Dominance of the suppressed: Power-law size structure in tropical forests

Farrior, Caroline E.; Bohlman, Stephanie A.; Hubbell, Stephen P.; Pacala, Stephen W.

doi:10.1126/science.aad0592

Cited by 113 publications

(140 citation statements)

References 34 publications

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“…Small trees are more frequent than large trees. The logarithm of frequency declines linearly with the logarithm of size 1 . Log-log linearity defines a power law pattern.…”

Section: Introductionmentioning

confidence: 94%

“…Figure 1A shows the distribution of tree size in a tropical forest 1 . Most of the trees lie along the green power law.…”

Section: Tree Sizementioning

confidence: 99%

“…In this plot, the metric is shifted so that the most common type associates with a value T z = 0. Data approximated from Figure 4 in Farrior et al 1 …”

Section: Tree Sizementioning

confidence: 99%

“…The data 1 in Figure 1 arose from measurements of trunk diameter, d . I sought a natural metric based on d that describes the data in a shift and stretch invariant manner 5 .…”

Section: The Metric Of Tree Size: Affine Invariancementioning

confidence: 99%

“…Farrior et al 1 used logarithmic scaling at small magnitudes and linear scaling at large magnitudes. However, they did not express a metric that smoothly changed the proportion of the two scalings with magnitude.…”

Section: The Metric Of Tree Size: Scalementioning

confidence: 99%

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The invariances of power law size distributions

Frank

2016

F1000Res

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Size varies. Small things are typically more frequent than large things. The logarithm of frequency often declines linearly with the logarithm of size. That power law relation forms one of the common patterns of nature. Why does the complexity of nature reduce to such a simple pattern? Why do things as different as tree size and enzyme rate follow similarly simple patterns? Here I analyze such patterns by their invariant properties. For example, a common pattern should not change when adding a constant value to all observations. That shift is essentially the renumbering of the points on a ruler without changing the metric information provided by the ruler. A ruler is shift invariant only when its scale is properly calibrated to the pattern being measured. Stretch invariance corresponds to the conservation of the total amount of something, such as the total biomass and consequently the average size. Rotational invariance corresponds to pattern that does not depend on the order in which underlying processes occur, for example, a scale that additively combines the component processes leading to observed values. I use tree size as an example to illustrate how the key invariances shape pattern. A simple interpretation of common pattern follows. That simple interpretation connects the normal distribution to a wide variety of other common patterns through the transformations of scale set by the fundamental invariances.

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“…Small trees are more frequent than large trees. The logarithm of frequency declines linearly with the logarithm of size 1 . Log-log linearity defines a power law pattern.…”

Section: Introductionmentioning

confidence: 94%

“…Figure 1A shows the distribution of tree size in a tropical forest 1 . Most of the trees lie along the green power law.…”

Section: Tree Sizementioning

confidence: 99%

“…In this plot, the metric is shifted so that the most common type associates with a value T z = 0. Data approximated from Figure 4 in Farrior et al 1 …”

Section: Tree Sizementioning

confidence: 99%

“…The data 1 in Figure 1 arose from measurements of trunk diameter, d . I sought a natural metric based on d that describes the data in a shift and stretch invariant manner 5 .…”

Section: The Metric Of Tree Size: Affine Invariancementioning

confidence: 99%

Section: The Metric Of Tree Size: Scalementioning

confidence: 99%

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The invariances of power law size distributions

Frank

2016

F1000Res

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Slow rate of secondary forest carbon accumulation in the Guianas compared with the rest of the Neotropics

Chave

Piponiot

Maréchaux

et al. 2019

Ecological Applications

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Secondary forests are a prominent component of tropical landscapes, and they constitute a major atmospheric carbon sink. Rates of carbon accumulation are usually inferred from chronosequence studies, but direct estimates of carbon accumulation based on long‐term monitoring of stands are rarely reported. Recent compilations on secondary forest carbon accumulation in the Neotropics are heavily biased geographically as they do not include estimates from the Guiana Shield. We analysed the temporal trajectory of aboveground carbon accumulation and floristic composition at one 25‐ha secondary forest site in French Guiana. The site was clear‐cut in 1976, abandoned thereafter, and one large plot (6.25 ha) has been monitored continuously since. We used Bayesian modeling to assimilate inventory data and simulate the long‐term carbon accumulation trajectory. Canopy change was monitored using two aerial lidar surveys conducted in 2009 and 2017. We compared the dynamics of this site with that of a surrounding old‐growth forest. Finally, we compared our results with that from secondary forests in Costa Rica, which is one of the rare long‐term monitoring programs reaching a duration comparable to our study. Twenty years after abandonment, aboveground carbon stock was 64.2 (95% credibility interval 46.4, 89.0) Mg C/ha, and this stock increased to 101.3 (78.7, 128.5) Mg C/ha 20 yr later. The time to accumulate one‐half of the mean aboveground carbon stored in the nearby old‐growth forest (185.6 [155.9, 200.2] Mg C/ha) was estimated at 35.0 [20.9, 55.9] yr. During the first 40 yr, the contribution of the long‐lived pioneer species Xylopia nitida, Goupia glabra, and Laetia procera to the aboveground carbon stock increased continuously. Secondary forest mean‐canopy height measured by lidar increased by 1.14 m in 8 yr, a canopy‐height increase consistent with an aboveground carbon accumulation of 7.1 Mg C/ha (or 0.89 Mg C·ha−1·yr−1) during this period. Long‐term AGC accumulation rate in Costa Rica was almost twice as fast as at our site in French Guiana. This may reflect higher fertility of Central American forest communities or a better adaptation of the forest tree community to intense and frequent disturbances. This finding may have important consequences for scaling‐up carbon uptake estimates to continental scales.

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Tropical tree size–frequency distributions from airborne lidar

Ferraz

Saatchi

Longo

et al. 2020

Ecological Applications

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In tropical rainforests, tree size and number density are influenced by disturbance history, soil, topography, climate, and biological factors that are difficult to predict without detailed and widespread forest inventory data. Here, we quantify tree size-frequency distributions over an old-growth wet tropical forest at the La Selva Biological Station in Costa Rica by using an individual tree crown (ITC) algorithm on airborne lidar measurements. The ITC provided tree height, crown area, the number of trees >10 m height and, predicted tree diameter, and aboveground biomass from field allometry. The number density showed strong agreement with field observations at the plot-(97.4%; 3% bias) and tree-height-classes level (97.4%; 3% bias). The lidar trees size spectra of tree diameter and height closely follow the distributions measured on the ground but showed less agreement with crown area observations. The model to convert lidar-derived tree height and crown area to tree diameter produced unbiased (0.8%) estimates of plot-level basal area and with low uncertainty (6%). Predictions on basal area for tree height classes were also unbiased (1.3%) but with larger uncertainties (22%). The biomass estimates had no significant bias at the plot-and tree-height-classes level (À5.2% and 2.1%). Our ITC method provides a powerful tool for tree-to landscape-level tropical forest inventory and biomass estimation by overcoming the limitations of lidar area-based approaches that require local calibration using a large number of inventory plots.

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Dominance of the suppressed: Power-law size structure in tropical forests

Cited by 113 publications

References 34 publications

The invariances of power law size distributions

The invariances of power law size distributions

Slow rate of secondary forest carbon accumulation in the Guianas compared with the rest of the Neotropics

Tropical tree size–frequency distributions from airborne lidar

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