Last week the second of two papers describing our forest tree regeneration, growth, and harvest simulation model was published in *Ecological Modelling*. These two papers initially started out as a single manuscript, but on the recommendation of a reviewer and the editor at *Ecological Modelling* we split that manuscript into two. That history explains why this second paper to be published focuses on a component of the integrated model we presented a couple of months ago.

There’s a nice overview of the work these two papers contribute to on the MSU Center for System Integration and Sustainability (CSIS) website, and abstracts and citations for both papers are copied at the bottom of this blog post. Here I’ll go into a little bit more detail on the approach to our modelling:

“The model simulates the initial height of the tallest saplings 10 years following gap creation (potentially either advanced regeneration or gap colonizers), and grows them until they are at least 7 m in height when they are passed to FVS for continued simulation. Our approach does not aim to produce a thorough mechanistic model of regeneration dynamics, but rather is one that is sufficiently mechanistically-based to allow us to reliably predict regeneration for trees most likely to recruit to canopy positions from readily-collectable field data.”

In the model we assume that each forest gap contains space for a given number of 7m tall trees. For each of these spaces in a gap, we estimate the probability that it is in one of four states 10 years after harvest:

- occupied by a 2m or taller sugar maple tree (SM)
- occupied by a 2m or taller ironwood tree (IW)
- occupied by a 2m or taller tree of another species (OT)
- not occupied by a tree 2m or taller (i.e., empty, ET)

To estimate the probabilities of these states for each of the gap spaces, given different environmental conditions, we use regression modelling for composition data:

“The gap-level probability for each of the four gap-space states (i.e., composition probabilities) is estimated by a regression model for composition data (Aitchison, 1982 and Aitchison, 1986). Our raw composition data are a vector for each of our empirical gaps specifying the proportion of all saplings with height >2 m that were sugar maple, ironwood, or other species (i.e., SM, IW, and OT). If the total number of trees with height >2 m is denoted by t, the proportion of empty spaces (ET) equals zero if t > n, otherwise ET = (n − t)/n. These raw composition data provide information on the ratios of the components (i.e., gap-space states). The use of standard statistical methods with raw composition data can lead to spurious correlation effects, in part due to the absence of an interpretable covariance structure (Aitchison, 1986). However, transforming composition data, for example by taking logarithms of ratios (log-ratios), enables a mapping of the data onto the whole of real space and the use of standard unconstrained multivariate analyses (Aitchison and Egozcue, 2005). We transformed our composition data with a centred log-ratio transform using the ‘aComp’ scale in the ‘compositions’ package (van den Boogaart and Tolosana-Delgado, 2008) in R (R Development Core Team, 2009). These transformed data were then ready for use in a standard multivariate regression model. A centred log-ratio transform is appropriate in our case as our composition data are proportions (not amounts) and the difference between components is relative (not absolute). The ‘aComp’ transformation uses the centred log-ratio scalar product (Aitchison, 2001) and worked examples of the transformation computation can be found in Tolosana-Delgado et al. (2005).”

One of the things I’d like to highlight here is that the R script I wrote to do this modelling is available online as supplementary material to the paper. You can view the R script here and the data we ran it for here.

If you look at the R script you can see that for each gap, proportions of gap-spaces in the four states predicted by the regression model are interpreted as the probability that gap-space is in the corresponding state. With these probabilities we predict the state of each gap space by comparing a random value between 0 and 1 to the cumulative probabilities for each state estimated for the gap. Table 1 in the paper shows an example of this.

With this model setup we ran the model for scenarios of different soil conditions, deer densities, canopy openness and Ironwood basal area (the environmental factors in the model that influence regeneration). The results for these scenarios are shown in the figure below.

Hopefully this gives you an idea about how the model works. The paper has all the details of course, so check that out. If you’d like a copy of the paper(s) or have any questions just get in touch (email or @jamesmillington on twitter)

Millington, J.D.A., Walters, M.B., Matonis, M.S. and Liu, J. (2013) Filling the gap: A compositional gap regeneration model for managed northern hardwood forests *Ecological Modelling* 253 17–27

doi: 10.1016/j.ecolmodel.2012.12.033

Regeneration of trees in canopy gaps created by timber harvest is vital for the sustainability of many managed forests. In northern hardwood forests of the Great Lakes region of North America, regeneration density and composition are highly variable because of multiple drivers that include browsing by herbivores, seed availability, and physical characteristics of forest gaps and stands. The long-term consequences of variability in regeneration for economic productivity and wildlife habitat are uncertain. To better understand and evaluate drivers and long-term consequences of regeneration variability, simulation models that combine statistical models of regeneration with established forest growth and yield models are useful. We present the structure, parameterization, testing and use of a stochastic, regression-based compositional forest gap regeneration model developed with the express purpose of being integrated with the US Forest Service forest growth and yield model ‘Forest Vegetation Simulator’ (FVS) to form an integrated simulation model. The innovative structure of our regeneration model represents only those trees regenerating in gaps with the best chance of subsequently growing into the canopy (i.e., the tallest). Using a multi-model inference (MMI) approach and field data collected from the Upper Peninsula of Michigan we find that ‘habitat type’ (a proxy for soil moisture and nutrients), deer density, canopy openness and basal area of mature ironwood (*Ostrya virginiana*) in the vicinity of a gap drive regeneration abundance and composition. The best model from our MMI approach indicates that where deer densities are high, ironwood appears to gain a competitive advantage over sugar maple (*Acer saccharum*) and that habitat type is an important predictor of overall regeneration success. Using sensitivity analyses we show that this regeneration model is sufficiently robust for use with FVS to simulate forest dynamics over long time periods (i.e., 200 years).

Millington, J.D.A., Walters, M.B., Matonis, M.S. and Liu, J. (2013) Modelling for forest management synergies and trade-offs: Northern hardwood tree regeneration, timber and deer *Ecological Modelling* 248 103–112

doi: 10.1016/j.ecolmodel.2012.09.019

In many managed forests, tree regeneration density and composition following timber harvest are highly variable. This variability is due to multiple environmental drivers – including browsing by herbivores such as deer, seed availability and physical characteristics of forest gaps and stands – many of which can be influenced by forest management. Identifying management actions that produce regeneration abundance and composition appropriate for the long-term sustainability of multiple forest values (e.g., timber, wildlife) is a difficult task. However, this task can be aided by simulation tools that improve understanding and enable evaluation of synergies and trade-offs between management actions for different resources. We present a forest tree regeneration, growth, and harvest simulation model developed with the express purpose of assisting managers to evaluate the impacts of timber and deer management on tree regeneration and forest dynamics in northern hardwood forests over long time periods under different scenarios. The model couples regeneration and deer density sub-models developed from empirical data with the Ontario variant of the US Forest Service individual-based forest growth model, Forest Vegetation Simulator. Our error analyses show that model output is robust given uncertainty in the sub-models. We investigate scenarios for timber and deer management actions in northern hardwood stands for 200 years. Results indicate that higher levels of mature ironwood (*Ostrya virginiana*) removal and lower deer densities significantly increase sugar maple (*Acer saccharum*) regeneration success rates. Furthermore, our results show that although deer densities have an immediate and consistent negative impact on forest regeneration and timber through time, the non-removal of mature ironwood trees has cumulative negative impacts due to feedbacks on competition between ironwood and sugar maple. These results demonstrate the utility of the simulation model to managers for examining long-term impacts, synergies and trade-offs of multiple forest management actions.