Forest growth modelling and the 3-PGmix model

There are countless combinations of species, silvicultural treatments, soil and climatic conditions in any given region. Often foresters are interested in situations that do not currently exist, e.g. novel species combinations, new climatic conditions, new silvicultural treatments. Therefore, forest growth and yield models are required to predict forest dynamics while we wait for actual empirical results from long-term experiments. Surprisingly, very few studies have examined whether the predicted effects of species interactions on forest functions (e.g. growth) are correlated with measurements. A review of more than 50 forest growth models found that while many models are used to predict the growth of mixtures, their ability to predict how different species will interact has rarely been tested against actual measurements of those mixing effects (5). There have also been very few studies that examined whether predicted growth of different size or age cohorts within uneven-aged forests correspond with measurements (14). If we assume that there are no interactions between tree species, age classes or size classes, we can simply model the even-aged monocultures of each species, size class or age class and then calculate the functioning of the whole stand as a weighted average (e.g. by species contribution to stand basal area) of those even-aged monocultures. However, there are often significant departures from the weighted average (3) and these mixing effects can make the mixture more attractive than monocultures to foresters. The ability of forest growth models to accurately predict mixing effects or the growth of different size classes within uneven-aged forests, has very rarely been validated, and this was the aim of this project.

While there are many empirical models that have been used to predict mixing effects, empirical models require large data sets to build and are restricted to the species combinations, silvicultural treatments, soil and climatic conditions where they were developed. Therefore they are less likely to be appropriate to use for new climatic or silvicultural conditions, or different species combinations or proportions (5).

Alternatively, there are detailed tree-level, process-based models that have the potential to predict mixing effects (5). However, these are relatively complex and can require detailed and expensive physiological data to parameterise and validate. The calculations done at the leaf or tree levels can lead to errors that are propagated when upscaling to the stand level. With tree-level models (empirical and process-based), it is also difficult to account for all processes that strongly influence tree-level growth. For example, and individual trees growth is strongly influenced by the soil resources and light conditions within its immediate neighbourhood, which may differ greatly from the mean conditions of the whole stand. This is rarely considered in tree level models, which often consider resource availability at the stand level (e.g. mean site conditions), or use proxies such as neighbourhood indices that have rarely been shown to correlate with local soil resource availability in the way that appears to be assumed for the tree level models. The effects of spatial heterogeneity of resources are further complicated because of the plasticity of tree crown (and root) positioning relative to the base of the tree trunk. These issues could be avoided by using stand level models when the desired outputs are at lower temporal (months or years) or spatial (stands) resolutions, such as those often required by foresters (7,14).

The 3-PG_mix model (freely available as an R package (11) or as an Excel file from here)

As a compromise between empirical models and complex process-based models, several stand-level process based models have been developed that replace complex leaf- or tree-level physiological relationships with simpler stand-level (and sometimes more empirical) relationships. This can reduce data input and parameterisation requirements and provide outputs at the desired resolution without any need to scale up. This compromise makes them attractive as management tools. One such model is the forest growth model 3-PG (Physiological Principles Predicting Growth). For more details about 3-PG go here. It has been used in many different types of forests, and critically, it has been validated for all the processes it considers, such as growth, biomass partitioning, light absorption, water balance, responses to CO₂, diameter distributions and mortality. It may seem obvious that a model needs to be validated thoroughly in this way, but surprisingly, many models have only been tested for their ability to predict growth or mortality, and not for all of the other processes that the given model calculates before it can predict growth and mortality.

3-PG was originally designed for even-aged monospecific forests. We therefore extended its capacity, in the form of 3-PG_mix, to mixed-species (7) and uneven-aged forests (14). The main change required was to develop a light absorption sub-model (3,4) that was capable of predicting the light absorbed by different species within a mixture. This sub-model also needed to work for any stand density, from open grown trees to closed canopy stands. The new light absorption sub-model has been tested in a wide range of forest types, in terms of species compositions, stand densities and stand structures, in Australia, Brazil, Vietnam, China and Germany (4). Additional modifications made to 3-PG_mix allowed for within-canopy vertical gradients in climate for the water balance sub-model and it was also adapted for deciduous species and to predict diameter distributions (7).

The 3-PG_mix model was initially parameterised, calibrated and validated for subtropical forests in China and tested for its ability to reproduce spatial and temporal dynamics of mixtures (7). Very few models have been tested for their ability to predict mixing effects. Therefore, predictions of mixing effects from 3-PG_mix were compared with empirical measurements of mixing effects from Pinus sylvestris and Fagus sylvatica mixtures distributed across Europe (8) and mixtures of Pinus sylvestris and Quercus robur in the Netherlands (12). 3-PG_mix has also been validated for a range of uneven-aged forests (14) in Switzerland, and parameter sets for 12 common European tree species have been developed (13).

The 3-PG_mix model is described in detail in 7. A more detailed description, published parameter sets (including new sets for European species; 13), and information about measurements needed to calculate each parameter or input/output variable can be found in the documentation here. 3-PG_mix is freely available as an Excel file from here and as an R package (11). To visit the official 3-PG website, click here.

These are examples of the forests where the 3-PG_mix model was developed. The monocultures (above) were used to parameterise and calibrate the model before validating it using the mixtures (below).

Journal articles related to this project:

1. Miehle, P., Battaglia, M., Sands, P.J., Forrester, D.I., Feikema, P.M., Livesley, S.J., Morris, J.D., Arndt, S.K. (2009). A comparison of four process-based models and a statistical regression model to predict growth of Eucalyptus globulus plantations. Ecological Modelling 220, 734-746. doi:10.1016/j.ecolmodel.2008.12.010

2. Binkley, D., Campoe, O. C., Gspaltl, M., Forrester, D.I. (2013). Light absorption and use efficiency in forests: Why patterns differ for trees and forests. Forest Ecology and Management. 288, 5-13. doi:10.1016/j.foreco.2011.11.002

3. Forrester, D.I. (2014). A stand-level light interception model for horizontally and vertically heterogeneous canopies. Ecological Modelling. 276, 14-22. doi:10.1016/j.ecolmodel.2013.12.021

4. Forrester, D.I., Guisasola, R., Tang, X., Albrecht, A.T., Dong, T.L., le Maire, G. (2014). Using a stand-level model to predict light absorption in stands with vertically and horizontally heterogeneous canopies. Forest Ecosystems. 1, 17 doi:10.1186/s40663-014-0017-0

5. Pretzsch, H., Forrester, D.I., Rötzer, T. (2015). Representation of species mixing in forest growth models. A review and perspective. Ecological Modelling 313, 276-292. doi:10.1016/j.ecolmodel.2015.06.044

6. Guisasola, R., Tang, X., Bauhus, J., Forrester, D.I. (2015). Intra- and inter-specific differences in crown architecture in Chinese subtropical mixed species forests. Forest Ecology and Management 353, 164-172. doi:10.1016/j.foreco.2015.05.029

7. Forrester, D.I., Tang, X. (2016). Analysing the spatial and temporal dynamics of species interactions in mixed-species forests and the effects of stand density using the 3-PG model. Ecological Modelling. 319, 233-254. doi:10.1016/j.ecolmodel.2015.07.010

8. Forrester, D.I., Ammer, C., Annighöfer, P.J., Avdagic, A., Barbeito, I., Bielak, K., Brazaitis, G., Coll, L., Río, M.d., Drössler, L., Heym, M., Hurt, V., Löf, M., Matović, B., Meloni, F., Ouden, J.d., Pach, M., Pereira, M.G., Ponette, Q., Pretzsch, H., Skrzyszewski, J., Stojanović, D., Svoboda, M., Ruiz-Peinado, R., Vacchiano, G., Verheyen, K., Zlatanov, T., Bravo-Oviedo, A., (2017) Using the 3-PGmix model to predict the spatial and temporal dynamics of species interactions in Fagus sylvatica and Pinus sylvestris forests across Europe. Forest Ecology and Management 405, 112-133. doi:10.1016/j.foreco.2017.09.029

9. Trotsiuk, V., Hartig, F., Cailleret, M., Babst, F., Forrester, D.I., Baltensweiler, A., Buchmann, N., Bugmann, H., Gessler, A., Gharun, M., Minunno, F., Rigling, A., Rohner, B., Stillhard, J., Thuerig, E., Waldner, P., Ferretti, M., Eugster, W., Schaub, M. (2020). Assessing the response of forest productivity to climate extremes in Switzerland using model-data fusion. Global Change Biology 26, 2463-2476 doi:10.1111/gcb.15011

10. Forrester, D.I., Trotsiuk, V., Mathys, A.S., (2020). 3-PG: ein physiologisches Waldwachstumsmodell. Schweizerische Zeitschrift fur Forstwesen 171, 158-164.

11. Trotsiuk, V., Hartig, F., Forrester, D.I., (2020). r3PG – an R package for simulating forest growth using the 3-PG process-based model. Methods in Ecology and Evolution. 11, 1470-1475. doi:10.1111/2041-210X.13474

12. Bouwman, M., Forrester, D.I., Ouden, J.d., Nabuurs, G.-J., Mohren, G.M.J., (2021). Species interactions in mixed stands of Pinus sylvestris and Quercus robur in the Netherlands: competitive dominance shifts in favor of P. sylvestris under projected climate change. Forest Ecology and Management, 481, 118615. doi:10.1016/j.foreco.2020.118615

13. Forrester, D.I., Hobi, M.L., Mathys, A.S., Stadelmann, G., Trotsiuk, V., (2021). Calibration of the process-based model 3-PG for major central European tree species. European Journal of Forest Research. 140, 847-868 doi:10.1007/s10342-021-01370-3

14. Forrester, D.I., Mathys, A.S., Stadelmann, G., Trotsiuk, V., 2021. Effects of climate on the growth of Swiss uneven-aged forests: combining > 100 years of observations with the 3-PG model. Forest Ecology and Management 494, 119271. doi:10.1016/j.foreco.2021.119271

15. Trotsiuk, V., Babst, F., Grossiord, C., Gessler, A., Forrester, D.I., Buchmann, N., Schaub, M., Eugster, W., (2021). Tree growth in Switzerland is increasingly constrained by rising evaporative demand. Journal of Ecology 109, 2981-2990 doi:10.1111/1365-2745.13712

16. Serrano-León, H., Nitschke, R., Scherer-Lorenzen, M., Forrester, D.I., (in press). Intra-specific leaf trait variability of Fagus sylvatica, Quercus petraea and Picea abies in response to inter-specific competition and implications for forest functioning. Tree Physiology. doi:10.1093/treephys/tpab109

17. Forrester, D.I., Schmid, H., Nitzsche, J., (in press). Growth and structural changes in Swiss uneven-aged forests over 100 years, and comparisons between 15 uneven-aged forest types of Europe, North America and Australia. Forestry. doi:10.1093/forestry/cpab042