This is the lit review page for the tree competition paper. See also issue 144.

THE PHYLOGENETIC STRUCTURE OF A NEOTROPICAL FOREST TREE COMMUNITY

How does it measure tree growth?

• It doesn't measure tree growth.

How does it measure neighborhood?

• The authors divide the 50-ha forest plot into non-overlapping square quadrats at four spatial scales:1010 m, 2020m, 5050m, 100100m. At each scale, all trees and shrubs with DBH > 1cm within the same quadrat are considered a community or neighborhood.
• They then calculate the phylogenetic relationships for each neighborhood — specifically mean pairwise phylogenetic distance (MPD) and mean nearest-neighbor phylogenetic distance (MNND). They also simulated randomized communities to compare the null distribution of phylogenetic structure and the observed phylogenetic structure to see if there's significant phylogenetic clustering.

Distinction to our project?

• This paper doesn't define a neighborhood around a focal tree. Its focus is on the phylogenetic patterns of the co-occurring species, instead of the effect of phylogeny on neighboring competition and tree growth.

Latitudinal scaling of aggregation with abundance and coexistence in forests

How (and if) does it measure tree growth?

• It doesn't measure individual tree growth from the size change. Instead, it focuses on population-level demographic processes.

How does it measure neighborhood?

• The neighborhood is defined as all trees within 15m of a focal tree.
• Three indices are computed on each focal tree:
  • Conspecific Crowding (Cof): This counts the number of conspecific neighbors of the focal tree. The contribution (weight) of each neighbor of the same species is calculated as the inverse distance.
  • Heterospecific Crowding (Hof): Same as Cof but calculated on neighbors of a different species than the focal tree.
  • Heterospecific Interaction Crowding: This is an expanded version of Hof. In addition to inverse distance weighting, heterospecifics are also weighted by their relative competitive strength compared to the focal species.
• These indices are then used to determine the survival probability of individual trees

The forestecology R package for fitting and assessing neighborhood models of the effect of interspecific competition on the growth of trees

Main Goal:

Provides methods for fitting and assessing "neighborhood models" to measure the effect of interspecific competition on tree growth. Addresses the lack of a statistical method for the easy application of this model.

Model and Statistical Approach:

Bayesian linear regression model:

$$ y_{ij} = \beta_{0,j} + \beta_{\mathrm{dbh},j}\cdot \mathrm{dbh}{ij} + \sum{k=1}^{K}\lambda_{jk}\cdot x_{ijk}^{\mathrm{comp}} + \epsilon_{ij} $$

How it differs from the $\kappa$ model

• In modeling species-specific effects on tree growth, the forestecology R package fixed a set of competition species identities that will enter the model as predictors. It then fits the model and uses the following permutation test. For each focal species j,

$$ \begin{aligned} H_0 &: \lambda_{jk} = \lambda_j \quad \text{for all } k = 1,\ldots,K \ \text{vs.}\quad \ H_A &: \text{at least one } \lambda_{jk} \text{ is different} \end{aligned} $$

to find out whether it is necessary to make the coefficient of this predictor differ across species. In the κ model, species-specific parameters such as $\beta$, $\gamma$, and $y_0$ are specified based on ecological assumptions, while variation in competitive effects among competitor species is structured through phylogenetic similarity rather than estimated as unrestricted species-pair coefficients.

• In model assessment, forestecology emphasizes out-of-sample predictive performance, using RMSE under spatial cross-validation to account for spatial autocorrelation. By comparison, the current $\kappa$ model analysis emphasizes posterior inference, parameter identifiability, posterior reasonableness, and posterior predictive/retrodictive checks.

• Bayesian computation: forestecology uses a conjugate Bayesian linear regression with closed-form posterior distributions (normal/inverse Gamma conjugacy), whereas the nonlinear structure of the $\kappa$ model requires posterior approximation using HMC/MCMC.

How does it define neighborhood?

• The neighborhood is defined as all trees within a specified distance of a focal tree. (e.g., 7.5m)
• Whether neighbors are conspecific (k=j) or heterospecific (k≠j), they are all treated as 'competitor species k'. The model does not differentiate when calculating $x_{ijk}^{\mathrm{comp}}$; instead, it uniformly sums the numerical explanatory variables (e.g., basal area) of all individuals of the specified competitor species k within the neighborhood.

How does it measure tree growth?

• Average annual change in DBH.

The importance of competition and facilitation for global tree diversity

Main Goal: Quantifying the importance and latitudinal trends of competitive and facilitative interactions among neighboring species.

Method:

• 1. Data collection: Tree census data were obtained from 17 large, permanent forest dynamics plots distributed in latitudes ranging from 5.25° S to 47.20° N. The plot size varies from 15.32 to 60 ha. Plot census methods followed the ForestGEO network’s standard protocol (https://www.forestgeo.si.edu/), which includes all stems ≥1 cm in DBH (1.3 m above the ground). All of the main stems were identified to species, measured, and mapped to their relative spatial coordinates within each plot.
• 2. Latitude Adjustment: To prevent the confounding climate effect caused by the difference in elevation of the 17 forest plots, the latitudes of the plots were adjusted.

$$ \text{Adj.lat} = |\text{real lat}| + \frac{max.elevation + min.elevation} {2 \times 111} $$

• 3. Quantifying Neighborhood Interaction: The Individual Abundance-Area Relationship (IAAR) and Individual Species-Area Relationship (ISAR) were computed to represent the average abundance and richness within a defined region whose diameter equals to 2 around each focal species.
• 4. Defining Relative Interactions: $\text{IAAR}_i0$ and $\text{ISAR}_i0$ for each focal species i is a measurement of baseline or average expected neighborhood abundance and richness. They were calculated from the non-focal trees within the same DBH classes in a defined spatial area. The Relative Neighborhood Abundance (RNA) and the Relative Neighborhood Richness (RNS) is calculated as follows.

$$ \begin{aligned} \text{RNA}_i &= \frac{\text{IAAR}i}{\text{IAAR}{i0}} \ \text{RNS}_i &= \frac{\text{ISAR}i}{\text{ISAR}{i0}} \end{aligned} $$

If $\text{RNA}_i$ or $\text{RNS}_i$ is greater than 1, then this focal species has a facilitative interaction with its neighborhood compared to the null expectation over the whole forest plot. It suggests that the focal species directly or indirectly promotes the establishment, growth, or survival of the other tree species within its neighborhood. Otherwise, if $\text{RNA}_i$ or $\text{RNS}_i$ is less than 1, this focal species has a competitive interaction with its neighborhood.

• 5. Statistical Significance Test: Whether the postive/ neigative neighborhood interaction is statistically significant is evaluated using a local random labelling null model.
• 6. Latitudinal Gradient Analysis: The proportions of facilitative and competitive focal species were computed in each plot. Following that, the analysis was conducted on how the proportions changed across different adjusted latitudinal gradients, often in relation to MAT.

How does it define neighborhood?

• This work defines neighborhood as a circular plot centered on a focal tree. To test robustness, the radii of the circles range from 2m to 16m.
• All conspecific neighbors are used to compute $\text{IAAR}i$ and $\text{IASR}i$. All heterospecific neighbors within the same DBH class as the focal tree are used to compute $\text{IAAR}{i0}$ and $\text{ISAR}{i0}$ in the null model.
• The paper does not differentiate between individual heterospecific species in the overall calculation of IAAR and ISAR or in the null model.

Conclusion:

The focal species that has facilitative neighborhood effects decreases, and equivalently, the species that has competitive neighborhood effects increases from the tropics to higher latitudes. This is consistent with mechanisms such as a decrease in leguminous species, a reduced role of non-AM fungal symbioses, and weaker canopy nursing effects.

Near the equator, there are approximately equal proportions of positive and negative neighborhood interactions.

Mean Annual Temperature (MAT) is strongly correlated with the proportion of positive neighborhood effects, suggesting temperature modulates the importance of facilitation and competition