Appendix II. Expected suppression and release under a constant environment

Simulation of expected suppression and release history

A major study result was the observation of a U-shaped history of suppression and release observed among several stands covering a wide geographical area. It is crucial to ascertain that this result is not biased by the fact that we are looking at growth sequences from trees that are a) still alive and b) currently in the sapling size class.

We used saplings that were at least 41-years old. Over time, other saplings that established at a similar time (i.e., more than 40 years prior to sampling) likely died because of heavy suppression, or recruited to the canopy because they grew fast. Therefore, such saplings – although initially present in the seedling/sapling population – are not represented in our sample. A description of such a situation is mentioned in Landis and Peart (2005). Consequently, it is important to assess the null expectation under a constant light environment (i.e., a constant probability of release events).

To verify the pattern we observed was not an artefact of our methodological approach (inherent to such retrospective study), we simulated the process of mortality and recruitment from an initial population of saplings subjected to growth release. More specifically, the question we addressed was: under a constant environment, does the elimination of stems by growth and mortality processes create a history of suppression and release that is not constant over time?

The simulation proceeded as follows:

  1. We created an initial population of 10 000 individuals by sampling with replacement from the distribution of sugar maple and American beech DBH we measured in our 34 stands (range: 2-90 mm).
  2. For each tree, we simulated an independent time series of suppression and release over 40 years. Each year, a canopy gap occurred with a probability of 0.02. A canopy gap lasted for 4 years (to agree with our criteria to detect canopy gaps), but consecutive gaps could make the release episode last longer than 4 years.
  3. We assumed that radial growth was 0.2 mm/year under suppression and 1 mm/year during release (therefore meeting our criteria for detection of major release).
  4. A sapling was recruited to the canopy (adult stage) when its DBH exceeded 90 mm.
  5. We assumed the annual mortality probability was 0.01 during release and 0.10 during suppression. Each year and for each individual, we compared a random number from a uniform distribution to decide if the tree would survive or die. The growth and mortality parameters are within the range of values observed from field studies for sugar maple and American beech (Pacala et al., 1996).
  6. After 40 years, we removed from the population all trees that either died or were recruited during that time.
  7. We removed the first and last 3 years from the time series to avoid bias in the probability of a release event (see the Methods) and compiled for each year the proportion of stems in release. The results are presented on Fig. AII.1.

This simple simulation shows the proportion of stems in release is constant over time despite two strong selection mechanisms (Fig. AII.1). The selection process reduces the average proportion of stems in release (0.11) in comparison to the proportion expected without selection (0.15), but it does not influence the shape of the time series. Simulations with other combinations of parameters for mortality and growth showed this result to be robust to variation in the parameter values. More specifically, we also considered and simulated the following situations: i) without differential growth to focus on mortality; ii) without differential mortality to focus on growth, and iii) with more contrasted differences between suppression and release. We separated the effect of growth and mortality to ensure they are not cancelling each other under a particular parameter setting – the results were the same. Other parameter values did however affect the difference between the expected proportion of stems in release with and without selection, preventing any generalization on the direction of this change.

We conclude the U-shaped pattern in the suppression and release history we observed is robust against these two selection processes. Under a constant environment, a retrospective study is not biased because each individual, at any moment, has the same probability to be released by a canopy gap. The simulations show that the proportion of stems in minor release is however affected by the probability of canopy gap occurrence.

Effect of size on growth release probability

A second source of potential bias in retrospective dendroecological studies is that because measured saplings have been increasing in size over time, they may have gained better access to understory light and therefore benefited from an increased release probability over time (which may have contributed to the right-hand side increase in release proportion in our observed U-shape pattern). Light availability tends to increase with height in the understory of these forests because of understory competition (Beaudet et al., 2004). It is thus possible the stems had an increasing chance of release from understory competition over time simply because of growth. The recent increase of release events we observed could simply result in a change of the hierarchy under a constant environment.

We tested this hypothesis with our dataset by comparing the proportion of largest stems in release over time to the proportion of the smallest stems in release. To do so, we combined the 481 stems from all sites, mixing maple and American beech (the patterns were similar across sites and species – see Results). We divided the data in three groups based on quantiles of their diameter at 20 cm above-ground in 2003. The median diameter was 70.1 mm, the lower 25% limit was 52.1 mm and the upper 75% limit was 87.5 mm. Fig AII.2 illustrates the proportion of stems in minor release for the group of smaller (lower 25%) and larger stems (upper 75%). The stems from the two groups had very similar trends. If a strong size effect did indeed affect the probability of release, we would have expected the largest stems to show a more pronounced increase in proportion of release in 1990-2000. However, this pattern was not observed. Consequently, we are confident that the U-shape pattern we observed is not an artefact of our methods.

Figure AII.1. Proportion of stems under release in the simulated population of saplings subjected to selection by recruitment and mortality. 10 000 stems were simulated and 4157 remained in the final population.

Figure AII.2. Proportion of stems in minor release for groups based on the diameter at 20-cm height in 2003. Small stems correspond to the lower 25% of the size distribution and large stems to the upper 75%.