have a few comments which, I think, might improve the draft.

First, the treatment of the economics of land use is very sparse. I do not feel that the authors need to delve too deeply into land use incentives, but I imagine that a greater depth of understanding of how rent theory has been used to frame recent land use discussions would benefit both the reader and the manuscript. I encourage the authors to dedicate some discussion to the use and application of von Thunen and ricardo in the recent literature.

Second, the graphics, and much of the nuanced reporting of various coefficients or tests, are difficult to interpret. Some of it may also not be necessary (see, for example, the reporting on Moran’s I- mentioned below). I encourage the authors to streamline their reported statistics, and revise their graphics for readability and interpretation.

Third, there is too little information on the data generating process. I remain unclear on how you determined market access or suitability. And there is no clarity on how accurate these measures are, how dynamic they are, or how error might be spatially correlated. I encourage you to offer more information on the data inputs. This could be addressed with limited text in the manuscript and more detailed information in the supplementary materials. Ideally, you might also provide your code and datasets. Maps of the spatial data would also be useful.

A few more minor comments follow below.

Abstract

‘Classical land rent theories imply that the best land is cultivated first.‘

This sentence could be re-written or dropped. Rent theory states that a location will be used for its most economically advantageous use. Generally speaking, this relates to the marginal returns to the use of labor and capital; while this usually translates to ‘the best land is used first’ this is not always the case. There are also tremendous questions here about what is meant by ‘best’. This article explicitly engages with this issue, but, if anything, it seems to highlight that the definition of best is hardly as clear as it is presented in this initial sentence.

Introduction

L52-53. Add citations for this sentence.

L79. I’m wondering how you change the suitability of land. How often does that happen? (more info is needed to understand how you classified suitability, etc.)

A map of agricultural suitability here would be very helpful.

L88-89 There is a decent case to make that regulations and ‘types of actors’ are elements of suitability; the former, especially, for land suitability.

Figure 1: the use of red as null squared at left, then as the histogram fill in the middle is confusing. In general, I find this graphic to be quite confusing.

Pages-6-7. I’m not sure I fully understand what the authors are trying to say here (as well as in figure 1). Perhaps the main point of these spatial schematics is this: ‘. Cropland can be preferentially distributed on the best land either by allocating crops to the least densely cultivated areas (better allocation) or by concentrating more crops on already densely cultivated areas (higher intensity) or both.’ But if so, I’m not following as to how density (given the article so far) should factor into the preferential distribution of agricultural land? Density is hardly a factor in classic rent theory (although some might say that this is a weakness…).

L150. ‘beginning of the 20th century…’ beginning? Or end?

L175. It would be useful here to see a map of suitability and access. It is surprising to see that 9% of EE is classified as unsuitable (where?). At the same time, one might assume that much of South America might be unsuitable, although in percent terms the relative quantity might be small.

L240. I’m not understanding why the authors are reporting that market access and suitability are spatially correlated. How could they be anything but?

L275. Why do the authors think that NA favors suitable land? Is it luck? Is it better data (on suitability)? Is it better transportation systems?

General: I think some might suggest that the relative importance of market access vs. suitability has evolved over time. Similarly, transport costs per unit of distance likely vary from place to place.

**********

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Reviewer #2: No

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4 Sep 2020

We would like to thank the two reviewers for their careful reading of our paper. Their remarks were of great help to us to improve the paper. You will find in the attached file our answers as well as the modifications made to the paper.

Submitted filename: Response-Reviewers-R1-fin.docx

Click here for additional data file.

5 Oct 2020

PONE-D-20-17711R1

Assessing whether the best land is cultivated first: A quantile analysis

PLOS ONE

Dear Dr. BRUNELLE,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

Please, pay attention to exceptions raised by reviewer 1 on the use of the word "best" as well as other words. You may consider providing an explicit definition of what the submission considers as "best" (e.g. most suitable and most accessible). I may have accessed the wrong document, but reference 16 did not use the term "best". However, you may choose to interpret "most fertile and most favorable" as best, and provide this definition well ahead in the introduction to avoid any doubt. Kindly pay attention to the other two major concerns, and address them or provide  clear reasons why they need not be addressed.

Please submit your revised manuscript by Nov 19 2020 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

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If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: http://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols

We look forward to receiving your revised manuscript.

Kind regards,

Gerald Forkuor

Academic Editor

PLOS ONE

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #1: All comments have been addressed

Reviewer #2: (No Response)

**********

2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: Yes

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

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6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: I would like to thank the authors for addressing my comments. I am looking forward to seeing this paper in print.

Reviewer #2: Dear PLOS One,

Thank you very much for the opportunity to re-review the research article ‘Assessing whether the best land is cultivated first: A quantile analysis’. I have included a number of small suggestions below which I think might improve the manuscript.

I ask the editor to please make sure that the authors address the three concerns that I addressed in my initial review but which were not addressed in this revision:

1. The use of the term ‘best’ and the passive use of ‘allocation’, both of which are gross oversimplifications of, or even contrary. to rent theory)

2. The discussion of moran’s i in the methods (not needed here)

3. Please add maps of biophysical and access suitability to the main document.

Once the authors address these concerns and, ideally, address the points below, I recommend this manuscript for publication.

Thank you so much.

Abstract:

1st sentence. I continue to find this sentence as overly-simplistic and awkward. Please (please!) re-write this sentence to better align with classical rent theory or this current analysis. I would avoid using words like ‘best’ and ‘first’, since I’m not sure what constitutes ‘the best’ land or being used ‘first’. I raised my concern with this sentence in the first draft and continue to raise it here.

Introduction.

L39. I would hesitate to refer to sources 8-9 as foresight studies. I think that ‘projections’ or something similar is much better word choice.

L53. The wording ‘is allocated’ should be changed. This suggests that someone is doing the allocation, so to speak. This is presumably true for individual properties or land portfolios. But I don’t think that there are many scenarios where, outside of basic zoning laws, farmland use is allocated by land use planning commissions. Change the wording here to refer to influence rather than allocations. The former implies local decisions, whereas the latter implies some sort of authoritarian decision process. This use of allocated recurs throughout. Please adjust.

L60 ‘Many global land use models are rooted in classical rent theories by allocating land according to a profit function that depends on the intrinsic qualities of land provided by vegetation models (usually in terms of climatic potential yields) or based on index of agricultural suitability.’

Global land use models are generally rooted in elasticities and responses to market possibilities or climate trends. Classical rent theory, of course, is implicit in these relationships.

L67.

‘However, at the local scale, several empirical studies show inconsistent responses to agricultural suitability and market accessibility across regions24. Although strong relationships have been observed between cultivated area and agricultural suitability and market accessibility in several European regions, some croplands in China were recently moved to less fertile areas in response to urbanization dynamics.

This is very much aligned with classical rent theory, not inconsistent with it.

L69. Moreover, assessments carried out at the land system scale show contradictory effects of spatial determinants on land allocation24.

I’m not sure what this sentence is trying to say, why it is included, or what effects that are referring to.

L101. The use of the term ‘best land’ continues to be problematic. Do they mean ‘optimal’ in terms of suitability and access?

L258. This paragraph can be deleted or moved to the SI. I’m not sure what it adds. (somewhat annoyingly, I raised this clearly in the initial review)

L455. The note on fits by region is quite interesting and begs more discussion. Presumably, it’s not only that land optimization has increased over time, but that transportation costs have also shifted with time.

L496. This discussion of ‘grand theories’ and the warning against oversimplification in their application is in many respects and oversimplification in the characterization of these theories. In effect, there is tremendous nuance in how the theory is applied and manifested in land economics. While I find the simplicity of this analysis to be useful for clarifying a widely used model, the authors at times show a simplicity in their knowledge of the field and how these theories are used.

Map figure. Please include a map of the suitability and access regions in the main text.

**********

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If you choose “no”, your identity will remain anonymous but your review may still be made public.

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Reviewer #1: No

Reviewer #2: No

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.]

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22 Oct 2020

L39. I would hesitate to refer to sources 8-9 as foresight studies. I think that ‘projections’ or something similar is much better word choice.

Authors'response: done

L53. The wording ‘is allocated’ should be changed. This suggests that someone is doing the allocation, so to speak. This is presumably true for individual properties or land portfolios. But I don’t think that there are many scenarios where, outside of basic zoning laws, farmland use is allocated by land use planning commissions. Change the wording here to refer to influence rather than allocations. The former implies local decisions, whereas the latter implies some sort of authoritarian decision process. This use of allocated recurs throughout. Please adjust.

Authors'response: We agree that the word "allocated" implies that someone makes the allocation, but this does not imply anything about the type of decision making. An individual can allocate resources without any form of authoritian process. Nevertheless, in order to avoid any ambiguity, we have replaced the term "is allocated" by "is used".

L60 ‘Many global land use models are rooted in classical rent theories by allocating land according to a profit function that depends on the intrinsic qualities of land provided by vegetation models (usually in terms of climatic potential yields) or based on index of agricultural suitability.’ Global land use models are generally rooted in elasticities and responses to market possibilities or climate trends. Classical rent theory, of course, is implicit in these relationships.

Authors'response: True. We add in the paper the following comment (l.64): "Land supply elasticities are also generally used to determine land conversion rates in a given location. In this case, the elasticity is estimated based on assumptions derived from rent theories (Villoria et al., 2018)".

L.67 ‘However, at the local scale, several empirical studies show inconsistent responses to agricultural suitability and market accessibility across regions24. Although strong relationships have been observed between cultivated area and agricultural suitability and market accessibility in several European regions, some croplands in China were recently moved to less fertile areas in response to urbanization dynamics. This is very much aligned with classical rent theory, not inconsistent with it.

Authors'response: True. We removed the word "inconsistent" and we have modified the sentence l.68 as follows: "Several empirical studies at the local scale have investigated responses to agricultural suitability and market accessibility".

L69. Moreover, assessments carried out at the land system scale show contradictory effects of spatial determinants on land allocation24. I’m not sure what this sentence is trying to

say, why it is included, or what effects that are referring to.

Authors'response: For more clarity, we have modified the sentence as follows (l.72-74): "At the land system level, several assessments reported ambiguous effects of some spatial determinants on land use, like for example a negative effect of market accessibility on agricultural land use. 25".

L101. The use of the term ‘best land’ continues to be problematic. Do they mean ‘optimal’ in terms of suitability and access?

Authors'response: We have clarified this point l. 59-60 that: "In this paper, we refer to the highest grades of land in terms of potential productivity, location suitability or both as “best land". And in lines 80-81: "In this paper, we refer to the areas with the highest suitability and/or accessibility indices as "best land".

L258. This paragraph can be deleted or moved to the SI. I’m not sure what it adds. (somewhat annoyingly, I raised this clearly in the initial review)

Authors'response: We agree that the Moran test does not bring much information. It is only a confirmation. That is why we have replaced the term "reveals" by "confirms". However, we do not wish to remove this paragraph as we think it is important to include an explanation on how spatial auto-correlation has been treated in the paper.

L455. The note on fits by region is quite interesting and begs more discussion. Presumably, it’s not only that land optimization has increased over time, but that transportation costs have also shifted with time.

Authors'response: Reduction in transportation cost is indeed a key driver of the optimization process. We clarify this point in the discussion l.475-478: "The reduction in transport costs resulting from the development of the railways, combined with the reduction in transatlantic freight rates, made it possible to cultivate the fertile lands of the Midwest and export part of the agricultural production to Western Europe."

L496. This discussion of ‘grand theories’ and the warning against oversimplification in their application is in many respects and oversimplification in the characterization of these theories. In effect, there is tremendous nuance in how the theory is applied and manifested in land economics. While I find the simplicity of this analysis to be useful for clarifying a widely used model, the authors at times show a simplicity in their knowledge of the field and how these theories are used.

Authors'response: We agree that the theory can be applied in different ways. Here the term "grand theory" is not pejorative. It refers to the distinction made by Meyfroidt et al. between middle-range theory and general theoretical frameworks. This distinction is very nuanced as it accepts the need for generalization. The expression "oversimplified conception" is not ours and refers to the Boserupian conception of the use of cultivated land on which we are unable to conclude.

Map figure. Please include a map of the suitability and access regions in the main text.

Authors'response: done

Submitted filename: Response-Reviewers-R2-fin.docx

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29 Oct 2020

Assessing whether the best land is cultivated first: A quantile analysis

PONE-D-20-17711R2

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1 Dec 2020

PONE-D-20-17711R2

Assessing whether the best land is cultivated first: A quantile analysis

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