Economic Evaluation of an Invasive Forest Pathogen at a Large Scale: The Case of Ash Dieback in France


The invasion of a forest by a pathogen is a complex dynamic and spatial problem. The induced disturbances do not only reduce the present availability of the affected tree species but alter its future availability, population structure and distribution as well. These disturbances also have an impact on the prices of wood products via supply shocks, which, in turn, influence forest management choices, thus introducing feedback effects between market and ecological dynamics. The main objective of this paper is to evaluate the economic impact of an invasive pathogen at a large scale by integrating the biophysical and economic aspects of the invasion into a dynamic and spatially explicit setting. The analysis is developed using a modified version of the French Forest Sector Model (FFSM), a recursive partial equilibrium model, to which a specifically designed pathogen spread and mortality model have been coupled. We calibrated the model to represent the ash dieback invasion in France. Results showed that impacts are not homogeneous across regions and generally depend on the resource distribution, pathogen spread and market structure. We observed that the behavioural adaptation of forest managers (i.e. regeneration and harvesting choices) is a non-negligible component of the total standing volume loss.

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  1. 1.

    See the Appendix A for details on the ash volume estimation and distribution in diameter classes.

  2. 2.

    The assumption of imperfect substitutability between domestic and foreign products is justified by product heterogeneities that depend from production places, by the consumers habits or by the market structure [33].

  3. 3.

    The consumer surplus is the difference between what consumers are willing to pay for a given good and the actual market price. The producer surplus is the difference between the price at which producers are willing to supply that good and the actual market price.

  4. 4.

    Other studies report a disease progression rate in Europe (or in European countries) between 40-75 km per year [25, 39, 40], which is in line with the values indicated for France.

  5. 5.

    The annual harvested loss is the difference between the harvested ash volume without ash dieback and the harvested ash volume with ash dieback in a specific year.

  6. 6.

    The reduction in the ash harvested volume is robust for the tested values of the cross-elasticity of substitution between ash products and other hardwood species, i.e. 𝜖a, b: − 0.01, − 0.1, − 0.5, − 1, − 2.5, -5 (results not reported in the text, but available upon request).

  7. 7.

    It was not possible to directly estimate the Weibull parameters for 17 ecological regions because they did not have enough observations, i.e. less than 30 data points. When it was possible, these regions were merged with similar (in terms of soil pH, water stress, forest type composition and elevation) low-observation neighbouring ecological regions and the parameters were then estimated. This aggregation was not possible for three ecological regions due to the lack of other neighbouring ecological regions with low observations. In these cases, we used the estimated parameters from a similar neighbouring ecological region with enough observations as a proxy.


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The authors appreciate the helpful suggestions and comments of Anne Stenger and Pablo Andrés-Domenech (Université de Lorraine, Université de Strasbourg, AgroParisTech, CNRS, INRA, BETA), Benoit Marçais and Marie Grosdidier (UMR IAM, INRA, Université de Lorraine) as well as Christelle Robinet (INRA, UR0633, Zoologie Forestière). The authors would like to thank Alexandra Niedzwiedz at OLEF (Observatoire pour L’Economie de la Forêt) for the support with the empirical data. The authors are also grateful to the two anonymous reviewers and the advisory editor for their insightful comments and suggestions. The contribution of Claudio Petucco in this paper is the result of his PhD thesis work carried out at the Laboratory of Forest Economics, INRA, AgroParisTech.


This work was supported by a grant overseen by the French National Research Agency (ANR) as part of the “Investissements d’Avenir” program (ANR-11-LABX-0002-01, Lab of Excellence ARBRE).

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Appendix A: Ash Volume Distribution Estimation

Appendix A: Ash Volume Distribution Estimation

A.1 The Ash Volume Spatial Distribution

In order to analyse the impact of ash dieback in France, we adapted the original French Forest Sector Model by including ash forest as an additional forest type. The first step was to estimate the ash volume distribution in each cell. We used geostatistical techniques to spatially predict the ash volume distribution in unsampled areas based on the identified spatial structure derived from sampled locations [47]. Specifically, we used the kriging with external drift method in which the predictions from a regression model are adjusted using the spatial correlation between neighbouring observations as a function of distance. Kriging techniques have been previously used to predict forest biomass and other forest characteristics over large areas [27, 28].

Data on ash populations was taken from the French National Forest Inventory (FNFI) carried out by the French National Institute of Geographic and Forest Information (IGN) for the years 2006-2010 [29]. We know the forest cover type and structure, the number of trees for each species, tree volume, diameter at breast height and a weight for computing the volume per hectare for each sample plot. All together, we had a total of 30,879 inventory plots, and ash was present in about 10% of the plots.

In the regression model, we used the ash volume per hectare from the inventory plots as the dependent variable. For independent variables, we selected the soil water deficit as defined in [48], the soil pH obtained from the portal on forest spatial data, SILVAE [49], and the elevation, as well as a categorical variable representing the 83 different types of ecological regions present in French forests. We had no observations of the dependent variable in three ecological regions, so they were not included; ser1 was used as a reference. The digital elevation map and the map of the French ecological regions were downloaded from the IGN website (

We divided the sample into four subsets, each containing observations on ash trees measured in the four different forest types, corresponding to the ones defined in FFSM: conifers (C), broadleaf high forest (BH), broadleaf coppice (BC) and broadleaf mixed high forest and coppice (BH&C). We then ran a separate linear regression model for every subset. This was done to improve the prediction performance since the observed spatial structure of the residuals was not homogeneous across forest types. In Table 8, we present the estimated coefficient for the regression models that generate the residuals that were then used to derive the spatial structure of the ash volume via kriging.

Table 8 Estimated coefficients of the linear regression model used in the kriging with external drift to predict the spatial distribution of the ash volume per hectare in the four forest types: BH = broadleaved high forest; BH&C = broadleaved mixed high forest and coppice; BC = broadleaved coppice; C = coniferous

Once obtained the residuals from the linear regression (Table 8), we applyed the kriging procedure to adjust the prediction of the model in unsampled locations based on the spatial correlation structure between neighbouring observations expressed as a function of the distance. In other words, we fitted the theoretical variograms to the empirical ones to determine the variogram parameters. We used an exponential variogram model for the broadleaved high forest and the broadleaved high forest and coppice, whereas we used a spherical variogram model for the broadleaved coppice and the coniferous forest types (Fig. 9).

Fig. 9

Experimental and fitted variogram for ash volume per hectare in the four forest types

Successively, ash volumes per hectare were successively predicted on a 1-km2 grid covering the entire French territory, with the exception of Corsica for which we did not have data. The computation was carried out using the gstat package in R [50].

Once we estimated the ash volume per hectare within each forest type, we multiplied it by the forest area of the respective forest type in each pixel. By doing this, we were able to calculate the total ash volume per pixel. The forest-type areas were computed from a forest cover type map [51]. The total ash volume map was finally rescaled on a 8-km2 grid (Fig. 2) in order to correspond to the Forest Dynamics module (FD). Finally, we computed the total ash volume per pixel, we removed it from the general ”broadleaf” volume used in the original FFSM.

In the second step, we had to broke down the total ash volumes per cell by diameter classes, in order to match the data structure in FD module. Following the example of [52], we assumed that the volume distribution across diameters could be approximated by the 3-parameter Weibull distribution, with the third parameter (representing the minimum diameter) fixed at 7.5 cm. This is the minimum diameter measured in the forest inventory. The parameters were estimated via maximum likelihood for each ecological region using the FNFI data.Footnote 7 The volume within each diameter class was finally derived by multiplying the total ash volume in each pixel by the share of total volume within each diameter class obtained from the cumulative distribution function.

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Petucco, C., Lobianco, A. & Caurla, S. Economic Evaluation of an Invasive Forest Pathogen at a Large Scale: The Case of Ash Dieback in France. Environ Model Assess 25, 1–21 (2020).

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  • Invasive species
  • Forest economics
  • Economic evaluation
  • Hymenoscyphus fraxineus
  • Ash dieback
  • Recursive partial equilibrium model