Seminar 4 - Neighborhood competition C. D. Canham Seminar 4 Mechanism vs. phenomenology in choosing functional forms: neighborhood analyses of tree competition Likelihood Methods in Forest Ecology October 9th – 20th , 2005

Seminar 4 - Neighborhood competition C. D. Canham Key References Canham, C. D., P. T. LePage, and K. D. Coates. 2004. A neighborhood analysis of canopy tree competition: effects of shading versus crowding. Canadian Journal of Forest Research 34:778-787. Uriarte, M, C. D. Canham, J. Thompson, and J. K. Zimmerman. 2004. A maximum-likelihood, neighborhood analysis of tree growth and survival in a tropical forest. Ecological Monographs 74:591-614. Canham, C. D., M. Papaik, M. Uriarte, W. McWilliams, J. C. Jenkins, and M. Twery. 2006. Neighborhood analyses of canopy tree competition along environmental gradients in New England forests. Ecological Applications 16:540-554. Papaik, M. J. and C. D. Canham. Tree competition along environmental gradients in southern New England forests: An application of multi-model inference. Ecological Applications, in press.

Spatially-explicit, neighborhood analysis of tree growth Seminar 4 - Neighborhood competition C. D. Canham Spatially-explicit, neighborhood analysis of tree growth where Competition, Size and Site are “Multipliers” (0-1) that reduce Maximum Potential Growth… Why we did this -- we initially included site term just to factor it out so that it didn’t obscure the competition signal, but then we discovered that the site effects were just as interesting...

Seminar 4 - Neighborhood competition C. D. Canham Forest Inventory and Analysis (FIA) Plots in Vermont and New Hampshire Old 1/5 or 1/6 acre plot (49’ or 52.7’ radius) “Observations” = trees in new plot that were present in previous census Censused 1982-83 neighborhood search radius = 24’ For the past few years, we have been exploring the use of the extraordinary resource offered by the USDA FIA system of forest plots across the US. The plots have been used by ecologists as a source of inventory data for carbon studies, but the datasets can also be used for much more mechanistic studies. I’m not going to try to describe the FIA network in any detail, but for present purposes I will point out that for this talk, we have used the data for the 2 most recent censuses from the states of Vermont and New Hampshire. The most recent censuses (1996-98) use the new plot design with a set of 4 24 ‘ radius subplots, one of which is centered over the older, larger ~ 50’ radius plot from the previous census in 1982-83. For our purposes, this means we have growth data on all trees within the new 24 ‘ radius plot, and for each of those trees, we have a tally of all neighbors present at the beginning of the census period in at least a 24’ radius around each tree... There are over 1200 plots in the 2 states, but for our purposes, we selected plots that were in “FOREST-LAND” land-use categories, and that had not been logged during the census interval.. New 24’ radius plot (census all stems > 5”) Censused 1996-98 Selected plots in “forest land” land-use classes that were not logged during the census period (n = 802 plots)

Competitive “Effect”: A Neighborhood Competition Index (NCI) Seminar 4 - Neighborhood competition C. D. Canham Competitive “Effect”: A Neighborhood Competition Index (NCI) A simple size and distance dependent model: For j = 1 to n individuals of i = 1 to s species within a fixed search radius allowed by the plot size So I will only briefly describe our attempt to factor in competition – we follow the long tradition in forestry of calculating simple distance and density dependent competition indices that quantify the effects of neighbors on a target tree... I will say that one of the neatest things about these analyses is that they allow us to empirically quantify the competition coefficients that have played such a central role in the development of ecological theory, but that have proven to be very difficult to estimate, particularly for long-lived species such as trees... = species-specific competition coefficient (scaled to = 1 for the species with strongest competitive effect) NOTE: NCI is scaled to = 1 for the most crowded neighborhood observed for a given target tree species

Competitive “Response”: Relationship Between NCI and Growth Seminar 4 - Neighborhood competition C. D. Canham Competitive “Response”: Relationship Between NCI and Growth The maroon curve would represent a forester’s dream...

Effect of target tree size on sensitivity to competition Seminar 4 - Neighborhood competition C. D. Canham Effect of target tree size on sensitivity to competition

Effect of Tree Size (DBH) on Potential Growth Seminar 4 - Neighborhood competition C. D. Canham Effect of Tree Size (DBH) on Potential Growth Lognormal function, where: X0 = DBH at maximum potential growth Xb = variance parameter

Effect of Site Quality on Potential Growth Seminar 4 - Neighborhood competition C. D. Canham Effect of Site Quality on Potential Growth Alternate hypotheses from niche theory: Fundmental niche differentiation (Gleason, Curtis, and Whittaker): species have optimal growth (fundamental niches) at different locations along environmental gradients Shifting competitive hierarchy (Keddy): all species have optimal growth at the resource-rich end of a gradient, their realized niches reflect competitive displacement to sub-optimal ends of the gradient In all fairness – these two models are normally used at different scales: Whittaker (and Curtis) at broad geographic scales along major environmental gradients, while Keddy’s model is usually invoked in cases of co-occurrence of species along shorter gradients

Whittaker (fundamental niche differentiation) Seminar 4 - Neighborhood competition C. D. Canham Whittaker (fundamental niche differentiation) Normal function NOTE: Bivariate normal function can be used to test for effects of two environmental factors simultaneously (x is the axis score, and Xo and Xb are estimated)

Keddy (shifting competitive hierarchy) Seminar 4 - Neighborhood competition C. D. Canham Keddy (shifting competitive hierarchy) Logistic function (x is the axis score, and Xo and Xb are estimated) Bivariate form used to test for response to 2 axes simultaneously

What can we use as measures of site quality? Seminar 4 - Neighborhood competition C. D. Canham What can we use as measures of site quality? Direct measures of site conditions are limited i.e., physiographic class data Instead, use multivariate analyses of vegetation composition to produce an ordination that captures the effects of environmental gradients on trees in a given plot… detrended correspondence analysis (DECORANA)

Seminar 4 - Neighborhood competition C. D. Canham Detrended Correspondence Analysis of FIA Plots in VT and NH red crosses = species black circles = plots no obvious clustering into a few, discrete community types… DCA AXIS 2 DCA1 DCA2 Eigenvalues 0.69 0.54 Axis lengths 4.02 4.52 DCA AXIS 1

Seminar 4 - Neighborhood competition C. D. Canham DCA AXIS 1 DCA AXIS 2 XERIC MESIC LOW HIGH Soil Moisture Soil Fertility

Seminar 4 - Neighborhood competition C. D. Canham The full model (for any given species)... Radial growth = Maximum growth * site effect * size effect * competition effect Where: MaxRG is the estimated, maximum potential growth g = ordination axis score for the plot containing tree t, and Go and Gb are estimated parameters DBHt is the size of the target tree, and Xo and Xb are estimated parameters DBHij and distij are the size and distance to neighboring tree j of species group i, and C, D, ls and g are estimated parameters

Seminar 4 - Neighborhood competition C. D. Canham Relative Abundance – Live Trees target tree species Didn’t analyze white cedar because it occurs on such a limited range of sites, with very few other species as neighbors

A sample of basic questions addressed by the analyses Seminar 4 - Neighborhood competition C. D. Canham A sample of basic questions addressed by the analyses Do different species of competitors have distinctly different effects? How do neighbor size and distance affect degree of crowding? Are there thresholds in the effects of competition? Does sensitivity to competition vary with target tree size? How does potential growth vary along environmental gradients? Are species most abundant in the sites where they perform the best in the absence of competition? What is the underlying relationship between potential growth and tree size (i.e. in the absence of competition)?

Parameter Estimation and Comparison of Alternate Models Seminar 4 - Neighborhood competition C. D. Canham Parameter Estimation and Comparison of Alternate Models Maximum likelihood parameters estimated using simulated annealing (a global optimization procedure) Start with a “full” model, then successively simplify the model by dropping terms Compare alternate models using Akaike’s Information Criterion, corrected for small sample size (AICcorr), and accept simpler models if they don’t produce a significant drop in information. i.e. do species differ in competitive effects? compare a model with separate λ coefficients with a simpler model in which all λ are fixed at a value of 1

PDF and Error Distribution Seminar 4 - Neighborhood competition C. D. Canham PDF and Error Distribution Residuals were approximately normal, but variance was not homogeneous (it appeared to increase as a function of the mean predicted growth)... So, I fitted the models using the assumption that the residuals were normally distributed, but with a variance that was a linear function of the mean. Maximum likelihood estimates of a and b were determined as part of the optimization

Seminar 4 - Neighborhood competition C. D. Canham Analysis Summary Sufficient sample sizes for analysis of the 14 most common tree species (n = 53 – 930 target trees per species) Overall model fits generally poor (growth is noisy and unpredictable) (R2 = 0.125 – 0.351) 8 of the 14 species showed significant variation in potential growth along at least 1 of the 2 ordination axes

Seminar 4 - Neighborhood competition C. D. Canham Comparison of Models AICcorr of models with alternate forms for the effects of Axis 1 and Axis 2 (Gaussian vs. Logistic)

Comparison of Models (continued) Seminar 4 - Neighborhood competition C. D. Canham Comparison of Models (continued) AICcorr of models with and without gamma (effect of target tree DBH on sensitivity to competition)

How do neighbor size and distance affect degree of crowding? Seminar 4 - Neighborhood competition C. D. Canham How do neighbor size and distance affect degree of crowding? α mean value: 1.8 (range : 0.6 – 4.0) So, effects of neighbors on growth are roughly proportional to the neighbors’ basal area and biomass β mean value: 0.3 (range : 0 – 0.6) So, effects of neighbors on growth decline slowly with distance

Are there thresholds in the effects of competition on growth? Seminar 4 - Neighborhood competition C. D. Canham Are there thresholds in the effects of competition on growth? D = 5 D = 3 D =1 Basically NO: Simple negative exponential model was the most parsimonious fit for all of the species except black birch (i.e. D parameter = 1)

Do target tree species differ in their response to competition? Seminar 4 - Neighborhood competition C. D. Canham Do target tree species differ in their response to competition?

Does the size of the target tree affect its sensitivity to crowding? Seminar 4 - Neighborhood competition C. D. Canham Does the size of the target tree affect its sensitivity to crowding? Models including g were more likely for 6 of the 14 species: ABBA, ACRU, BEAL, PIST, POTR, and QURU mean value: –1.6 (range –1.1 to –1.9) White Pine So, smaller trees of these 6 mid- to early successional species are much more sensitive to competition than are larger trees…

How does potential growth vary with target tree size (DBH)? Seminar 4 - Neighborhood competition C. D. Canham How does potential growth vary with target tree size (DBH)? Potential growth = growth in absence of competition, and in optimal environment

Seminar 4 - Neighborhood competition C. D. Canham Does potential growth vary along the environmental gradients represented in the ordination? Compare alternate models (for each of the 14 target species) with: Gaussian or logistic variation along both axes Gaussian or logistic variation along the axis with the strongest effect No axes Choose the model with the lowest AICcorr (i.e. the least loss of information using the fewest parameters)

Results: Variation in Potential Growth along the Moisture Gradient Seminar 4 - Neighborhood competition C. D. Canham Results: Variation in Potential Growth along the Moisture Gradient

Variation in Potential Growth along the Fertility Gradient Seminar 4 - Neighborhood competition C. D. Canham Variation in Potential Growth along the Fertility Gradient

Shade tolerant species – fertility gradient Seminar 4 - Neighborhood competition C. D. Canham Do species grow best in the sites where they are most abundant? Shade tolerant species – fertility gradient dots = relative abundance in each of the plots line = estimated potential growth (in absence of competition) Note: similar pattern for shade tolerant species along the moisture gradient (Axis 1)

Fertility Gradient:Shade intolerant species Seminar 4 - Neighborhood competition C. D. Canham Fertility Gradient:Shade intolerant species

Seminar 4 - Neighborhood competition C. D. Canham Moisture Gradient – Shade tolerant Species

Seminar 4 - Neighborhood competition C. D. Canham Moisture Gradient Shade intolerant Species

Summary of niche patterns Seminar 4 - Neighborhood competition C. D. Canham Summary of niche patterns Fundamental niches: The individualistic hypothesis survives: species show optimal growth at different points along resource gradients... Realized niches: Shade tolerant species appear to reach greatest abundance in sites where they have highest potential growth Less tolerant species consistently displaced to lower ends of the 2 gradients

Seminar 4 - Neighborhood competition C. D. Canham Are different species of competitors equivalent in their effects on a given tree species? Compare 4 alternate models: “Full” model: separate competition coefficients (l) for all common species of neighbors (grouping rare species into an “other” species category) “Mixed” model: group interspecific competitors into weak, intermediate, and strong competitors, based on results of “full” model “Intra- vs. Interspecific” model: lump all interspecific competitors into 1 group, with a separate l for intraspecific competitors “Equivalent” model: set l = 1 for all species of neighbors

Seminar 4 - Neighborhood competition C. D. Canham Model Comparisons

The matrix of estimated competition coefficients (l) Seminar 4 - Neighborhood competition C. D. Canham The matrix of estimated competition coefficients (l)

Seminar 4 - Neighborhood competition C. D. Canham What species have the strongest and weakest per capita competitive effect on sugar maple? Weak competitors (l < 0.2): red maple and eastern white pine Strong Competitors (l > 0.8): balsam fir and beech Strongest Competitor (l = 1.0): other sugar maples

Seminar 4 - Neighborhood competition C. D. Canham Are species that co-occur in the same environments strong competitors with each other? Compared the average distance between pairs of species “centroids” in the ordination with the strength of competition between the two species Bottom line: no obvious pattern... Strong competitors were not necessarily either close to or far away from each other in ordination space... Ditto for weak competitors...

Seminar 4 - Neighborhood competition C. D. Canham Limitations Analysis ignores effects of crowding by trees smaller than 5” DBH changes in neighborhood during the census interval Scarcity of large trees and truly all-aged stands in the landscape

Results from temperate coniferous forests of British Columbia Seminar 4 - Neighborhood competition C. D. Canham Results from temperate coniferous forests of British Columbia AICcorr of alternate neighborhood competition models for growth of 9 tree species in the interior cedar-hemlock forests of north central British Columbia Coates and Canham, in preparation

Seminar 4 - Neighborhood competition C. D. Canham Next Steps… Extend analysis to entire NE U. S. (~100,000 plots) Finish development of the software (maximum likelihood estimation and SORTIE modeling) and hardware (clusters of workstations) needed for the expanded analyses Incorporate regional climatic gradients in the analyses Use the results to explore a wide range of partial harvesting scenarios