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Keywords:

  • CAIN;
  • competition;
  • dynamic vegetation models;
  • eastern USA;
  • forest dynamics;
  • gap model;
  • plant functional types;
  • process-based modelling;
  • range limits;
  • tree demography

Abstract

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

Aim

The geographic distributions of different forest types are expected to shift in the future under altered climatic conditions. At present, the nature, magnitude and timing of these shifts are uncertain because we lack a quantitative understanding of how forest distributions emerge from climate- and competition-related variation in underlying demographic processes. Forest dynamics result primarily from the manner in which the physical environment and competition for limiting resources affect tree growth, mortality and recruitment. We sought to uncover the relative importance of these processes in controlling the geographic limits of different forest types.

Location

Eastern USA.

Methods

We parameterized a climate-dependent forest dynamics model with extensive observations of tree growth, mortality and recruitment from forest inventory data. We then implemented the resulting demographic models in simulations of joint population dynamics for seven plant functional types (PFTs) across the region. By removing various climate effects in a series of simulation experiments, we assessed the importance of climate-dependent demography and competition in limiting forest distributions.

Results

Distributions that emerged from simulated population dynamics approximated the current distributions for all seven PFTs well and captured several known patterns of succession. Temperature-related increases in mortality determined the southern boundaries of three out of four boreal and northern temperate PFTs, whereas temperature-related decreases in recruitment controlled the northern limit of all three southern temperate PFTs. Changes in growth rates and competitor performance had only minor effects on the distribution limits of most PFTs.

Main conclusions

Our results imply that dynamic global vegetation models, which are widely used to predict future vegetation distributions under climate change, should seek to more appropriately capture the observed climate sensitivity of mortality and recruitment. Understanding the mechanisms controlling forest distributions will enable better predictions of their future responses to climate change.


Introduction

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

The geographic distribution of forest types is a major driver of the global carbon cycle. Forests store more than half of the world's terrestrial carbon (Bonan, 2008) and absorb one-quarter of anthropogenic CO2 emissions (Pan et al., 2011), but the rate at which trees fix and release carbon from the atmosphere varies across the world because of differences in climate, disturbance history and the functional traits of tree species within different forest types. Forest distributions are strongly correlated with the current climate (Holdridge, 1947), implying that they will likely shift in the future under altered climatic conditions. Such changes are expected to have consequences for forests' capacity to sequester carbon from the atmosphere, their role in sustaining much of the world's biodiversity, and the production of wood products and other renewable resources.

Accurately predicting the nature, magnitude and timing of future shifts – and their consequences – requires sound understanding of the factors that act to control the geographic limits of different forest types (Cheaib et al., 2012). Dynamic global vegetation models (DGVMs) are the primary tools used for predicting broad-scale terrestrial ecosystem dynamics, including carbon fluxes and vegetation distributions under future climate scenarios (Cramer et al., 2001; Sitch et al., 2008). These models focus heavily on short-term ecophysiological responses, which have been extensively validated against data. By contrast, their treatment of how demography, including competition between individual trees, affects forest and vegetation dynamics are fairly simplistic (Moorcroft, 2006). Some demographic processes are presumed to be unresponsive to climate, and predictions for plant demography are not informed by data (Purves & Pacala, 2008; Fisher et al., 2010). DGVMs may apply climatic limits to selected demographic processes (e.g. seedling establishment), but this is done by matching predicted and current vegetation distributions, without incorporating direct data on the climate sensitivity of the processes themselves (Foley et al., 1996; Haxeltine & Prentice, 1996; Sitch et al., 2003). An empirical understanding of how climate-related changes in demographic rates translate into the observed distribution of different forest types could inform the development of DGVMs that appropriately represent the roles of various demographic changes in limiting vegetation distributions.

Many studies confirm that tree growth, mortality and recruitment all vary across climatic gradients (Huang et al., 2010; Lines et al., 2010; Clark et al., 2011; Dietze & Moorcroft, 2011). There is also mounting evidence for widespread increases in tree growth and mortality in recent years as climatic conditions have become both warmer and more variable (Boisvenue & Running, 2006; van Mantgem et al., 2009; McMahon et al., 2010; Peng et al., 2011). However, it is impossible to predict how these demographic changes will affect geographic distributions without first understanding which demographic processes are most critical to regulating population dynamics at species' range limits.

Forest distributions are controlled by both the physical environment and competition for limiting resources, particularly light (in mesic regions). These two sets of factors act on rates of growth, mortality and recruitment to determine population dynamics in space and time, which in turn give rise to the fundamental and realized geographic niches of different species. Understanding exactly how these processes lead to the distributions of different forest types requires a quantitative framework through which demographic rates can be related to both climate and interactions with other species, then fed into appropriate population dynamics models to predict abundance in different locations over time. Such an approach should not only reproduce observed distributions but also do so based on processes, functional forms and parameter values that are inferred from observational data.

Over the past 40 years, many individual-based forest dynamics models have been developed to predict how the structure and composition of forests emerge through differential tree growth, mortality and regeneration, in response to height-structured competition for light (Bugmann, 2001; Jeltsch et al., 2008). Although most efforts have required intensive, site-specific data collection (Pacala et al., 1996), recent work has shown that accurate predictions of population dynamics can be obtained from simpler models for which the extensive data in national forest inventories provide all the measurements necessary to quantify the response of tree vital rates to climate and competitive interactions and to then infer population dynamics at regional scales (Purves et al., 2008). However, forest dynamics models have not yet been successfully applied to understand how forest distributions emerge from underlying controls on tree vital rates.

Adopting this individual-based demographic approach, we parameterized a variant of the CAIN forest dynamics model from forest inventory data across the eastern USA (Fig. 1). Using the resulting data-constrained model, we quantified the roles of climate-dependent growth, mortality, recruitment and competition in determining the range limits of seven plant functional types (PFTs) within this region. We interpret results in the context of DGVMs and other models that seek to predict the dynamics of forest and vegetation distributions under environmental change.

figure

Figure 1. We used tree- and plot-level observations of tree growth (grow.), mortality (mort.) and recruitment (recr.) in the US Forest Inventory and Analysis database to parameterize functions that predict these demographic rates for seven plant functional types (PFTs). The functions incorporate effects of mean annual temperature and precipitation (MAT and MAP), competition among trees (measured by crown area index), tree diameter, and county-level average PFT basal area. For further details, see Methods, Appendix S1 and Caspersen et al. (2011).

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Methods

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

Model description and parameterization

CAIN is a simple, scalable, individual-based model of forest stand dynamics (Caspersen et al., 2011). It consists of allometric sub-models for tree height, crown radius and crown depth, together with demographic sub-models for tree diameter growth, mortality and recruitment. We chose to use the CAIN model because it captures general properties of tree demography, especially its variation with tree size and height-structured competition for light, in a simple manner that allows the model to be readily parameterized from commonly available forest inventory data and allometric relationships (Fig. 1).

We first classified all trees found in the eastern USA into a set of six PFTs according to latitudinal range (boreal, northern temperate and southern temperate) and leaf habit (hardwood and conifer), plus a seventh type (southern temperate hydric) that encompassed species primarily associated with coastal plain swamps. This classification scheme allowed us to unambiguously group more than 200 species into a set of PFTs similar to those used in current DGVMs (Cramer et al., 2001). For each PFT, we parameterized the CAIN forest dynamics model against tree- (growth and mortality) and plot-level (recruitment) demographic observations in Forest Inventory and Analysis (FIA) data from across the eastern USA (see Appendices S1–S3 in Supporting Information). The full dataset incorporated repeat measurements for 1,329,056 individual trees ≥ 2.54 cm in diameter, across 47,723 plots spanning an area of 3.1 million km2. Measurement years ranged from 1995 to 2011. Allometric relationships between tree diameter, tree height, crown radius and crown height were all obtained from Purves et al. (2007) and are described in Appendix S1.

We modelled annual tree diameter growth (G, cm·y−1) and mortality rates (M, y−1; the inverse of longevity, L) as the product of maximum rate parameters (δ, ψ) and nonlinear terms that represent primary factors affecting vital rates at tree (diameter at breast height: DBH), stand (crown area index, CAIh) and regional (mean annual temperature and precipitation: MAT, MAP) levels:

  • display math
  • display math

Growth varies as a log-normal function of diameter (GS) that captures size-dependent carbon fixation and investment patterns (Coates et al., 2009; Gómez-Aparicio et al., 2011). Longevity both increases as a power function of diameter to capture juvenile mortality, and decreases as a sigmoidal function of diameter to capture senescence, to produce an overall U-shaped mortality function (LS) (Lines et al., 2010; Hurst et al., 2011). Both growth and longevity decrease as negative exponential functions (GC and LC) of CAIh, a measure of height-structured competition that we define as the projected area of tree crowns at a given height (h) above the ground (Caspersen et al., 2011). To account for the effects of climate, we defined the major environmental axes of variability in growth and mortality as linear combinations of mean annual temperature and precipitation, then allowed growth and mortality to vary as Gaussian functions (GE and LE) of these climate gradients. The Gaussian climate-response functions imply that each demographic rate peaks in a particular climatic optimum and decreases as conditions became less favourable in either direction (Gómez-Aparicio et al., 2011). Importantly, the functions could be extrapolated outside current PFT ranges under the parsimonious assumption that demographic rates have smooth (but nonlinear) responses to climate gradients. We also repeated these analyses with an alternative, more conservative formulation of the maximum effect of climate on vital rates (detailed in Appendix S8). This alternative climate response allowed us to assess the importance of the particular model form for extrapolation.

We defined annual recruitment for each PFT (I, ha−1·y−1) as the density of stems, per year, that reach the minimum DBH threshold (2.54 cm) for measurement in the FIA dataset. Recruitment was modelled as the product of a maximum rate parameter (τ) and proxy terms for propagule sources (landscape-level PFT basal area: LBA), light availability (crown area index) and climatic suitability:

  • display math

To account for variation in recruitment with the abundance of the PFT in the surrounding area, predicted recruitment increases as a power function (IL) of the average basal area of the PFT in plots from the same county (LBA). Recruitment decreases as a negative exponential function (IC) of crown area index evaluated at ground level. Climate effects on recruitment (IE) had the same form as those for growth and mortality. In fitting recruitment models for each PFT, we excluded plots that had been recently harvested, as well as plots in counties for which the average number of trees of that PFT per plot was < 1.0 (i.e. about 4% of all trees present, given plots contained an average of 28 trees). The latter filter was applied to exclude all plots that were outside a PFT's range. Further details of the model formulations for growth, mortality and recruitment can be found in Appendix S1.

We used a Markov Chain Monte Carlo (MCMC) approach, implemented by the Filzbach programming library (Purves & Lyutsarev, 2011), to estimate the posterior mean and credible interval of all model parameters in a Bayesian context. Parameter estimation was carried out separately for each combination of vital rate and PFT. All parameters were assigned uniform priors but were constrained to fall within lower and upper bounds that defined algebraic or biological limits. For each PFT and demographic model, we ran five replicate MCMC chains with 20,000 steps in both burn-in and sampling phases; visual inspection of likelihood trace plots indicated that these chain lengths were sufficient for most chains to reach convergence. To eliminate individual chains that failed to converge, only the chain with the highest average likelihood in the sampling phase was retained for estimating posterior parameter distributions.

Model simulations

In this section we describe how the demographic models described above were used to generate predictions for PFT distributions. We first describe the basic structure of the CAIN simulation model and how we configured it to run across the eastern USA. We then describe various scenarios that were set up within this simulation framework to estimate PFT geographic distributions and to infer which processes acted to limit them.

To run simulations using CAIN, we combined its allometric and demographic sub-models within a non-spatial framework that projected the dynamics of individual trees within a stand through time (see Appendix S5). Although CAIN is fundamentally individual based, it is computationally much more efficient to represent sets of trees with identical characteristics (including predicted growth and mortality rates) as a single cohort with changing density. The simulations do not incorporate any demographic stochasticity or process variability within cohorts. In all simulations, stands were initialized with bare-ground conditions (no cohorts present before recruitment first occurs) and were run for 600 years, by which time they had reached a quasi-equilibrium state. Because they contain information on individual tree cohorts within a stand, the simulations can produce summary metrics for the composition, size distribution, basal area and other properties of complex forest stands.

We created a 0.5° × 0.5° grid to simulate forest dynamics across the eastern USA. Within each grid cell, we represented an individual stand as a collection of tree cohorts that each held a certain number, d (ha−1), of trees per hectare of a single PFT and DBH. Stands did not have an explicit spatial extent but were considered to represent PFT population dynamics over a localized area with mean temperature and precipitation values for the grid cell and with a uniform abiotic environment and canopy structure. Stand dynamics were iterated over a series of discrete 5-year timesteps by changing the number (d) and DBH of trees in existing cohorts, by adding new cohorts with the minimum DBH (3 cm) and by removing cohorts with too few trees (d < 0.5).

In calculating PFT recruitment rates within each grid cell, we assumed a local landscape where all PFTs were represented at moderate abundance (i.e. we used the mean value of county-level PFT basal area among all PFTs in the FIA dataset, 5.66 m2·ha−1). This ensured that each PFT had an equal opportunity to establish anywhere in the region, so that resulting geographical distributions were purely the result of climate-related demographic variation. Put otherwise, our simulation setup eliminated dispersal as a potential limiting factor to PFT distributions.

We developed six simulation scenarios to characterize the realized distribution and fundamental niche of each PFT and to assess the degree to which the realized distribution of each PFT was constrained by various demographic processes. Firstly, we carried out simulations of joint PFT population dynamics within each of 1280 0.5° grid cells covering the region. In this scenario, all seven PFTs could recruit into each stand throughout the simulation period. The only factors driving differences in population dynamics from one grid cell to another were differences in mean annual temperature and precipitation. Thus, predicted PFT distributions were an emergent consequence of the demographic functions extracted from tree- and plot-level data, assuming that all PFTs compete with one another within individual stands.

Next, we repeated the simulations described above but for each PFT in isolation (i.e. where only a single PFT could recruit into each stand). The resulting distributions are a first estimate of each PFT's fundamental niche (Hutchinson, 1957). This scenario provides an estimate of the area each PFT could occupy in the absence of competition from other PFTs. In all cases, the estimated fundamental niche must be larger than the realized distribution obtained in the first scenario.

Now consider a focal PFT. Either a climate-related decrease in its demographic rates or an increase in the demographic rates of its competitors must explain the difference between the focal PFT's realized distribution and fundamental niche. To isolate the relevant processes, we carried out simulations for each focal PFT in which the other PFTs were present but where we removed, in turn, four climate dependencies: focal PFT growth, focal PFT mortality, focal PFT recruitment and all aspects of the demography of non-focal PFTs. We then assessed the amount by which the focal PFT could extend its distribution under each of these conditions. If, according to our model, a focal PFT substantially extends its distribution when the climate dependency of a given process is removed, then we infer that the climate dependency of that process acts to constrain the focal PFT's realized distribution. The four scenarios with fixed climate dependencies were specified as follows:

Fixed growth

All seven PFTs were included in this scenario, but climatic effects on growth (GE) for a focal PFT were fixed to a constant, representative value (inline image). This value was calculated as the mean across the study region, weighted by the focal PFT's basal area in each grid cell:

  • display math

where the summations are performed over the n 0.5° × 0.5° grid cells in the region, BAi is the mean basal area of the focal PFT across FIA plots in grid cell i, and MATi and MAPi are the mean annual temperature and precipitation in grid cell i. All non-focal PFTs retained their usual formulation for climatic effects on growth. The simulations were repeated with each PFT as the focal PFT in turn. This scenario tested whether the realized distribution of each PFT was constrained by climate effects on growth.

Fixed mortality

As above but with fixed climatic effects for mortality (LE) rather than growth (GE) for a focal PFT. This scenario tested whether the realized distribution of each PFT was constrained by changes in mortality.

Fixed recruitment

As above but with fixed climatic effects for recruitment (IE) rather than growth (GE) for a focal PFT. This scenario tested whether the realized distribution of each PFT was constrained by changes in recruitment.

Fixed competition

As above but with climatic effects for all non-focal PFT demographic rates (GE, LE and IE) fixed to representative values. These values (inline image, inline image, inline image) were each calculated using the focal PFT's basal area in each grid cell as a weighting factor in the equation above. The focal PFT retained its usual formulation for climatic effects on each demographic rate. This scenario tested whether the realized distribution of each PFT was constrained by climate dependencies in the performance of competitors.

Results

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

Demographic models

Within our model, climate dependencies in growth, mortality and recruitment for each PFT were each represented by Gaussian-shaped functions (Fig. 2) while also accounting for effects of tree size, crown-based competition for light and density-dependent recruitment. Comparisons of observed and predicted vital rates across the range of each of these predictor variable showed that our models consistently captured nonlinear variation in PFT demographic performance well (Figs S1–S3).

figure

Figure 2. Predicted tree diameter growth rate, mortality rate and recruitment rate (ingrowth of stems surpassing 2.54 cm diameter) for seven plant functional types (PFTs) in the eastern USA against mean annual temperature and precipitation. The climate dependency of each rate was modelled as a Gaussian-shaped response to a linear combination of temperature and precipitation. The solid portion of each line indicates the interval between the 1st and 99th percentiles of temperature or precipitation for each PFT; the dashed portion represents extrapolations outside this range. All other covariates were fixed to their mean values in calculating these responses. PFT legend abbreviations are as in Fig. 3.

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All PFTs but one exhibited increasing growth up to a mean annual temperature of about 15 °C. Above 15 °C, the growth rates of three out of four PFTs decreased (growth of a fourth changed little; the remaining three were not found in areas this warm). Mortality rates generally increased with temperature, with boreal and northern temperate PFTs tending to exhibit greater climate sensitivity than more southern PFTs. Recruitment rates for the three southernmost PFTs decreased strongly in both colder and wetter environments, even when controlling for potential seed rain from the surrounding landscape. Analysis of seedling counts within plots showed that climate-dependent decreases in recruitment for these PFTs correlated both with lower seedling survival and with the establishment of fewer seedlings (Appendix S7). Recruitment of boreal hardwoods decreased in warmer and drier climates; this decrease correlated with seedling establishment but not survival. Climate-related trends in the demographic rates of the most common individual species were generally well correlated with model predictions for their respective PFTs (Appendix S6), confirming that, with a few exceptions, species within a PFT respond to climate in a similar manner.

The PFTs responded to competition through changes in demographic rates as shading from other tree crowns increased (Table 1). Southern temperate conifers and boreal hardwoods expressed the largest relative decreases in growth and recruitment and greatest increases in mortality, at mean levels of crown shading compared with open conditions. Northern and southern temperate hardwoods had intermediate responses by these measures, with the latter consistently less tolerant of shading than the former. The remaining PFTs each had one demographic rate with the smallest response to competition.

Table 1. Predicted proportional decrease in growth, longevity and recruitment for each plant functional type under typical closed-canopy conditions, as compared with open-grown or bareground conditions in which there is no competition for light.
Plant functional typeRelative decrease in
GrowthaLongevityabRecruitmentc
  1. a

    Crown area index at tree's mid-crown height = 1.0.

  2. b

    Longevity is the inverse of the annual mortality rate.

  3. c

    Crown area index at ground level = 1.5.

Boreal conifer0.1580.4050.808
Boreal hardwood0.7080.5670.889
Northern temperate conifer0.6610.1090.794
Northern temperate hardwood0.5920.3810.640
Southern temperate conifer0.7740.8190.962
Southern temperate hardwood0.7020.5520.726
Southern temperate hydric0.2810.4230.381

Emergent PFT distributions

The degree to which emergent distributions correspond with reality is an important test of our model. The set of predicted geographical distributions showed a good match to the observed distributions for all seven PFTs (Fig. 3), providing confirmation that our data-constrained demographic sub-models can largely explain current PFT distributions. Across all 0.5° grid cells, the simulated basal area of each PFT had a moderately strong correlation with its average basal area in FIA plots (Spearman's rho = 0.55–0.78). Moreover, our model predicted the key temporal (successional) transitions known to occur among these PFTs – boreal hardwoods to northern temperate hardwoods and conifers in the upper lake states; boreal conifers to northern temperate hardwoods in the northeast; and southern temperate conifers to hardwoods in the southeast (Fig. 4). Most of the PFTs showed substantial extensions to their predicted ranges when they did not face competition from other PFTs, but none had a fundamental niche that included the entire region (Fig. 3).

figure

Figure 3. Observed and simulated distributions of seven plant functional types (PFTs, panels a–g) across the eastern USA. Contour lines show the distribution of each PFT's basal area (BA) at either year 50 (early-successional forest types) or year 200 (late-successional forest types) of simulations when run in competition with all other PFTs (red lines, estimating their realized distribution) or in isolation (blue lines, estimating their fundamental niche). Bar plots indicate the proportion of the difference in area between the realized distribution and fundamental niche (defined by BA = 5 m2 ha–1 contours) that exceeded 5 m2 ha–1 BA when the climate dependency of growth, mortality, recruitment and competition were each removed in turn. This measures the extent to which each process controls the limits of the PFT distribution.

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figure

Figure 4. Examples of plant functional type (PFT) succession at six locations spanning gradients in mean annual temperature (MAT) and precipitation (MAP). Boreal conifers responded to differences in precipitation in cold localities (compare top panels), but all other PFTs segregated primarily along a temperature gradient. PFT legend abbreviations are as in Fig. 3. A web application is available for exploring additional visualizations of modelled forest dynamics (Appendix S9).

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For three of the four most northern PFTs, the southern edge of the realized distribution was limited by increasing mortality in warmer climates (the fourth, boreal hardwoods, was limited by a combination of factors). For example, 73% of the area that is beyond the realized distribution of the boreal conifer PFT, but that is part of its fundamental niche (defined by a minimum basal area of 5 m2·ha−1), can be incorporated into its distribution when climatic effects on mortality are removed (Fixed Mortality scenario; Fig. 3b). This finding indicates that increased mortality related to climate acts to limit the southern expansion of boreal conifers. Conversely, the northern edges of the three southern PFTs were limited by decreasing recruitment (and alternatively growth in one instance) in colder climates. For example, southern temperate hardwoods could occupy 98% of the area between their current realized and fundamental niche if recruitment rates did not vary across a climate gradient (Fixed Recruitment scenario; Fig. 3e), implying that their distribution is limited by temperature-related seedling establishment and survival.

Climate-related variation in growth did not control the limits to most PFT distributions, even though climate is known to be a major determinant of ecosystem productivity. Similarly, removing the climate dependency of competitor performance had little effect on the distribution of any PFT. The implication is that although competition for light excludes PFTs from much of their fundamental niches and drives successional changes through time, climate-related changes in competitor performance do not account for the limits of these PFT distributions.

Discussion

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

Demographic controls on distribution limits

Variation in growth has received disproportionate attention as a demographic control on range limits in general (Sexton et al., 2009). Recently, ecologists have called for a more comprehensive treatment of demographic processes affecting population dynamics across space (Gaston, 2009; Doak & Morris, 2010). A number of studies have highlighted climate-related variation in mortality and reproduction within forests of eastern North America (Lines et al., 2010; Clark et al., 2011; Dietze & Moorcroft, 2011) and some have inferred population fitness in different locations from these patterns (Morin et al., 2007; Purves, 2009). Yet, despite such indications that demography offers an important lens for understanding forest biogeography, it has proven a considerable challenge to formally integrate demographic variation with a suitable platform for modelling geographic distributions.

The present work represents an important development in this regard. We applied a scalable model of forest dynamics, constrained by extensive empirical data on individual demographic rates, to quantify the effects of different aspects of demography, and competitor performance, in determining the distributions of seven forest types. By parsing out climate dependencies of different vital rates, we found that mortality is the most important process limiting the southern boundary of three out of four boreal and northern temperate PFTs. By contrast, the northern boundary of three southern temperate PFTs is determined by decreasing recruitment due to both lower establishment and survival of seedlings. The northern boundary of all boreal and northern temperate PFTs extended at least to the USA–Canada border; additional inventory data from Canada would be needed to determine which processes ultimately determine their northern limits.

We modelled demographic responses to a linear combination of mean annual temperature and precipitation. Although tree demography probably does not respond to either of these variables directly, temperature and precipitation jointly define flexible climate gradients that would correlate with more specific climate features. Mean annual temperature and precipitation are also widely understood and directly correspond with predictions of general circulation models. Tree growth increased with mean annual temperature because of the temperature dependency of photosynthesis rate, coupled with a longer growing season in warmer areas (Boisvenue & Running, 2006). Tree growth also decreased above a mean annual temperature of 15 °C. High temperatures increase transpiration rates and water demand and may thereby impede tree growth when soil moisture is low. Mortality increases with temperature for each PFT may reflect a cascade of factors related to drought stress, including carbon starvation due to higher respiration costs (Adams et al., 2009), as well as increased pressure from pathogenic insects and fungi (Allen et al., 2010). The mechanisms underlying climate-dependent recruitment processes are not well understood but appear to be positively related to spring temperature in the southeastern USA (Ibáñez et al., 2007).

The importance of biotic interactions to species distributions is a major unresolved question in ecology (Kissling et al., 2012). Ecologists have speculated that biotic interactions and the physical environment will tend to limit opposite sides of a species' range (MacArthur, 1972; Brown et al., 1996; Loehle, 1998), but our results do not support this generalization. Competition was important in restricting PFT distributions, as manifested in the differences between realized distributions and fundamental niches (Fig. 3). It also acted to drive successional dynamics (Fig. 4). Nevertheless, changes in competitor performance from the core to the periphery of each PFT's range had only a minor influence on their distributions. To a large extent, this is because northern temperate hardwoods were both the most widespread PFT and had the least climate-sensitive demography (Fig. 2). Northern temperate hardwoods constituted the main competitor for the other PFTs, but the climate dependence of that competitor's performance was relatively weak. For example, red maple (Acer rubrum) is the most broadly distributed and abundant tree species in the eastern USA and has been called a ‘super-generalist’ because it exhibits good performance under a wide variety of ecological conditions (Abrams, 1998). Removing climate dependence from the vital rates of northern temperate hardwoods thus had little effect on other PFTs (Fig. 3).

Model performance

The conclusions we derive from our model are supported by four key tests of model performance. Firstly, mean predicted vital rates show strong correspondence with observations across the range of each of the predictor variables (MAT, MAP, DBH, CAIh and LBA; Figs. S1–S3). Secondly, the match between predicted and observed PFT distributions, which is an independent test of the model's higher level emergent behaviour, was reasonably strong (Fig. 3). Thirdly, as discussed in the next section, the inferences we draw concerning mortality and recruitment limitation for different PFTs are broadly substantiated by demographic trends across climate gradients for 33 of the most common constituent species (Fig. S4). Lastly, as described in Appendix S8, our results were robust under an alternative model formulation with more restricted climatic effects on demographic rates (Table S5).

Given the simplified formulation of our model, our results are particularly notable in producing good approximations to the spatial distributions and temporal dynamics of seven different forest types from demographic information alone. Ecologists have long been interested in understanding how species' distributions emerge from a combination of environmental controls on demography and species interactions. Process-based models of species distributions, which are largely built around ecophysiological limitations, have garnered recent interest in the context of environmental change (Crozier & Dwyer, 2006; Buckley, 2008; Kearney & Porter, 2009). However, to date, there has been limited progress in elucidating the effects of species interactions to quantitatively differentiate species' fundamental and realized niches based on underlying population dynamics (Kissling et al., 2012). Although applied at the scale of PFTs rather than individual species, our results represent a significant advance in using a well-established and important competition mechanism alongside climatic factors to make credible bottom-up predictions for the geographic distributions of, and demographic controls on, forest communities.

Assessing model assumptions

Aggregating tree species into PFTs provides less detail than species-level analyses but is an approach that is universal to DGVMs (Cramer et al., 2001) and has also been applied in forest-based terrestrial ecosystem models (Medvigy et al., 2009). Similar classification schemes are employed for forest management purposes in this (Ruefenacht et al., 2008) and many other forest regions. As well as matching the scale of these other applications, the use of PFTs facilitated our analysis by increasing sample sizes and the length of climate gradients in the data. The approach carries an implicit assumption that species within a PFT respond to environmental gradients in a similar manner. We checked the validity of this assumption by examining climate-related trends in the data for the most common individual species (Fig. S4). Our species assignments to PFTs retained the predominant responses of individual species to climate while still capturing the climate- and competition-related variation in demographic rates that distinguish spatial distributions and successional patterns of the different PFTs.

Our approach extrapolated predicted demographic rates outside the range of each PFT by assuming that responses to climate were Gaussian shaped. While these predictions are necessarily uncertain, we are confident that the main conclusions from the model are well grounded. For instance, our simulations showed that the southern boundaries of boreal conifers, northern temperate hardwoods and northern temperate conifers were limited by increasing mortality. At the species level, this was supported by 11 of 14 species from these PFTs showing increasing mortality towards the warmer edge of their climate gradient (vs. 9 of 19 from other PFTs; Fig. S4). Our simulations further predicted that the southwards expansion of boreal hardwoods and the northwards expansion of all three southern temperate PFTs were limited by decreasing recruitment. This pattern was supported by decreasing recruitment towards the climatic range limit for 17 of 19 species from these PFTs (vs. 8 of 14 for the other PFTs; Fig. S4). Again, conclusions from our PFT-based model were broadly supported at the species level.

Implications for modelling climate change

The roles of mortality and recruitment in limiting PFT distributions inferred here imply new directions for development of DGVMs, most of which assume that the primary determinant of dominant vegetation type is climatic variation in growth (Cramer et al., 2001). However, translating climate-related demographic patterns into process-based sub-models within DGVMs is challenging because ecophysiological mechanisms driving tree mortality are poorly understood (Allen et al., 2010; McDowell et al., 2011; Stephenson et al., 2011). Mechanistic models for recruitment are daunting as well because numerous ecological processes, any of which could have complex climate dependencies, combine to determine seedling recruitment rates. For example, recent work shows that the climate-driven phenology of flowering and fruit ripening limits reproductive success (Morin et al., 2007) but that model does not consider recruitment dynamics beyond the stage of seed production.

Despite such challenges, accurate prediction of forest responses to climate change requires improved models for the environmental sensitivity of tree mortality and recruitment (Medvigy & Moorcroft, 2012). If suitable process-based models are unavailable, one practical way forward would be to incorporate phenomenological climate dependencies for mortality and recruitment like those derived here. Regardless of how such demographic models are developed and applied, it is essential that they be routinely confronted with data to ensure the models capture actual demographic patterns rather than simply produce credible high-level output. Forest inventories like the one used in the present study provide indispensible data that, in combination with large-scale experiments, process studies, and model insights (Luo et al., 2011), can help in developing better models for understanding and predicting the responses of forests to climate change.

Acknowledgements

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

We extend our thanks to D. Coomes, A. Hector, G. McInerny, S. Pacala, M. Smith, L. Turnbull and three anonymous referees for reviewing earlier drafts of this paper.

References

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

Mark Vanderwel is a postdoctoral researcher interested in the application of data-constrained, process-based models to understand consequences of human-induced disturbance and environmental change on different aspects of forest ecosystems.

Vassily Lyutsarev works at the interface of computing and ecology. He concentrates on data mining, visualization techniques and languages that have the potential to accelerate fundamental advances in science.

Drew Purves is an ecologist who focuses on combining ecological theory with large amounts of data via computational statistics, in order to produce predictive models of ecological systems. In so doing he hopes to make new findings about nature, help to mitigate important environmental problems and identify new priorities for ecological research and data gathering.

Supporting Information

  1. Top of page
  2. Abstract
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information
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Figure S1 Goodness of fit for the CAIN tree growth model.

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Figure S2 Goodness of fit for the CAIN tree mortality model.

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Figure S3 Goodness of fit for the CAIN recruitment model.

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Figure S4 Climate-related demographic trends for PFTs and individual species.

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Figure S5 Histograms of correlations between PFT and species climate responses.

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Table S1 Assignment of tree species to PFTs.

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Table S2 Estimated model parameters.

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Table S3 Fixed and calculated model parameters.

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Table S4 Seedling correlations with recruitment climate responses.

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Table S5 Comparison of original and alternative climate responses.

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Appendix S1 Detailed description of CAIN forest dynamics model.

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Appendix S2 Description of source data.

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Appendix S3 Likelihood functions for parameter estimation.

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Appendix S4 Goodness-of-fit.

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Appendix S5 Simulation model framework.

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Appendix S6 Comparison of PFT- and species-level demography.

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Appendix S7 Seedling dynamics and recruitment.

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Appendix S8 Alternative climate responses.

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Appendix S9 Web application.

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