Christian Frølund Damgaard’s research while affiliated with Aarhus University and other places

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Publications (6)


The Lorenz curves (A,C) and their rotated and right-shifted forms (B,D). xc′,yc′ (the blue open circle) in panels (A,C) is the point of tangency at which the tangent of the Lorenz curve is parallel to the egalitarian line through the points (0, 0) and (1, 1). The dashed line through the two points (0, 1) and (1, 0) is defined as the axis of symmetry. Panels (B,D) exhibit the rotated and right-shifted Lorenz curves, which can be described by the performance equation. xc, yc is the maximum value point of the performance curve, which is obtained by rotating xc′,yc′ counterclockwise by 3/4π and shifting it to the right by 2. In panels (B,D), AL represents the area of the region formed by the performance’s left part and the x-axis, and AR represents the area of the region formed by the performance’s right part and the x-axis.
Box plot of the adjusted root-mean-square errors (Equation (8)) of the performance equation fit to the 480 shoots. Here, the vertical dashed line represents the value of 0.05.
Fitted results for an individual shoot (the 223rd shoot) of S. chinensis using the performance equation. Panel (A) shows the comparison of the observations and the predicted original Lorenz curve, and the 45° straight line represents the egalitarian line; panel (B) shows the comparison of the observations and the predicted Lorenz curve after being rotated and right-shifted. The closed circles represent the observations, and the red curve represents predicted values; the open circle represents the point of tangency in panel (A), or the maximum value point of the performance curve in panel (B). In panel (A), the letters c, K1, and K2 with hats represent the estimated parameters of the performance equation; RMSEadj represents the adjusted root-mean-square error; and n represents the number of leaves on the individual shoot. The Gini coefficient is estimated as double the area of the region between the performance curve (i.e., the red curve in panel (B)) and the x-axis.
Distributions of three asymmetry measures (S, PL, and PA) for the Lorenz curves (A–C), and the Gini coefficients (D) for the 480 S. chinensis shoots. “Mean” and “Median” represent the mean and median, respectively; CV is the coefficient of variation; and p is the probability that the data are consistent with the null hypothesis of a normal distribution.
Linear fit to the two asymmetry measures (PA versus PL). The open circles represent the observations; CIintercept represents the 95% confidence interval of the intercept; CIslope represents the 95% confidence interval of the slope; r² is the coefficient of determination of the linear fitting; and N is the sample size, i.e., the total number of shoots.
Re-Expression of the Lorenz Asymmetry Coefficient on the Rotated and Right-Shifted Lorenz Curve of Leaf Area Distributions
  • Article
  • Full-text available

April 2025

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12 Reads

Yongxia Chen

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Feixue Jiang

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Christian Frølund Damgaard

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Jacob Weiner

The Gini coefficient, while widely used to quantify inequality in biological size distributions, lacks the capacity to resolve directional asymmetry inherent in Lorenz curves, a critical limitation for understanding skewed resource allocation strategies. To address this, we extend our prior geometric framework of the rotated and right-shifted Lorenz curve (RRLC) by introducing two original asymmetry metrics: the positional shift ratio (PL, defined as xc/2, where xc is the x-coordinate of the RRLC’s maximum value point) and the area ratio (PA, defined as AL/(AL + AR), where AL and AR denote the areas under the left and right segments of the RRLC). These indices uniquely dissect contributions of dominant versus small individuals to overall inequality, with PL reflecting the peak position of the RRLC and PA quantifying the area dominance of its left segment. Theoretically, PL directly links to the classical Lorenz asymmetry coefficient S (defined as S=xc′+yc′, where xc′,yc′ is the tangent point on the original Lorenz curve with a 45° slope) through S = 2 − 2PL, bridging geometric transformation and parametric asymmetry analysis. Applied to 480 Shibataea chinensis Nakai shoots, our analysis revealed that over 99% exhibited pronounced left-skewed distributions, where abundant large leaves drove the majority of leaf area inequality, challenging assumptions of symmetry in plant canopy resource allocation. The framework’s robustness was further validated by the strong correlation between PA and PL. By transforming abstract Lorenz curves into interpretable bell-shaped performance curves, this work provides a novel toolkit for analyzing asymmetric size distributions in ecology. The proposed metrics can be applied to refine light-use models, monitor phenotypic plasticity under environmental stress, and scale trait variations across biological hierarchies, thereby advancing both theoretical and applied research in plant ecology.

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The effect of nitrogen on the growth of Calluna vulgaris and Avenella flexuosa in a dune heath ecosystem: competition and frequency-dependence

September 2024

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7 Reads

Nitrogen was manipulated in a dune heath ecosystem and using time-series pin-point data it was demonstrated that both Lotka-Volterra type interspecific competition and frequency dependency play significant roles in determining plant growth. For modelling simplicity, plant taxa were divided into heather, wavy hair-grass, and all other vascular species. Significant interspecific competition was observed among all species, except wavy hair-grass on the growth of all other vascular species, and nitrogen addition was found to increase the competitive effect of heather on the growth of all other vascular species. Both heather and wavy hair-grass showed positive feedback dynamics on growth when they were relatively dominant at the plot scale and the effect increased with added nitrogen. Such positive feedback dynamics may lead to the formation of patches, which are a characteristic feature of heath ecosystems. Oppositely, there was a beneficial effect of being relatively rare on the growth of all other vascular species in plots with added nitrogen. The study highlights the importance of the combined effects of interspecific competition and frequency dependency in regulating plant communities, and consequently undermine both theoretical and empirical conclusions of modern coexistence theory.


Overview of vegetation plots (black dots), showing their distribution in Denmark. Because of lacking satellite data on the date selected for this study, islands including Zealand and Bornholm (the right-most parts of the country) are missing from the plot data. Green dots and numbers mark the location of the examples shown in Figure 3.
Predicted vs. actual values (purple circles) for the average Ellenberg indicator values (EIVs [21]) from the validation plots (n = 28,017). The dotted line shows where perfect predictions would be. F, N, and R: EIVs for plants’ preferences for soil moisture, fertility, and pH, respectively.
Actual (colored dots) mean Ellenberg indicator values (EIVs) for soil moisture (F), fertility (N), pH (R), and the nutrient ratio (N/R). Blue error bars show the absolute prediction error for each plot for the model including both satellite data and habitat type as predictors. The red lines connect the error bars to their respective dot. The location of the examples is marked on Figure 1 with numbers. Example 1 (i.e., first column of panels) is from Tversted in northern Jutland, example 2 is from Fuglbæk in western Jutland, and example 3 is from Otterup on Funen. The scales are 1:10,000, 1:5000, and 1:2800, respectively, for the three examples (when viewed or printed in original figure size).
Overview of the input data used for modelling. Res.: resolution, Quant.: quantity.
Predicting Abiotic Soil Characteristics Using Sentinel-2 at Nature-Management-Relevant Spatial Scales and Extents

August 2024

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29 Reads

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1 Citation

Knowledge of local plant community characteristics is imperative for practical nature planning and management, and for understanding plant diversity and distribution drivers. Today, retrieving such data is only possible by fieldwork and is hence costly both in time and money. Here, we used nine bands from multispectral high-to-medium resolution (10–60 m) satellite data (Sentinel-2) and machine learning to predict local vegetation plot characteristics over a broad area (approx. 30,000 km²) in terms of plants’ preferences for soil moisture, soil fertility, and pH, mirroring the levels of the corresponding actual soil factors. These factors are believed to be among the most important for local plant community composition. Our results showed that there are clear links between the Sentinel-2 data and plants’ abiotic soil preferences, and using solely satellite data we achieved predictive powers between 26 and 59%, improving to around 70% when habitat information was included as a predictor. This shows that plants’ abiotic soil preferences can be detected quite well from space, but also that retrieving soil characteristics using satellites is complicated and that perfect detection of soil conditions using remote sensing—if at all possible—needs further methodological and data development.


Figure 1. Overview of vegetation plots, showing their distribution in Denmark. Because of lacking satellite data on the date selected for this study, Zealand including islands and Bornholm (the rightmost parts of the country) are missing from the plot data. Green dots and numbers mark the location of the examples shown in Figure 3.
Modelling results and characteristics for each response (columns) and each selected model (rows). F, N and R: EIVs for plants' preferences for soil moisture, nutrients and reaction (pH) respectively. Std.: Standard deviation, GBT: Gradient boosted trees, RF: Random forest, DT: Decision tree, NN: Nearest neighbors, LR: Linear regression.
Predicting Abiotic Soil Characteristics Using Sentinel-2 at Nature-Management-Relevant Spatial Scales and Extent

May 2024

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12 Reads

Knowledge of local plant community characteristics is imperative for practical nature planning and management, and for understanding plant diversity and distribution drivers. Today, retrieving such data is only possible by fieldwork and is hence costly both in time and money. Here we used 9 bands from multispectral high-to-medium resolution (10–60 m) satellite data (Sentinel-2) and machine learning to predict the local vegetation plot characteristics at broad extent (approx. 30.000 km2) in terms of plants’ preferences for soil moisture, soil fertility, and pH, mirroring the levels of the corresponding actual soil factors. These factors are believed to be among the most important for local plant community composition. Our results showed that there are clear links between the Sentinel-2 data and plants abiotic soil preferences and using solely satellite data we achieved predictive powers between 26–59% improving to about 70% when habitat information was included as a predictor. This show that plants abiotic soil preferences can be detected quite well from space, but also that retrieving soil characteristics using satellites is complicated and that perfect detection of soil conditions using remote sensing – if at all possible – needs further methodological and data development.



How Do Nitrogen Deposition, Mowing, and Deer Grazing Drive Vegetation Changes on Dune Heaths?

February 2024

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45 Reads

Ecologies

Heathland vegetation has undergone significant changes in the past century, e.g., due to airborne pollutants and a lack of proper management. Understanding the interactions between these factors in combination is pivotal for heathland conservation. Here, we studied the vegetation changes at a dune heath in a four-year manipulation experiment analysing the combined effects of nitrogen deposition, mowing, and deer grazing. Our results showed no significant effect of nitrogen deposition and deer grazing on plant growth and cover of dwarf shrubs within the experimental plots. However, high loads of nitrogen decreased bryophyte cover and increased the growth and cover of sand sedge Carex arenaria L. Mowing adversely affected the dwarf shrub community, e.g., the dwarf shrub species crowberry Empetrum nigrum L., and facilitated increased cover and plant growth of graminoids. Plant growth and the cover of C. arenaria increased in plots without deer grazing, whereas bryophyte cover decreased significantly without grazing. We do not recommend intensive mowing of vegetation as a conservation method for dune heaths because it promotes graminoids. From a conservation aspect, it is essential to consider the effect of deer on heathlands because they both impede some species and benefit others and mitigate the adverse effects of nitrogen deposition on dune heaths.

Citations (2)


... Generally, the use of NDVI to explain vegetation change is hindered by the fact that vegetation change itself may affect the measured NDVI, especially in ecosystems that are dominated by few plant species. However, using satellite data it was possible to predict the observed Ellenberg N values across several habitat types (Moeslund and Damgaard 2024), which corroborate the current finding that satellite data encompass important signals that are associated with general ecological processes. ...

Reference:

Identifying causal factors underlying vegetation changes in wet heathlands
Predicting Abiotic Soil Characteristics Using Sentinel-2 at Nature-Management-Relevant Spatial Scales and Extents

... They also represent a group of insects that include some of the potentially most destructive invasive species [2]. As ants affect the flow of material and energy within ecosystems, ant behaviours may have cascading effects on soil structure and other animals and plants [3][4][5]. Their ecological importance has fuelled the development of numerous monitoring methods attempting to quantify their abundance in natural settings. Methods include different soil extraction techniques (sifting, aspirators, Berlese-Tullgren funnels, Winkler funnels, etc.), baiting, and various forms of traps [6,7]. ...

Effects of ant mounts (Formica exsecta) on subsoil properties, in a heathland
  • Citing Article
  • March 2024

European Journal of Soil Biology