Simulating Vegetation Migration in Response to Climate Change in a Dynamic Vegetation-Climate Model

Rebecca Shira Snell

A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Faculty of Forestry University of Toronto

Rebecca Shira Snell

Doctor of Philosophy

Faculty of Forestry University of Toronto

2013 Abstract

A central issue in climate change research is to identify what species will be most affected by variations in temperature, precipitation or CO 2 and via which underlying mechanisms. Dynamic global vegetation models (DGVMs) have been used to address questions of habitat shifts, extinctions and changes in carbon and nutrient cycling. However, DGVMs have been criticized for assuming full migration and using the most generic of plant functional types (PFTs) to describe vegetation cover. My doctoral research addresses both of these concerns. In the first study, I added two new tropical PFTs to an existing regional model (LPJ-GUESS) to improve vegetation representation in Central America. Although there was an improvement in the representation of some biomes such as the pine-oak forests, LPJ-GUESS was still unable to capture the distribution of arid ecosystems. The model representations of fire, soil, and processes unique to desert vegetation are discussed as possible explanations. The remaining three chapters deal with the assumption of full migration, where plants can arrive at any location regardless of distance or physical barriers. Using LPJ-GUESS, I imposed migration limitations by using fat- tailed seed dispersal kernels. I used three temperate tree species with different life history strategies to test the new dispersal functionality. Simulated migration rates for Acer rubrum (141 m year -1) and Pinus rigida (76 m year -1) correspond well to pollen and genetic reconstructed ii rates. However, migration rates for Tsuga canadensis (85 m year -1) were considerably slower than historical rates. A sensitivity analysis showed that maturation age is the most important parameter for determining rates of spread, but it is the dispersal kernel which determines if there is any long distance dispersal or not. The final study demonstrates how northerly refugia populations could have impacted landscape recolonization following the retreat of the last glacier. Using three species with known refugia ( Acer rubrum , Fagus grandifolia , Picea glauca ), colonization rates were faster with a northerly refugia population present. The number of refugia locations also had a positive effect on landscape recolonization rates, which was most pronounced when populations were separated. The results from this thesis illustrate the improvements made in vegetation-climate models, giving us increasing confidence in the quality of future climate change predictions.

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Acknowledgments

I would like to thank my supervisor, Dr. Sharon Cowling, for providing me with both professional and personal support over the years. Dr. Cowling allowed me the freedom to pursue my interests, yet was always there to share her advice and enthusiasm. I have the utmost respect for Dr. Cowling as a scientist and as a person, and to be able to say that at the end of a Ph.D. is something I am grateful for! I would also like to extend my appreciation to Dr. Brad Bass (University of Toronto and Environment Canada), Dr. Sarah Finkelstein (University of Toronto) and Dr. Marie-Josée Fortin (University of Toronto) for their time on my supervisory committee and for their excellent research advice over the years. I would also like to acknowledge my internal and external examination members, Dr. Sean Thomas (University of Toronto) and Dr. Stephen Sitch (University of Exeter) for their constructive comments on the final version of my thesis.

My Ph.D. thesis is based upon an existing model, LPJ-GUESS. I would like to thank Dr. Ben Smith (Lund University) for permitting me to use his model which allowed me to accomplish my goals. I would also like to thank Dr. Jing Chen (University of Toronto) and Bruce Huang for access to the Unix cluster in PGB.

Thank you to the entire Cowling lab, and everyone who ever shared PG201B with me. Your companionship, conversation and many, many coffee breaks helped to make my graduate experience an enjoyable one!

On a personal note, I would like to thank all my friends and family who have supported me throughout my graduate experience. I could always count on your love, encouragement and emergency babysitting. I would also like to thank my father for suggesting a Latin Hypercube sampling design for Chapter 4. Who knew there was so much in common between plant ecology and nuclear physics! To my husband, Jason. I can only say thank you and know that it is not enough.

Table of Contents

Acknowledgments...... iv

Table of Contents...... v

List of Tables ...... x

List of Figures...... xii

List of Appendices ...... xv

Chapter 1...... 1

1 Introduction...... 1

1.1 Seed dispersal and vegetation migration...... 2

1.2 Vegetation-climate models ...... 2

1.2.1 Species distribution models ...... 2

1.2.2 Dynamic global vegetation models...... 3

1.3 Dispersal in vegetation-climate models...... 4

1.3.1 Species distribution models ...... 4

1.3.2 Dynamic global vegetation models...... 5

1.4 Adding dispersal into a DGVM ...... 6

1.4.1 Challenges to simulating dispersal in DGVMs...... 6

1.4.2 The model, LPJ-GUESS ...... 7

1.5 Outline of chapters and objectives...... 9

1.6 Glossary of terms ...... 11

1.7 References...... 16

Chapter 2...... 20

2 Simulating regional vegetation-climate dynamics for Central America: tropical versus temperate applications...... 20

2.1 Abstract...... 20

2.2 Introduction...... 20 v

2.3 Methods...... 22

2.3.1 Description of LPJ-GUESS ...... 22

2.3.2 PFT parameterizations ...... 23

2.3.3 Modelling protocol...... 24

2.3.4 Model evaluation from biome comparison...... 25

2.3.5 Model evaluation from remote sensing data...... 26

2.4 Results...... 26

2.4.1 Biome comparison with Olson map...... 26

2.4.2 Biome comparison with Haxeltine & Prentice map ...... 27

2.4.3 MODIS comparison...... 28

2.5 Discussion...... 28

2.6 References...... 50

Chapter 3...... 55

3 Simulating long distance seed dispersal in a Dynamic Global Vegetation Model ...... 55

3.1 Abstract...... 55

3.2 Introduction...... 55

3.3 Development of the dispersal module...... 57

3.3.1 The model, LPJ-GUESS ...... 57

3.3.2 Communication between cells ...... 58

3.3.3 Dispersal between grid cells ...... 59

3.3.4 Seed production ( seed n) ...... 59

3.3.5 Number of patches close to the edge of the cell ( pPFT )...... 59

3.3.6 Seed dispersal kernels ( k(x) ) ...... 60

3.3.7 Dispersal within a grid cell ...... 61

3.3.8 Simulation protocol...... 63

3.3.9 Test species ...... 64 vi

3.3.10 Calculating migration...... 64

3.4 Results...... 65

3.5 Discussion...... 66

3.6 References...... 78

Chapter 4...... 82

4 A sensitivity analysis of dispersal and climate change related migration in a dynamic ecosystem model ...... 82

4.1 Abstract...... 82

4.2 Introduction...... 82

4.3 Methods...... 85

4.3.1 The model, LPJ-DISP ...... 85

4.3.2 Testing the sensitivity of simulated migration rates ...... 85

4.3.2.1 Maturation age ( age_repr )...... 86

4.3.2.2 Distance parameter in dispersal kernel ( αdisp )...... 86

4.3.2.3 Spread rate between patches within a grid cell ( r_log ) ...... 86

4.3.2.4 Fecundity ( kest_repr and reprfrac )...... 87

4.3.3 Sampling design...... 88

4.3.4 Simulation protocol...... 89

4.3.5 Output measures...... 90

4.3.6 Sensitivity analysis...... 91

4.4 Results...... 92

4.5 Discussion...... 93

4.6 References...... 103

Chapter 5...... 107

5 Simulating vegetation migration and landscape colonization with northerly refugia populations ...... 107

5.1 Abstract...... 107 vii

5.2 Introduction...... 107

5.3 Methods...... 110

5.3.1 The model, LPJ-DISP ...... 110

5.3.2 Simulation protocol...... 110

5.3.3 Test species ...... 111

5.3.4 Vegetation movement metrics ...... 112

5.4 Results...... 113

5.4.1 Migration...... 113

5.4.2 Landscape colonization...... 114

5.5 Discussion...... 115

5.6 References...... 128

Chapter 6...... 132

6 Conclusion...... 132

6.1 Summary of results ...... 132

6.2 Future work...... 134

6.2.1 Masting ...... 134

6.2.2 Reproductive effort ...... 136

6.2.3 Dispersal kernels...... 136

6.2.4 Simulating the trailing population ...... 137

6.2.5 Tropical plants and migration...... 138

6.2.6 Arid PFTs...... 138

6.3 Significance of Ph.D. research...... 138

6.4 References...... 142

Appendix 1. Parameter values for plant functional types ...... 145

Appendix 2. C++ code used in LPJ-DISP to simulate dispersal ...... 151

Appendix 3. Additional simulations with a smaller grid cell size ...... 160 viii

List of Tables

Table 2-1. Parameter values that were used to describe the two new plant functional types, Tropical needleleaf evergreen and Desert/xeric shrub ...... 38

Table 2-4. Summary of modifications made to both the Olson et al. (2001) [designated by "Olson"] and Haxeltine & Prentice (1996) [designated by "H&P"] vegetation maps. Grid size was increased from 0.166 to 1º (Olson et al. , 2001) and from 0.5 to 1.0º (Haxeltine & Prentice, 1996) and the number of biomes was reduced from 9 to 4 (Olson et al. 2001) and 12 to 4 (Haxeltine & Prentice, 1996) ...... 41

Table 2-6. Comparison of our simulated results against the Olson et al. (2001) [designated by "Olson"] and Haxeltine & Prentice (1996) [designated by "H&P"] vegetation maps using a modified Kappa statistic. Modifications included decreasing the number of biomes down to four and increasing grid cell size to 0.10º. PFT is plant functional type. TrNE is tropical needleleaf evergreen. DeSH is desert shrub ...... 43

Table 3-1. Values used to parameterize the three test species (additional PFT values listed in Table A-2). αdisp is a distance parameter used in the dispersal kernel. reprfrac is the fraction of carbon allocated to reproduction and k est_repr is a constant in the equation for seed production ...... 72

Table 3-2. Migration rates for each species. Shown is the average ± standard deviation (minimum – maximum values) ...... 73

Table 4-1. Parameters tested in the sensitivity analysis and the range of values used for generating input values for the Latin hypercube sampling design ...... 97

Table 4-2. Results of a sensitivity analysis for dispersal dichotomous outcomes; whether or not seeds entered the first row of grid cells (Dispersal), and whether or not PFTs migrated through the first row (Migration) ...... 98

Table 5-1. Original climate data used and the degree of climate change applied (shown by ∆Temperature and ∆Precipitation) for the different simulations described in section 5.3.2 and Figure 5-1 ...... 120

Table 5-2. Values used to parameterize the three test species (additional PFT values listed in Table A-2). αdisp is a distance parameter used in the dispersal kernel. There was no published value for αdisp for F. grandifolia . Since it has very short dispersal distances, the smallest value the model accepts was chosen (Chapter 4). reprfrac is the fraction of carbon allocated to reproduction and kest_repr is a constant in the equation for seed production. F. grandifolia is a masting species, so the higher values for reprfrac and kest_repr were used during mast years and the lower values were used during non-mast years ...... 121

Table 5-3. Colonization rates (defined as the cumulative number of occupied grid cells regressed against the simulation year), with and without refugia. For the linear model, a = intercept and b = slope. For the exponential model, a = asymptote, b = scale and r = growth rate. Equations can be seen in the corresponding graphs in Figure 5-5 ...... 122

List of Figures

Figure 1-1. Comparison of plant functional type (PFT) representation in a grid cell between (a) a typical dynamic global vegetation model (DGVM) and (b) a hybrid dynamic vegetation model (LPJ-GUESS) ...... 14

Figure 1-2. Flow diagram illustrating the processes already included in LPJ-GUESS and how the new seed dispersal module fits within this framework. The new processes/decisions are those in bold, and the pathways which are no longer used are illustrated with a dashed line. Processes are in squares, lines connect the flow of information between modules and decisions are in diamonds. A more detailed flow diagram for LPJ-GUESS can be found in Smith et al. (2001) ...... 15

Figure 2-1. (a) Olson et al. (2001) biome map for the study area. (b) LPJ-GUESS simulated distribution of biomes using the global PFT parameterization and (c) including the two new PFTs (tropical needleleaf evergreen tree and xeric shrub). Both simulations shown include fire as a disturbance. The small inset maps show the distribution of prediction errors (red indicates a difference between the Olson biome and the predicted biome from LPJ-GUESS) ...... 44 - 45

Figure 2-2. (a) Haxeltine & Prentice (1996) biome map for the study area. (b) LPJ-GUESS simulated distribution of biomes using the global PFT parameterization and (c) including the two new PFTs (tropical needleleaf evergreen tree and xeric shrub). Both simulations shown include fire as a disturbance. The small inset maps show the distribution of prediction errors (red indicates a difference between the Haxeltine & Prentice biome and the predicted biome from LPJ-GUESS) ...... 46 - 47

Figure 2-3. Annual carbon flux to atmosphere from burnt vegetation and litter. The model was run for 1000 years, shown are the number of years which had (a) small fires ( ≥ 0.1 kg C/m 2 and < 1.0 kg C/ m2) and (b) large fires ( ≥ 1.0 kg C/m 2). Note the difference in scale ...... 48

Figure 2-4. (a) Comparison of simulated LAI values from LPJ-GUESS to satellite-derived LAI value from MODIS. The LAI values from LPJ-GUESS are from the simulation which included fire and the new PFTs, TrNE and DeSh. The 1:1 line is shown. The LAI values from MODIS are for July 2005, the maximum annual LAI. (b) The spatial representation of simulated LAI from LPJ-GUESS and (c) satellite-derived LAI from MODIS ...... 49

Figure 3-1. Schematic diagram illustrating (a) the original way LPJ-GUESS simulates the landscape in one-dimension, and (b) the new way LPJ-DISP simulations the landscape in two- dimensions. The new scheme allows seed dispersal to occur between grid cells since grid cells exist at the same time as their neighbouring cells, and they all progress through the simulation one year at a time. t s represents the spin up period ...... 74

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Figure 3-2. The number of patches in a grid cell located within a certain distance from the edge and which contain the PFT in question. Since patches don’t have an actual location within the grid cells, a Poisson distribution of patches was generated 1000 times and the average number of patches within certain distances was calculated. The following equation describes this relationship: pPFT (x) = (( /1.0 cell _ size )∗ x)∗ nPFT (equation 3.3, described in text) ...... 75

Figure 3-3. Migration of tree species over time. Each line represents one grid cell and there are 10 grid cells in every row. Each grid cell was ~18 km 2 (0.166°). For graphing purposes, distance was calculated by multiplying the proportion of occupied patches within a grid cell by 18 km. For example, if 30% of the patches were occupied in year 2150 then it had moved 5.4 km through that grid cell ...... 76 - 78

Figure 4-1. Different ways to sample a 2-parameter space (X 1 and X 2) with 9 input combinations. (a) A full factorial design, (b) a random sample, (c) Latin hypercube sampling (LHS) which maximizes the minimum distance between points (shown by the line connecting two points), and (d) an alternative Latin hypercube sampling design with very poor representation of the input space...... 99

Figure 4-2. Logistic regression for probability of dispersal (whether or not seeds entered the first row of grid cells). αdisp is the distance parameter used in the dispersal kernel. Values below 7 have no dispersal ...... 100

Figure 4-3. Results from a sensitivity analysis for migration rates for (a) overall migration rate – shortest amount of time to travel the greatest distance, (b) average migration rate, first row only, and (c) average migration rate for the rest of the grid cells. SRC –standardized regression coefficient, LCC – linear correlation coefficient, PCC – partial correlation coefficient, SRRC – standardized ranked regression coefficient, LRCC – linear ranked correlation coefficient, PRCC – partial ranked correlation coefficient ...... 101 - 102

Figure 5-1. Theoretical locations of refugia populations. Light green grid cells are the southern refugia, dark green grid cells are the more northerly refugia, white are unoccupied, and blue is the glacier. Configuration (a) was used for Acer rubrum and Fagus grandifolia , configuration (e) was used for Picea glauca. Additional simulations testing the number and location of refugia (b – d) were done using Acer rubrum ...... 123

Figure 5-2. Simulation of Acer rubrum migration across a landscape, (a) from the southern refugia only and (b) with the addition of a northerly refugia population. The colour represents the year after climate warming (in 200 year steps) when Acer moved all the way through the grid cell. Acer was considered to have moved all the way through a grid cell once > 80% of the patches were occupied ...... 124

Figure 5-3. Simulation of Fagus grandifolia migration across a landscape, (a) from a southern refugia solely and (b) with a northerly refugia population. The colour represents the year (in 200 year steps) when Fagus moved all the way through the grid cell ...... 125

Figure 5-4. Simulation of Picea glauca migration across a landscape, (a) from a southern refugia solely and (b) with a northerly refugia population. The colour represents the year (in 200 year steps) when Picea moved all the way through the grid cell ...... 126

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Figure 5-5. Landscape colonization rate, calculated as the cumulative number of colonized grid cells (i.e. > 80% of the patches within a grid cell occupied by that species) regressed against the simulation year. The northerly refugia location was located in the middle of the landscape for (a) Acer rubrum and (c) Fagus grandifolia , and in the top corner for (d) Picea glauca . (b) shows the effect of changing the number and location of refugia for Acer rubrum . See Figure 5-1 for a diagram of the landscape and refugia locations ...... 127

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List of Appendices

Appendix 1. Parameter values for plant functional types ...... 144

Table A-1. Plant functional type (PFT) parameterization implemented in LPJ-GUESS (Smith et al. , 2001; Sitch et al., 2003). The abbreviations refer to the following PFTs: TeBE–Temperate broad-leaf evergreen, TeBS–Temperate broad-leaf summergreen, TrBE–Tropical broad-leaf evergreen, TrBR–Tropical broad-leaf raingreen, TrNE–Tropical needle-leaf evergreen, TeH– Temperate herbaceous, TrH–Tropical herbaceous ...... 146 - 147

Appendix 2. C++ code used in LPJ-DISP to simulate dispersal ...... 150

Appendix 3. Additional simulations with a smaller grid cell size ...... 159

Table A-3. The effect of cell size on average migration rates ...... 160

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Chapter 1

1 Introduction

Ecological modelling can be a valuable tool, allowing us to create experiments which would either be too costly, potentially harmful, or logistically impossible to do in the real world (Petrovskii & Petrovskaya, 2012). Studying how climate change impacts organisms and/or ecosystems is an area where computer models have been extremely useful (e.g. Shugart et al. , 1992; Cramer et al. , 2001; Cowling & Shin, 2006; Ni et al. , 2006). Applying future climate change scenarios can identify which species or ecosystems are at risk and allow conservationists and land managers to react accordingly (Scott et al. , 2002; Bernazzani et al. , 2012).

All vegetation-climate models have the same goals. First, to simulate the current distribution of a species or vegetation type using a combination of input factors, such as climate, elevation, soil, and biotic interactions (where are they found and why ?). Second, to determine how the distribution will be affected when climate changes (using the why explanations developed from the first step). Yet a crucial step in the middle is typically overlooked – how will they expand into their new distribution?

Migration is less of an issue for animals, which are already modifying their ranges in response to climate change (Thomas & Lennon, 1999; Parmesan & Yohe, 2003). However, it is not as simple for long-lived sessile organisms, like trees, which can take hundreds of years to shift their distributions (Pitelka et al. , 1997; Williams et al. , 2004). Effective plant migration starts with long distance seed dispersal, followed by successful establishment in new habitats, seedling growth and subsequent attainment of reproductive maturity (Pitelka et al. , 1997). In general, there are two approaches to vegetation-climate models: the statistical (species distribution models) and the mechanistic (dynamic global vegetation models). Thus far, no vegetation-climate model currently includes all of the necessary steps to accurately simulate vegetation migration in response to climate change.

1.1 Seed dispersal and vegetation migration

Seed dispersal is the transportation of seeds away from their parent plant. Seed dispersal is important in several respects; it reduces competition between parents and offspring and between siblings, it allows plants to colonize newly disturbed sites, and to discover microhabitats suitable for establishment and growth (Howe & Smallwood 1982). The fruit of the plant is designed to protect the seeds and to aid in dispersal. Fruit or seed morphology is used to determine the dispersal mechanisms, which is typically based on the disperser agent or vector (Howe & Smallwood 1982). Wind dispersal (anemochory) typically has light weight seeds, or fruit with wings or plumes. Water dispersed seeds (hydrochory) usually contain large spaces filled with air, or are covered in slime or hair to prevent sinking. Animal dispersal (zoochory) use a variety of adaptations; hooks or spines can attach to fur or feathers, and fleshy fruits are designed to be eaten. Dispersal by the plant itself (autochory) is achieved through explosive fruits which can throw their seeds several meters.

Vegetation migration and range expansion is a reflection of successful seed dispersal (Levin et al . 2003). Different seed dispersal vectors will have consequences for the frequency and success of long distance dispersal. For example, bird-dispersed seeds have the potential for higher mean dispersal distances and more frequent long distance dispersal events. Compare this to plants which use ants as their main dispersers, and the consequences for population expansion rates become clear. This is the reason why seed dispersal needs to be incorporated into vegetation-climate models, to reflect the variation between plants and their ability to respond to climate change.

1.2 Vegetation-climate models

1.2.1 Species distribution models

Species distribution models (SDM, aka niche-based models or climatic envelope models) are one of the more commonly used techniques to describe current and future species ranges ( reviewed in Guisan & Thuiller, 2005). These statistical models find the

3 correlation between current species distribution and a variety of climate/landscape variables (Pearson & Dawson, 2003). Once this climatic niche has been established, future climate scenarios can be applied to test the potential shift in a species distribution. SDMs have been very useful for determining potential future distributions for individual species, indentifying those with the highest risk of extinction due to habitat loss (Pearson et al. , 2002; Peterson et al. , 2002).

However, SDMs make several assumptions which can compromise the quality of their predictions (Hampe, 2004). Distribution models don’t allow for species to change their climatic tolerances (Woodward, 1990), they assume species are in equilibrium with the current climate (Svenning & Skov, 2007; Willner et al. , 2009) and they do not consider the importance of biotic interactions, such as competition, herbivory, or predation. Especially at smaller scales, the realized distribution of species is more a reflection of biotic interactions instead of climate (Davis et al. , 1998). Finally, SDMs rarely include dispersal capability for individual species. Most models assume either no dispersal or full dispersal, where species can arrive at any location regardless of distance or physical barriers. Depending on the assumptions made about dispersal, there can be a huge difference in future estimates of extinction rates and habitat shifts (Thomas et al. , 2004; Thuiller et al. , 2005).

1.2.2 Dynamic global vegetation models

An alternative approach to the correlative models are physiologically-based models, which simulate the processes through which climate can control vegetation distribution, form and function. Dynamic global vegetation models (DGVMs) simulate biogeochemical cycles, vegetation structure and the ecological processes that determine the balance between different plant types, such as establishment, competition, growth and mortality (e.g. Friend et al ., 1997; Cox et al ., 2000; Cramer et al. , 2001). DGVMs also include feedbacks between the atmosphere and biosphere, allowing the vegetation to respond to changes in climate. However, DGVMs have limitations in both scale and generality. DGVMs are designed to predict global or continental patterns of vegetation which means a coarse resolution (grid cell sizes are a minimum of 0.5°, approximately 55 km 2) and minimal plant types. Due to computational and parameter limitations, DGVMs

4 do not simulate individual species, but instead group similar vegetation into plant functional types (PFTs). This limits their usefulness in predicting patterns of biodiversity and potential species extinctions. Within a grid cell, each PFT is represented as one average individual (Figure 1-1a) which makes it difficult to simulate population dynamics and competition.

The next generation of DGVMs are the so-called hybrid models, which address some of the limitations by incorporating a forest gap model into a DGVM framework (Smith et al. , 2001; Sato et al. , 2007; Fisher et al. , 2010). Hybrid models simulate multiple forest patches and multiple individuals for each PFT within a grid cell (Figure 1-1b). This allows hybrid models to simulate vertical structure and competition for light, as well as more realistic representations of mortality, gap formation and succession. Hybrid models were also designed to simulate smaller areas at a finer resolution. Moving from a global to a regional perspective also allows the parameterization of PFTs to better represent local or regional vegetation (Hickler et al. , 2004; Hély et al. , 2006; Sato, 2009).

1.3 Dispersal in vegetation-climate models

1.3.1 Species distribution models

Despite their limitations, most of the progress towards simulating vegetation migration has occurred using species distribution models. To constrain the potential future range of species, some SDMs use a technique called ‘decadal time slices’ (Midgley et al. , 2006; Fitzpatrick et al. , 2008). Range shifts are projected at 10 year intervals and the maximum spread of a species during each time slice is restricted by a predetermined distance. For example, Midgley et al. (2006) allowed ant- and rodent-dispersed seeds to move a maximum of one grid cell per time slice (average of 150 m year -1), and wind-dispersed seeds a maximum of three grid cells per time slice (average of 400 m year -1). Although this approach provides a more conservative estimate of future range shifts, it still overestimates dispersal. The best case scenario (i.e. long distance dispersal) is applied to every individual, even though only a very small percentage of seeds travel significant distances from their parent (Cain et al. , 2000).

Some interesting work been done by linking species distribution models to external models, such as cellular automata models which place limits on grid-to-grid movement (Iverson et al ., 2004; van Loon et al ., 2011). Engler & Guisan (2009) also incorporated additional population measures such as reproduction, growth and senescence into the cellular automata. Conlisk et al. (2012) linked a SDM with a demographic model to determine population structure and dynamics within grid cells. These two studies (i.e. Engler & Guisan, 2009; Conlisk et al ., 2012) were able to examine the effect of changing local and maximum dispersal distances. Not surprisingly, it was the maximum dispersal distance that had the largest impact on the species ability to move into suitable habitat under future climate change. However, the tested range for long distance dispersal was enormous (100 m – 10 km in Engler & Guisan, 2009; 4 – 40 km in Conlisk et al ., 2012) which could result in an overestimation of migration potential. Interestingly, when Conlisk et al . (2012) applied a more moderate dispersal scenario (average migration 1 km, maximum migration 4 km), the abundance of Oak trees remained almost the same as when there was no dispersal.

1.3.2 Dynamic global vegetation models

Compared to the SDMs, the physiological models may be better suited to simulate vegetation migration since most already include plant establishment, growth, reproduction and competition. Neither the DGVMs nor hybrid models include seed dispersal, an essential step when simulating migration in response to climate change. Most DGVMs (i.e. IBIS, LPJ, SDGVM) allow all the climatically suitable PFTs to establish in the available spaces (Cramer et al. , 2001), and it is the competition between PFTs that results in the final vegetation composition. There is no function which limits the seedling population by the density or even presence of parent trees. The hybrid model LPJ-GUESS, is unique in that it uses the reproductive output from each PFT to determine the number of seedlings establishing within a grid cell (Smith et al. , 2001). However after a patch is destroyed, all climatically tolerant PFTs are allowed to repopulate the space regardless of the presence/absence of parent trees within the grid cell. In this respect, physiological models also make the assumption of full migration

6 where plants can arrive in new, climatically suitable areas regardless of physical barriers or seed dispersal limitations.

1.4 Adding dispersal into a DGVM

1.4.1 Challenges to simulating dispersal in DGVMs

Although the assumption of full migration is clearly flawed, DGVMs are restricted by their model architecture. DGVMs only appear to represent the landscape as a 2- dimensional grid. In reality, the model actually simulates a one-dimensional surface (Fisher et al. , 2010). Each grid cell is simulated independently and is not retained in memory once it reaches the total number of simulation years. Grid cells don’t know what their neighbours are doing or even who their neighbours are, making it impossible to simulate movement between cells. The problems continue inside each grid cell. Representing vegetation as one average individual for each PFT (Figure 1-1a) allows new PFTs to arrive and establish as one large individual that immediately covers the distance of the grid cell. Migration rates would essentially be equal to grid cell resolution, 55 km year -1 in most models. Adding a residency time (i.e. forcing the PFT to stay in the current cell for a set number of years before spreading to the next cell) would be an artificial solution since the choice of a lag time would predetermine the simulated migration rates.

The unique patch architecture of the hybrid model LPJ-GUESS (Figure 1-1b) presents an opportunity to simulate dispersal through a grid cell, without immediately travelling the entire distance of the cell. New PFTs would need to travel from patch to patch across the cell. LPJ-GUESS already simulates carbon assimilation, allocation of carbon to growth and reproduction, seedling establishment and competition between PFTs (Figure 1-2). To simulate plant migration in LPJ-GUESS, I will be introducing limitations on patch-to- patch movements, adding a maturation age and allowing communication between grid cells.

1.4.2 The model, LPJ-GUESS

LPJ-GUESS is a generalized ecosystem model that combines the dynamic global vegetation model LPJ with a forest gap model (Smith et al. , 2001). The model requires a variety of environmental input (i.e. temperature, precipitation, solar radiation, soil characteristics, and CO 2 concentration). To clarify, I refer to LPJ-GUESS as a vegetation-climate model because it uses climate data to simulate vegetation. However, it is not a true vegetation-climate model since there is no feedback between vegetation and climate. It is a one-way system, where climate influences vegetation but the reciprocal is not true. LPJ-GUESS is part of the DGVM family of models that could be linked to a GCM (General Circulation Model), which would enable us to simulate the bi- directional vegetation climate feedback in future applications.

Carbon assimilation is calculated using a modified Farquhar photosynthesis scheme

(Haxeltine & Prentice, 1996) which is influenced by temperature, atmospheric CO 2 concentration, absorbed photosynthetically active radiation and stomatal conductance. At the end of a year, the amount of carbon available for tree height and growth is reduced by maintenance respiration, growth respiration, leaf and root turnover, and a fixed allocation to reproduction (Smith et al. , 2001). A complete description of LPJ-GUESS is given by Smith et al. (2001), and further details on the physiological and biogeochemical components of the model are provided by Sitch et al. (2003). The improved hydrology module described by Gerten et al. (2004) is included.

LPJ-GUESS can be run in population or cohort mode. In population mode, vegetation is represented as one average individual for each plant functional type within each grid cell (Figure 1-1a). This is essentially the same as the global model, LPJ-DGVM (Smith et al. , 2001). When LPJ-GUESS is run in cohort mode, each grid cell contains a number of replicate patches. Within each patch, each PFT is represented by many different individuals, each from a different age cohort (Figure 1-1b). This allows the model to simulate competition for light and vertical stand structure, interactions between shade tolerant and intolerant PFTs, and succession in a more realistic fashion. Consider the impact on modeling vegetation migration as well. In DGVMs, a seed is allowed to establish if the environment is suitable and there is space (i.e. if the grid cell is not 100%

8 covered already). In cohort mode, seeds may enter a patch in a grid cell if the environment is suitable and they are able to establish, which is now influenced by competition for space and light. As with other forest gap models, establishment, mortality and disturbance are implemented as stochastic processes allowing for different dynamics in different patches.

The global model, LPJ-DGVM, has been shown to produce fairly robust estimates of land-atmosphere flux and current global vegetation distribution (Zaehle et al. , 2005). One important model output is net primary productivity (NPP). Estimates for NPP are most sensitive to parameters which control photosynthesis, light interception and absorption. Parameters used for the various water balance processes (e.g. stomatal conductance, water extraction) become more important in water-limited environments (Zaehle et al. , 2005). One reason why NPP is so important is because it is used to determine the carbon available for growth. Vegetation carbon pools are determined by the rate of conversion of sapwood to hardwood, the leaf-to-sapwood-area ratio, and vegetation dynamics such as mortality and establishment (Zaehle et al., 2005; Wramneby et al. , 2008).

The variation in vegetation composition is determined by PFT specific climatic tolerances, and factors which influence the competitive balance between them. In the global model, factors such as lower self-thinning coefficient, faster rate of canopy closure, higher re-establishment rate, and a lower maximum mortality tend to increase the cover of the dominant PFT (Zaehle et al ., 2005). In LPJ-GUESS, competition between shade-tolerant and shade-intolerant PFTs determines the final vegetation structure (Wramneby et al ., 2008). The sapwood to hardwood conversion rate and the minimum forest-floor light requirements are the most important parameters for describing the degree of shade tolerance in PFTs (Wramneby et al ., 2008).

1.5 Outline of chapters and objectives

My Ph.D. thesis consists of 6 chapters: this introduction chapter, four data chapters, and a conclusion chapter. Chapters 2, 3, 4 and 5 were written as stand-alone manuscripts and thus, may contain some repetition between chapters.

Chapter 2 addresses the first question for vegetation-climate models: where are vegetation types found and why are they there? Most dynamic vegetation-climate models were designed with temperate or boreal regions in mind. However, tropical ecosystems have a greater variety of seed dispersal syndromes (Jordano, 2000) and the potential for more long-distance dispersal by animals (Clark et al. , 1999; Campos-Arceiz & Blake, 2011). A dynamic vegetation model which includes seed dispersal would be invaluable for the tropics; however LPJ-GUESS has never been used to represent the neotropics. In Chapter 2, I used LPJ-GUESS to simulate the current vegetation distribution in Central America for the first time. Despite adding in new tropical PFTs, the model was still not able to accurately capture the distribution of ecosystems in Mexico and Central America. This chapter discusses possible reasons why the model failed, and which processes unique to tropical ecosystems need to be included for LPJ-GUESS to simulate the neotropics. Chapter 2 has been submitted to Biotropica and is under review. Sharon A. Cowling and Ben Smith (Lund University, Sweden) are co-authors on this paper. SAC contributed to the development of research questions, discussion of results and editing. BS designed LPJ-GUESS and has kindly allowed me use of his model for my Ph.D. research.

Although I initially planned to simulate seed dispersal in the tropics, the limited ability of LPJ-GUESS to represent neotropical vegetation prevented me from pursuing this. Fortunately, the lack of seed dispersal in DGVMs is not only relevant to tropical ecosystems. I continued to work towards adding dispersal limitations in LPJ-GUESS and used PFTs that had been previously validated in temperate forests in North America (Hickler et al. , 2004). In Chapter 3, I describe how I used the unique patch architecture in LPJ-GUESS to simulate vegetation migration through a grid cell, and between grid cells (Figure 1-2). This is the first time a mechanistic representation of seed dispersal has

10 been incorporated into a dynamic vegetation-model, and the first time all the steps required for plant migration (i.e. seed production, dispersal, establishment, growth and reproductive maturity) have been included in a vegetation-climate model. LPJ-DISP refers to the new version of LPJ-GUESS that includes seed dispersal. LPJ-DISP was tested using three temperate species ( Acer rubrum , Pinus rigida and Tsuga canadensis ). Simulated plant migration rates in response to climate change were then compared to reconstructed migration rates from pollen records and from phylogenetics.

Chapter 4 is a sensitivity analysis for LPJ-DISP. This analysis indentifies which parameters have the strongest impact on the simulated migration rates. Several parameters were added to the model in Chapter 3 to represent seed dispersal between patches and grid cells. Although some of the parameters can be measured in the field, some cannot. It is important to identify the level of uncertainty in model predictions based upon uncertainty in parameter values.

In Chapter 5, I demonstrate how LPJ-DISP can be used to address different hypotheses about rapid plant migration. Following the retreat of the last glacier in North America and Europe, trees appear to have spread much faster than expected based on known seed dispersal distances (Clark et al. , 1998). Possible explanations include rare, long distance seed dispersal (Clark, 1998) and the presence of undetected northern refugia populations (Birks & Willis, 2008). Both are difficult to prove based on field data, but both can contribute to rapid landscape re-colonization. I use LPJ-DISP to simulate vegetation migration for three species with known northern refugia ( Acer rubrum , Fagus grandifolia and Picea glauca ). I compare landscape colonization rates when trees only use long distance seed dispersal and when trees also have small, northerly refugia populations.

Chapter 6 provides an overall summary and synthesis for the Ph.D. I discuss the significance of my work and future research needs that were identified during the course of my study.

The objectives of my thesis do not include improving the representation of vegetation and ecological processes previously included in LPJ-GUESS (i.e. the formulas, parameters and constants which have already been presented and evaluated (Smith et al. , 2001; Sitch

11 et al. , 2003; Gerten et al ., 2004; Zaehle et al. , 2005; Hickler et al. , 2006; Wramneby et al. , 2008)). The scope of my thesis was to determine how well the existing model could simulate vegetation dynamics in a previously untested region (i.e. the neotropics) and to incorporate and evaluate a new ecological process (i.e. seed dispersal) in LPJ-GUESS. The scope of this thesis does not include an evaluation of the realism of vegetation- climate models. Simulating ecological processes at a large scale is always a compromise between complex, chaotic relationships and simple mathematical approximations. My intention for incorporating a representation of seed dispersal in LPJ-GUESS was not to make the model more “realistic”, but it will certainly improve predictions and offer a more conservative estimate of vegetation migration in response to climate change.

1.6 Glossary of terms

These words and phrases are commonly used throughout my thesis. This is how they have been defined within the context of my research.

Average migration rate (m year -1) The mean migration rate through each grid cell in a simulation. Another way to think of this is the average number of years it took to move the vertical distance of one grid cell (18 km).

Barriers to migration Factors which prevent seeds from reaching a potential habitat. This can include obstacles such as large water bodies, mountains and landscape fragmentation. Potential migration barriers may be different for each dispersal vector (some factors will limit some seeds but not others).

Dispersal between cells Describes seed dispersal between grid cells. Patches close to the edge of the grid cell recieve seeds from a neighbouring grid cell. The probability of dispersal is determined by the seed dispersal kernel (see Section 3.3.6).

Dispersal within cells Describes seed dispersal between patches within a grid cell. The probability of dispersal is determined by a logistic growth function (see Section 3.3.8).

Dynamic Global Vegetation Models (DGVM) Group of models which simulate biogeochemical cycles, vegetation structure and include process-based representations of vegetation dynamics. Dynamic models can also simulate the changes in vegetation structure after a disturbance or in reaction to a changing climate.

Full migration No limitations on vegetation migration (i.e. does not consider the presence/absence of parent trees, seed dispersal limitations, or barriers to migration). Plants can arrive at any location provided the climate is suitable.

Grid cell An 18 km 2 location specified by latitude and longitude in LPJ-DISP or LPJ- GUESS. In the thesis, also referred to as cell(s).

Hybrid models Models which include a forest gap model within a DGVM framework. They are intended to improve the representation of regional vegetation dynamics, by running at a finer resolution and including more realistic representations of vertical structure and light competition between PFTs.

LPJ-DISP The version of LPJ-GUESS which includes seed dispersal.

LPJ-GUESS A hybrid dynamic vegetation-climate model which combines the forest gap model FORSKA with the global model LPJ DGVM (Smith et al. , 2001; Sitch et al. , 2003).

Migration rate (m year -1) The movement of plants over time (see Average migration rate and Overall migration rate).

Overall migration rate (m year -1) The fastest amount of time to move the greatest distance. Depending on the simulation, the maximimum vertical distance is anywhere from 90 km – 234 km.

Plant functional types (PFTs) Phylogenetically independent group of plant species that show similarities in their resource use, growth and response to environmental conditions.

Seed dispersal The movement or transport of seeds away from their parent plant.

Species distribution models (SDM) Group of models that relate species distribution data (presence and/or abundance) with environmental and/or landscape variables. Also referred to as ecological niche models or bioclimatic envelope models.

Vegetation migration The movement of plants into new habitats, via seed dispersal, establishment and growth.

(a) Typical grid cell in a DGVM (b) Typical grid cell in LPJ-GUESS in cohort mode

Grid cell Grid cell

PFT 1 PFT 2 PFT 3 Patch

Input variables (climate, soil, CO 2, lat/long, elevation)

Daily processes (for each patch, for each grid cell) Climate and soil calculations Figure 1-2. Flow diagram illustrating the processes already included in LPJ-GUESS and how the new Leaf phenology Light interception seed dispersal module fits within this framework. Photosynthesis The new processes/decisions are those in bold, and Water balance Soil water and dynamics the pathways which are no longer used are illustrated with a dashed line. Processes are in squares, lines connect the flow of information Annual processes (for each patch, for each grid cell) between modules and decisions are in diamonds. A more detailed flow diagram for LPJ-GUESS can be Maintenance respiration Turnover found in Smith et al. (2001). Carbon allocation and growth

Reached maturation age?

Yes Allocation to Propagule pool by PFT reproduction

Yes PFT present Establishment in patch?

No Disturbance and mortality Dispersal Yes PFT present between patches in grid cell?

Neighbouring grid cell Dispersal between grid cells Propagule pool by PFT

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Engler, R. & Guisan, A. (2009) MIGCLIM: Predicting plant distribution and dispersal in a changing climate. Diversity and Distributions , 15 , 590-601. Fisher, R., McDowell, N., Purves, D., Moorcroft, P., Sitch, S., Cox, P., Huntingford, C., Meir, P., & Woodward, F.I. (2010) Assessing uncertainties in a second-generation dynamic vegetation model caused by ecological scale limitations. New Phytologist , 187 , 666-681. Fitzpatrick, M.C., Gove, A.D., Sanders, N.J., & Dunn, R.R. (2008) Climate change, plant migration, and range collapse in a global biodiversity hotspot: the Banksia (Proteaceae) of Western Australia. Global Change Biology , 14 , 1337-1352. Friend, A.D., Stevens, A.K., Knox, R.G., & Cannell, M.G.R. (1997) A process-based, terrestrial biosphere model of ecosystem dynamics (Hybrid v3.0). Ecological Modelling , 95 , 249-287. Gerten, D., Schaphoff, S., Haberlandt, U., Lucht, W., & Sitch, S. (2004) Terrestrial vegetation and water balance - hydrological evaluation of a dynamic global vegetation model. Journal of Hydrology , 286 , 249-270. Guisan, A. & Thuiller, W. (2005) Predicting species distribution: offering more than simple habitat models. Ecology Letters , 8, 993-1009. Hampe, A. (2004) Bioclimatic envelope models: what they detect and what they hide. Global Ecology and Biogeography , 13 , 469-471. Haxeltine, A. & Prentice, I.C. (1996) BIOME3: An equilibrium terrestrial biosphere model based on ecophysiological constraints, resource availability, and competition among plant functional types. Global Biogeochemical Cycles , 10 , 693-709. Hély, C., Bremond, L., Alleaume, S., Smith, B., Sykes, M.T., & Guiot, J. (2006) Sensitivity of African biomes to changes in the precipitation regime. Global Ecology and Biogeography , 15 , 258-270. Hickler, T., Smith, B., Sykes, M.T., Davis, M.B., Sugita, S., & Walker, K. (2004) Using a generalized vegetation model to simulate vegetation dynamics in northeastern USA. Ecology , 85 , 519-530. Hickler, T., Prentice, I.C., Smith, B., Sykes, M.T., & Zaehle, S. (2006) Implementing plant hydraulic architecture within the LPJ Dynamic Global Vegetation Model. Global Ecology and Biogeography , 15 , 567-577. Howe, H.F. & Smallwood, J. (1982) Ecology of seed dispersal. Annual Review of Ecology and Systematics , 13 , 201-228. Iverson, L.R., Schwartz, M.W., & Prasad, A.M. (2004) Potential colonization of newly available tree-species habitat under climate change: an analysis for five eastern US species. Landscape Ecology , 19 , 787-799. Jordano, P. (2000). Fruits and frugivory. In Seeds: The ecology of regeneration in plant communities (ed M. Fenner), pp. 125-165. CABI Publishing, New York.

Levin, S.A., Muller-Landau, H.C., Nathan, R., & Chave, J. (2003) The ecology and evolution of seed dispersal: a theoretical perspective. Annual Review of Ecology and Systematics , 34 , 575-604. Midgley, G.F., Hughes, G.O., Thuiller, W., & Rebelo, A.G. (2006) Migration rate limitations on climate change-induced range shifts in Cape Proteaceae. Diversity and Distributions , 12 , 555-562. Ni, J., Harrison, S.P., Prentice, I.C., Kutzbach, J.E., & Sitch, S. (2006) Impact of climate variability on present and Holocene vegetation: a model-based study. Ecological Modelling , 191 , 469-486. Parmesan, C. & Yohe, G. (2003) A globally coherent fingerprint of climate change impacts across natural systems. Nature , 421 , 37-42. Pearson, R.G. & Dawson, T.P. (2003) Predicting the impacts of climate change on the distribution of species: are bioclimate envelope models useful? Global Ecology and Biogeography , 12 , 361-371. Pearson, R.G., Dawson, T.P., Berry, P.M., & Harrison, P.A. (2002) SPECIES: A spatial evaluation of climate impact on the envelope of species. Ecological Modelling , 154 , 289-300. Peterson, A.T., Ortega-Huerta, M.A., Bartley, J., Sanchez-Cordero, V., Soberon, J., Buddemeier, R.H., & Stockwell, D.R.B. (2002) Future projections for Mexican faunas under global climate change scenarios. Nature , 416 , 626-629. Petrovskii, S. & Petrovskaya, N. (2012) Computational ecology as an emerging science. Interface Focus , 2, 241-254. Pitelka, L.F., Gardner, R.H., Ash, J., Berry, S., Gitay, H., Noble, I.R., Saunders, A., Bradshaw, R.H.W., Brubaker, L., Clark, J.S., Davis, M.B., Sugita, S., Dyer, J.M., Hengeveld, R., Hope, G., Huntley, B., King, G.A., Lavorel, S., Mack, R.N., Malanson, G.P., McGlone, M., Prentice, I.C., & Rejmanek, M. (1997) Plant migration and climate change. American Scientist , 85 , 464-473. Sato, H. (2009) Simulation of the vegetation structure and function in a Malaysian tropical rain forest using the individual-based dynamic vegetation model SEIB- DGVM. Forest Ecology and Management , 257 , 2277-2286. Sato, H., Itoh, A., & Kohyama, T. (2007) SEIB-DGVM: A new dynamic global vegetation model using a spatially explicit individual-based approach. Ecological Modelling , 200 , 279-307. Scott, D., Malcolm, J.R., & Lemieux, C. (2002) Climate change and modelled biome representation in Canada's national park system: implications for system planning and park mandates. Global Ecology and Biogeography , 11 , 475-484. Shugart, H.H., Smith, T.M., & Post, W.M. (1992) The potential for application of individual-based simulation models for assessing the effects of global change. Annual Review of Ecology and Systematics , 23 , 15-38. Sitch, S., Smith, B., Prentice, I.C., Arneth, A., Bondeau, A., Cramer, W., Kaplans, J.O., Levis, S., Lucht, W., Sykes, M.T., Thonicke, K., & Venevsky, S. (2003)

Evaluation of ecosystem dynamics, plant geography and terrestrial carbon cycling in the LPJ dynamic global vegetation model. Global Change Biology , 9, 161-185. Smith, B., Prentice, I.C., & Sykes, M.T. (2001) Representation of vegetation dynamics in the modelling of terrestrial ecosystems: comparing two contrasting approaches within European climate space. Global Ecology and Biogeography , 10 , 621-637. Svenning, J.C. & Skov, F. (2007) Could the tree diversity pattern in Europe be generated by postglacial dispersal limitation? Ecology Letters , 10 , 453-460. Thomas, C.D., Cameron, A., Green, R.E., Bakkenes, M., Beaumont, L.J., Collingham, Y.C., Erasmus, B.F.N., de Siqueira, M.F., Grainger, A., Hannah, L., Hughes, L., Huntley, B., van Jaarsveld, A.S., Midgley, G.F., Miles, L., Ortega-Huerta, M.A., Peterson, A.T., Phillips, O., & Williams, S.E. (2004) Extinction risk from climate change. Nature , 427 , 145-148. Thomas, C.D. & Lennon, J.J. (1999) Birds extend their ranges northwards. Nature , 399 , 213-213. Thuiller, W., Lavorel, S., Araujo, M.B., Sykes, M.T., & Prentice, I.C. (2005) Climate change threats to plant diversity in Europe. Proceedings of the National Academy of Sciences of the United States of America , 102 , 8245-8250. van Loon, A.H., Soomers, H., Schot, P.P., Bierkens, M.F.P., Griffioen, J., & Wassen, M.J. (2011) Linking habitat suitability and seed dispersal models in order to analyse the effectiveness of hydrological fen restoration strategies. Biological Conservation , 144 , 1025-1035. Williams, J.W., Shuman, B.N., Webb, T., Bartlein, P.J., & Leduc, P.L. (2004) Late- quaternary vegetation dynamics in North America: scaling from taxa to biomes. Ecological Monographs , 74 , 309-334. Willner, W., Di Pietro, R., & Bergmeier, E. (2009) Phytogeographical evidence for postglacial dispersal limitation of European beech forest species. Ecography , 32 , 1011-1018. Woodward, F.I. (1990) The impact of low temperatures in controlling the geographical distribution of plants. Philosophical Transactions of the Royal Society of London Series B-Biological Sciences , 326 , 585-593. Wramneby, A., Smith, B., Zaehle, S., & Sykes, M.T. (2008) Parameter uncertainties in the modelling of vegetation dynamics - Effects on tree community structure and ecosystem functioning in European forest biomes. Ecological Modelling , 216 , 277-290. Zaehle, S., Sitch, S., Smith, B., & Hatterman, F. (2005) Effects of parameter uncertainties on the modeling of terrestrial biosphere dynamics. Global Biogeochemical Cycles , 19 , GB3020.

Chapter 2

2 Simulating regional vegetation-climate dynamics for Central America: tropical versus temperate applications

2.1 Abstract

Regional vegetation-climate modelling studies have typically focused on boreal or temperate ecosystems in North America and Europe, almost completely overlooking tropical ecosystems. We present the first results of simulated regional vegetation-climate dynamics in Central America as simulated by the model, LPJ-GUESS. Two new PFTs were added (a tropical pine tree and a xeric shrub) and the model was run using fire as the main disturbance. The overall Kappa statistic indicated poor agreement, with a Kappa value of 0.301. By aggregating cell sizes and using more generalized biomes, the Kappa value increased to 0.543, indicating a fair agreement. Total LAI simulated from LPJ- GUESS was strongly correlated to remotely-sensed LAI values (r = 0.75). Simulations indicate that fire frequency was overestimated in tropical moist forests and underestimated in savannas. This underestimation of fire resulted in an over-simulation of dry tropical forest at the expense of savanna. Additional reasons for the initially poor representation of vegetation in Central America include factors such as seed dispersal, non-parameterized plant functional types (desert shrub, cacti and other succulents), rugged topography, and biogeographical history of vegetation migrations due to Pleistocene glacial-interglacial cycles.

2.2 Introduction

Dynamic global vegetation models (DGVMs) have adequately represented broad-scale global biomes, reproduced global trends in leaf area index (LAI), and provided realistic

21 estimates of annual net primary productivity (e.g. Prentice et al. , 1992; Friend et al. , 1997; Roelandt, 2001). Most current global vegetation models are so generic that tropical areas are almost exclusively predicted to be covered by one biome type: tropical broadleaf evergreen forest . At a regional scale, however, the tropical landscape exhibits substantially greater heterogeneity in vegetation cover. Most current global vegetation models do not include tropical biomes such as mangroves, desert (xerophytic) shrubland, and montane vegetation; all of which may be critically altered by future global change. Cloud forests in particular may be especially sensitive to climate change (Tellez-Valdés et al. , 2006) and are generally not represented in global models. An inability to capture more subtle differences in tropical vegetation types could severely limit our ability to realistically predict how tropical regions will respond to future climate change.

Regional dynamic vegetation models (e.g. Smith et al. , 2001) have been developed to address some of the limitations identified for DGVMs (Peng, 2000; Smith et al. , 2001; Thuiller et al. , 2008). Regional vegetation models can generally capture processes at the scale of plant functional type (PFT; evergreen tree, C 4 grass) or individual plant species (e.g. Hickler et al. , 2004; Weng & Zhou, 2006). For the most part, regional vegetation studies have focused on boreal or temperate ecosystems in North America and Europe (Kittel et al. , 2000; Badeck et al. , 2001; Smith et al. , 2001; Hickler et al. , 2004; Wolf et al. , 2008). A few regional vegetation-climate models have been applied to warmer regions including the Mediterranean Basin (Gritti et al. , 2006), China (Weng & Zhou, 2006) and central Africa (Hély et al. , 2006). To my knowledge, no regional vegetation model has been applied to Central America, a region containing a large expanse of arid and tropical vegetation types normally not seen in global model simulations.

The objective of this study is twofold: (1) to evaluate the ability of a regional dynamic vegetation model (LPJ-GUESS) to simulate current vegetation patterns and dynamics in a tropical region; and (2) to try to improve simulations by adding plant functional types more indicative of ecosystems in sub-tropical to tropical latitudes. Central America was chosen because it represents a tropical region with one of the highest diversities in vegetation types, excluding diversity at the species level. The study approaches the research objectives by: (1) identifying potential limitations in simulating diverse tropical

22 vegetation by using PFT definitions (types) currently represented in the regional model, LPJ-GUESS; (2) developing a modified PFT parameterization scheme to improve current regional vegetation representation; and (3) comparing simulation results against observational biome maps and against remote sensing data on leaf area index.

2.3 Methods

2.3.1 Description of LPJ-GUESS

LPJ-GUESS is a generalized ecosystem model (Smith et al. , 2001) that combines representations of vegetation dynamic processes from the forest gap models FORSKA (Prentice et al. , 1993) with the plant physiology and biogeochemistry of the global model LPJ DGVM (Sitch et al. , 2003). The model was used in cohort mode, in which tree and shrub populations are represented in ways similar to forest gap models. Within each grid cell, the growth of plants is simulated using a number of replicate patches, 100 in the present study. Within each patch, each PFT cohort is represented by an average individual. Each PFT is represented by many different individuals, each from a different cohort. The exception is for grass, which is modelled as one individual for each patch. Establishment, mortality and disturbance are implemented as stochastic processes allowing for different dynamics in different patches. In cohort mode, competition for light and vertical stand structure, interactions between shade tolerant and intolerant PFTs, and succession are simulated in a more realistic fashion (Smith et al ., 2001).

Carbon assimilation is calculated using a modified Farquhar photosynthesis scheme

(Haxeltine & Prentice, 1996) which is influenced by temperature, atmospheric CO 2 concentration, absorbed photosynthetically active radiation and stomatal conductance. At the end of a year, the amount of carbon available for tree height and growth is reduced by maintenance respiration, growth respiration, leaf and root turnover, and a fixed allocation to reproduction (Smith et al. , 2001). A complete description of LPJ-GUESS is given by Smith et al . (2001), and further details on the physiological and biogeochemical components of the model are provided in Sitch et al . (2003). The improved hydrology module described by Gerten et al. (2004) is included.

The model has been evaluated in several studies. LPJ-GUESS correctly predicted the dominant PFT and the PFT composition for several test sites in Europe (Badeck et al. , 2001; Smith et al. , 2001). Wolf et al . (2008) also found good agreement between the model and measured values for LAI, productivity, total biomass and vegetation distribution for northern Europe. Hickler et al . (2004) parameterized the PFTs to represent 26 different species and successfully simulated the species composition and vegetation dynamics of old-growth forest sites in the north eastern USA. LPJ-GUESS has also been used to successfully simulate vegetation distribution and LAI in central Africa (Hély et al. , 2006).

2.3.2 PFT parameterizations

To test how well the global PFTs could describe tropical vegetation at a regional scale, we initially used the seven tropical and temperate PFTs as described by Sitch et al . (2003). Although only three of the PFTs are strictly tropical (i.e. Tropical Broadleaf

Evergreen tree, Tropical Broadleaf Raingreen tree, and C 4 grass), the four temperate PFTs may be important to simulate some of the cooler montane and desert habitats.

To improve the representation of tropical vegetation in the study area, we altered one PFT and added another. The Temperate Needleleaf Evergreen PFT was modified and replaced by a Tropical Needleleaf Evergreen (Table 2-1) to represent the tropical pine trees in the montane regions of Mexico and Central America. The list of Pinus species found in the study area was generated from Gómez-Mendoza & Arriaga (2007) and Farjon & Styles (1997). We used that list to reference the bioclimatic limits for individual species found in the North American atlas for trees and shrubs (Thompson et al. , 1999). The Tropical Needleleaf Evergreen PFT was also made more drought resistant and fire tolerant than the original temperate needleleaf evergreens (Koonce & González-Caban, 1990; Martin et al. , 2007). All other parameters remained the same as for the Temperate Needleleaf Evergreen (Table A-1).

A Desert Shrub PFT was added to more accurately represent the desert and xeric shrublands in many arid parts of Mexico and northern South America. Although the global model does not simulate shrub layers, subsequent applications of LPJ-GUESS

24 have successfully incorporated shrubs by modifying certain structural parameters of woody trees, such as allometric scaling constants, crown area and root distribution in the soil profile (Gritti et al. , 2006; Wolf et al. , 2008; Table 2-1). Photosynthesis, respiration and water uptake functions in shrubs are considered to be the same as for trees. Bioclimatic limits for the desert shrub PFT were based on published data for the creosote bush ( Larrea tridentata ), a common desert shrub observed in the American Southwest and north-central Mexico (Thompson et al. , 1999). Fire resistance appears highly variable and ranges anywhere from 0.03 – 0.88 (Parmenter, 2008), so a middle value of 0.5 was selected. The complete list of parameter values for all PFTs can be found in Appendix 1 (Table A-1).

2.3.3 Modelling protocol

LPJ-GUESS requires climate data as input (mean monthly temperature, total monthly precipitation, number of rain days per month, mean monthly percentage sunshine). The climate data was extracted from the Climatic Research Unit global gridded data set (New et al. , 2002). The data represents the mean monthly surface climate from 1961 – 1990 and has a resolution of 10', or approximately 0.166°. The area selected was from the northern border of Mexico south to 4°N, and from 118°W – 51°W (Figure 2-1a). This area was chosen due to its range of climates and changes in elevation. The precipitation ranges from 42 mm year -1 to over 7500 mm year -1, the average yearly temperature spans 5°C – 30°C, and the elevation ranges from sea level to over 4000 masl. The area also encompasses a variety of tropical biomes, including the desert and xeric shrublands in Mexico, the savanna (páramo) in Venezuela and Columbia, the tropical rain forests and dry forests in Central America, and montane cloud forests in the Andes.

The climate data was used repeatedly for 1000 years (i.e. “spin-up” protocol), the approximate time required for the vegetation, soil and litter pools to reach equilibrium with the climate. The atmospheric CO 2 concentration was set to 340 parts per million by

volume for all simulations, as a moderate estimate for modern atmospheric CO 2 levels (Keeling et al. , 1995). The model was run five times using different combinations of PFTs and fire, including: i) global PFTs, ii) global PFTs + fire, iii) Tropical Needleaf Evergreen (TrNE), iv) TrNE + fire, v) TrNE + Desert Shrub (DeSh) + fire. The model

25 produces annual average leaf area index (LAI), net primary productivity (NPP), and carbon mass for each PFT and as vegetation totals. The average for the last 10 years of simulation was calculated and used for model evaluation.

2.3.4 Model evaluation from biome comparison

As several different potential vegetation maps are available for the study area, simulated vegetation was compared against both the Olson et al. (2001) biome map (Figure 2-1a) and the Haxeltine & Prentice (1996, Plate 1) biome map (Figure 2-2a). A gridded version of the Olson et al . (2001) map was created in ArcGIS at the same resolution as LPJ-GUESS output files. The Haxetine & Prentice (1996) map was available at a 0.5° resolution.

As LPJ-GUESS simulates vegetation as PFTs, a classification scheme was required to transform combinations of PFTs into biomes. We used the classification scheme from Haxeltine & Prentice (1996) to compare to their biome map (Table 2-2). There was no such classification scheme for the Olson map, hence a classification scheme was developed using a combination of Haxeltine & Prentice (1996) and Hély et al . (2006) to fit the Olson biomes (Table 2-3). A measurement of the similarity between the simulated vegetation from LPJ-GUESS and those two observational vegetation maps was calculated using the Kappa statistic (Monserud & Leemans, 1992). The Kappa statistic can range from 0 (no fit) to 1 (perfect fit). Generally Kappa values < 0.2 are considered to have very poor agreement, 0.2 – 0.4 poor, 0.4 – 0.55 fair, 0.55 – 0.7 good, 0.7 – 0.85 very good and > 0.85 excellent (Monserud & Leemans, 1992).

As the Kappa statistic only compares individual grid cells as discrete land patches, it is limited in its ability to detect biogeographical trends across the landscape. Prentice et al . (1992) suggested a generalized Kappa statistic where grid cells are grouped into larger blocks, and the proportion of different categories in these larger blocks compared. Therefore, we also performed a modified version of the statistical protocol described by Prentice et al. (1992) by aggregating grid cells to one larger size (1.0º) and by aggregating biomes into four vegetation categories: wet forest, dry forest, grassland and

26 desert (Table 2-4). The Kappa statistic was used to compare modified simulated and observed vegetation distributions.

2.3.5 Model evaluation from remote sensing data

The MODIS instrument onboard the Aqua and Terra satellite produces several products which are comparable to LPJ-GUESS output, including total leaf area index (LAI). The average LAI for July 2005 was used as representative of the total maximum annual LAI (monthly LAI derived from MOD15A2, Boston University, Collection 5). MODIS data, available at a 1 km resolution, was aggregated to the same grid cell size as modeled output. Agreement between modelled and satellite-derived LAI was quantified by the Pearson correlation coefficient ( r).

2.4 Results

2.4.1 Biome comparison with Olson map

Using the global PFT parameterization, the overall agreement between the modelled vegetation distribution and the Olson et al . (2001) map was poor (Table 2-5). Including fire actually decreased the level of agreement, probably because the mixed pine-oak biome was only present when fire was excluded. Fire did increase the coverage of savannas, dry tropical forests, seasonal forests, and montane forests, but this resulted in little or no change in the individual Kappa values (Table 2-5).

Adding the Tropical Needleleaf Evergreen PFT did improve the representation of the mixed-pine oak forests and slightly increased the overall Kappa to 0.340 when fire was included (Table 2-5). Adding the Desert Shrub PFT lowered the overall Kappa value (Table 2-5), probably due to the very low individual Kappa value for xeric shrublands. The model was not able to capture the xeric shrublands just south of the Chihuahua desert and just north of the Orinoco savanna in South America (compare Figures 2-1a and 2-1c).

In general, deserts were in good agreement with the potential vegetation map and had the highest accuracy in all simulations (Table 2-5). Tropical broadleaf evergreen forests

27 were successfully simulated for most areas, but tended to be over-predicted, covering a much wider area than indicated by the potential vegetation map. Tropical montane forests were appropriately predicted in the South American Andes, but overestimated in the central Mexican highlands. Tropical dry forest was absent in the simulated vegetation for Mexico, but correctly simulated along the southern coast of Central America and on the Yucatan peninsula. However, the model consistently predicted a tropical dry forest instead of savanna in the northern part of South America (Figure 2-1). Overall, ecosystems containing grasses were predicted very poorly. The Olson biome map only shows grasslands at high elevations in the Andes (Figure 2-1). The model did predict grasslands at high elevations but it also simulated grasslands instead of deserts or xeric shrubland which lowered its accuracy measure. Including fire did not significantly increase the simulated area of savannas, which were predicted very poorly in all simulations (Kappa < 0.1). This is likely because fire was underestimated in regions which support savannas (Figure 2-3). Aggregating cell sizes to 1.0º and generalising the original biomes into four moderately improved overall Kappa values (Table 2-6). With modifications to how Kappa statistic is calculated (original versus aggregated biomes and for block size of 1º), the LPJ-GUESS results showed fair agreement with Olson’s potential vegetation map (Kappa > 0.40).

2.4.2 Biome comparison with Haxeltine & Prentice map

Using the global PFT parameterization, the overall agreement between the modelled vegetation distribution and the Haxeltine & Prentice (1996) map was poor (Table 2-5). Including fire did not affect the overall Kappa value even though fire did increase the representation of tropical rain forests, tropical deciduous forests, grasslands and xeric woodlands. The coniferous forest biome was entirely absent when using the global PFTs. Drier biomes, such as savannas and arid shrublands, were only represented by a few grid cells (Figure 2-2b).

Adding the Tropical Needleleaf Evergreen PFT and the Desert Shrub PFT slightly increased the overall Kappa to 0.284 (Table 2-5). This was still a poor agreement between the two maps despite the significant improvement in the representation of coniferous forests and arid shrublands (Table 2-5, Figure 2-2c). Similar to the Olson

28 biomes, tropical broadleaf evergreen forests were successfully simulated in the areas predicted by the potential vegetation map, but were over-predicted in other areas. Temperate broadleaf evergreen forests were again, appropriately predicted in the South American Andes but overestimated in the Mexican highlands. Savanna was always very poorly represented.

Similar to the Olson biome comparison, aggregating biome types and cell size improved overall Kappa values (Table 2-6). The maximum value (Kappa = 0.428) for the comparison between the Haxeltine & Prentice biome map and the LPJ-GUESS results is lower relative to the comparison with the Olson map (Kappa = 0.543) and can be considered a fair level of agreement. The maximum Kappa values were always achieved when both the Tropical Needleleaf Evergreen and the Desert Shrub PFTs were included.

2.4.3 MODIS comparison

Total LAI simulated by LPJ-GUESS was strongly correlated with remotely sensed LAI values (global PFTs no fire: r = 0.76, global PFTs with fire: r = 0.74, TrNE no fire: r = 0.76, TrNE with fire = 0.74, TrNE + DeSh with fire: r = 0.75, n = 13615 for all runs). LAI simulated in LPJ-GUESS was consistently higher than satellite-derived LAI (Figure 2-4a) although the spatial distribution of LAI was similar between the simulated and observed maps (Figures 2-4b and 2-4c).

2.5 Discussion

Using LPJ-GUESS to simulate regional vegetation-climate processes and corresponding biogeography for Central America had a limited level of success. The overall and individual Kappa values generally indicated a very poor to poor level of agreement between simulated vegetation and biome maps (Table 2-5). In addition, simulated LAI was often much higher than remote-sensing values for LAI. If our aim is to improve modelled representation of biogeographical processes in tropical regions, then does this imply that we must create an entirely new regional vegetation-climate model, completely overhauling existing northern temperate-biased vegetation models? Or should the focus

29 be on revising model-data evaluation techniques and better parameterization of tropical PFTs and processes? We believe the latter two activities should be the center of research focus and will discuss the following topics as they relate to future vegetation-climate modelling in tropical regions: (1) a re-examination of model evaluation techniques; (2) selection and parameterization of plant functional types; (3) the representation of fire in LPJ-GUESS and its relative role as an ecological process in northern temperate versus tropical ecosystems; and (4) representation of soil heterogeneity at the regional versus global scale.

Model evaluation

The traditional approach for evaluating DGVMs is to compare the simulated vegetation distribution to a biome map using the Kappa statistic (e.g. Haxeltine & Prentice, 1996; Wolf et al. , 2008). This approach has several benefits. First, models simulate potential vegetation and biome maps are often the only vegetation map available that illustrates a landscape free from anthropogenic influences. Second, the Kappa statistic is a straightforward way to compare the two maps since it encompasses the successes as well as omission and commission errors (Monserud & Leemans, 1992).

Unfortunately, a biome is a human construct and biome definitions are not always published with the detail that is needed for vegetation-climate modellers, and they are definitely not defined according to PFT composition. Hence, modellers need to develop their own biome classification scheme to transfer PFT composition into biomes (Tables 2-2, 2-3). This is an issue. We are comparing one classification scheme (human defined biome map of the world) to another classification scheme (PFTs into biomes) without any guarantee that the biome definitions are fundamentally equal.

The Kappa statistic itself has been under increasing criticism (e.g. Foody, 2002; Allouche et al ., 2006; Pontius & Millones, 2011) and may not be appropriate at a regional or global scale (Foody, 2002). Any two maps with a large number of grid cells are going to be significantly different when compared with the Kappa statistic (Prentice et al., 1992).

This may be why Kappa statistics are not always reported for DGVM studies. The comparison between the modeled vegetation and biome maps (Sato et al. , 2007) or between the modeled vegetation and satellite maps (Sitch et al. , 2003; Zeng et al. , 2008) are often done using a qualitative, visual comparison describing overall trends instead of using a Kappa value. In addition, the Kappa statistic can be improved by aggregating cell sizes (Table 2-6; Prentice et al. , 1992; Haxeltine & Prentice, 1996; Hély et al ., 2006). This may explain why global simulation studies running at a coarser resolution generally report better Kappa values for tropical and semi-tropical regions than our simulation (Prentice et al. , 1992; Foley et al. , 1996). Although aggregating biomes or cell sizes can improve the Kappa statistic, it moves us further away from our original goal; using a regional model to provide a finer resolution and more detail for the simulated area.

An alternative method for model evaluation is to use remote sensing data. The appeal is that remote sensing products are more similar to model output (e.g. annual net primary production, leaf area index (LAI)) which eliminates the need to process model output to match satellite data. In this study, the modelled LAI was consistently higher than the satellite-derived LAI (Figure 2-4a). Although MODIS LAI is supposed to range from 0 – 10 (Pfeifer et al., 2011), higher LAI values tended to saturate around six (Figure 2-4; Chen et al. , 2005). Cloud contamination can also lead to erroneously lower LAI estimates, an issue occurring most often in boreal and tropical regions (Running et al ., 2004). The difference may also be because LPJ-GUESS simulates potential vegetation and satellite measurements reflect the actual vegetation (i.e. with anthropogenic effects such as development and agriculture).

Finding appropriate methods for evaluating vegetation-climate models is an ongoing challenge. We chose to start this discussion by illustrating the difficulty of evaluating the results. This does not imply that the statistics are wrong and the model did a good job. Even with the limitations of the Kappa statistic and biome maps, it is clear that there are important processes which are missing (which are discussed below). We will use the Kappa statistic as suggested by Prentice et al. (1992), discussing the values in terms of rank to identify which categories have better agreement than other categories and to evaluate the degree of improvement from adding new plant functional types.

Plant functional types

Conducting simulations with LPJ-DGVM’s global PFTs (Sitch et al. , 2003) indicated two major areas of concern. First, Temperate Needleleaf Evergreen must be modified into an equivalent PFT for tropical regions (Figure 2-1b). Mixed pine-oak forests are a unique biome occupying volcanic slopes in Mexico and Guatemala between 1900-3100 masl (Arredondo-Leon et al. , 2008). The model was only able to simulate mixed pine-oak forests when the upper temperature tolerance limitations in Temperate Needleleaf Evergreen were increased. Developing a PFT to represent tropical pine trees in general improved the representation of pine-oak forests (Figures 2-1c and 2-2c). Although it is important to recognize that these pine-oak forests in Central America may never be entirely captured in vegetation-climate models. Their modern-day biogeography patterns have been substantially influenced by vegetation movement during the colder and drier glacial phases of the Pleistocene (Ortega-Rosas et al. , 2008). Simulating complex glacial-interglacial evolutionary processes (i.e. allopatry) is beyond the scope of DGVMs.

Second, there was a severe limitation imposed by the lack of adequate representation of desert-adapted vegetation types. In the initial simulations, grass was the only PFT that would grow in arid regions, making productivity the only factor distinguishing grasslands from desert. Desert vegetation is represented by more than just sparse grass. Even with the creation of a Desert Shrub PFT (Figures 2-1c and 2-2c) the cover of desert vegetation types was still underestimated. One suggestion for further improvement is to create multiple shrub PFTs that are distinguishable by their degree of temperature- and drought- tolerance. Zeng et al. (2008) incorporated a modified shrub framework into the global vegetation-climate model, CLM-DGVM. Even with improved shrub representation in various places across the globe, CLM-DGVM was still unable to simulate desert vegetation types over their entire range across Mexico. Mexico is one of the biodiversity hot-spots for desert vegetation (Ortega-Baes & Godínez-Alvarez, 2006; Arakaki et al. , 2011) and it would be beneficial to be able to simulate and predict the impact of future climate change on this region.

The woody-herbaceous ecotone in dry regions may be difficult to represent in current vegetation-climate models, in part because the ecological processes in arid regions are often fundamentally different than those in temperate and boreal areas (Cox et al. , 2006; Robertson et al. , 2009; Búrquez & Martínez-Yrízar, 2011). Vegetation in arid ecotones is affected by processes not typically simulated in global vegetation models such as hydraulic redistribution and age-facilitation interactions (McClaran & Angell, 2007; Simmons et al. , 2008). These two processes have been shown to increase vegetation cover in places like the American Midwest and northern Mexico (Nilsen et al. , 1983).

Moreover, even though models simulate C 4 photosynthesis and therefore capture arid grasslands and some cacti vegetation, they do not contain other succulent PFTs that photosynthesize via the CAM pathway. Developing a succulent PFT with CAM photosynthesis to represent cacti-dominated vegetation in dry woodlands would go a long way in improving simulations of vegetation cover in areas of marginal soils, high temperatures and low rainfall.

A CAM succulent PFT could also help to distinguish between tropical dry forest and savanna, two biomes that were often mistaken for each other in our simulations (Figures 2-1 and 2-2). Tropical dry forests contain succulent CAM plants but savannas do not. CAM plants have a much harder time establishing in savannas due to competition for light and soil nutrients with grasses, in addition to their inability to quickly re-establish following frequent fires (Luttge, 2004).

It has been necessary for other regional studies to modify or create specialized PFTs (e.g. Gritti et al. , 2006; Hély et al. , 2006). The application of a global set of PFTs may be permissible for some regions in northern temperate latitudes but are likely too general to capture competition between vegetation types in tropical regions. Even within the tropics, it may not be possible to agree upon a common suite of PFTs for regional simulations owing to fundamental differences in evolutionary history and ecological interactions (i.e. herbivory-fire, facilitation-age, root depth: Weltzin et al. , 1998; Eggemeyer & Schwinning, 2009). For example, we tried using the PFTs that were developed for Africa as described in Hély et al . (2006). This resulted in most of Central America being simulated as dry tropical forest or savanna (results not shown). Instead of developing

33 generalized PFTs, perhaps more effort should be invested into developing generalized protocols for parameterizing regional PFTs in the tropics.

Another point to be made about PFT parameterizations and varieties of PFTs has to do with subtle (but important) differences between seemingly similar ecosystem types. Thus far, the savanna ecosystem has been used to describe the dry grassland/shrub ecoregions from Mexico to Honduras. From Costa Rica to the northern Andes of South America, the savanna ecotype is replaced by páramo (Sklenar et al. , 2011). Páramo is described as a unique grass-dominated ecosystem found at altitudes above tree-line in the Andean Mountains and may be described as both wet and dry (Cuello et al. , 2010). The diversity of plants in páramo is extremely high because of the evolutionary history of migrating temperate, tropical and cosmopolitan elements into the ecosystem. The number of bryophyte species (Holz & Gradstein, 2005) and ferns is particularly high in the wetter páramo. Moreover, páramo plants have ecophysiological tolerance mechanisms to survive nightly frosts that occur nearly year-round (Sklenar et al. 2010); all of which may have consequences for fire frequency and intensity (see next section). Fires are a reported occurrence in páramo for at least the past 10,000 years (League & Horn, 2000) but are likely to burn differently than the "traditional" savanna. The southeastern Brazilian Highlands is home to the Brazilian version of the páramo, called campos de altitude, similar to páramo in many ways but also different (DeForest-Safford, 1999a, b). LPJ-GUESS clearly had problems simulating savanna-type ecosystems. Future work in this area could examine other smaller-scale, process-based models (e.g. Coughenour & Chen, 1997; Simioni et al ., 2000) which have had success simulating these tree-grass ecosystems.

Fire frequency and intensity

Fire is known to play an important role in ecosystem structure, plant composition and the global carbon cycle (Bond et al. , 2005). LPJ-GUESS incorporated the fire module Glob- FIRM (Thonicke et al. , 2001) which predicts the occurrence of fire based upon fuel load

34 and litter moisture. The fraction of area burnt is based on the length of the fire season and PFT-specific fire resistances. Fires were predicted to occur very rarely in the desert, which is what one would expect. Small fires were predicted to be quite frequent in the pine-oak forest (Figure 2-3), which was also expected as fire plays a small but critical role in maintaining pine-oak forests in the highlands of central Mexico (Rodriguez-Trejo & Fule, 2003; Myers et al. , 2009). Slightly more forest fires were simulated for tropical dry forests, which is also appropriate (Koonce & González-Caban, 1990). LPJ-GUESS simulated quite a few fires in the moist tropical forests which was unexpected (Figure 2-3). Natural forest fires in the rain forest are fairly rare, with fire return intervals of hundreds of years (Kauffman & Uhl, 1990). The large number of fires predicted to occur in the wet forest may be a reflection of high productivity and fuel loading. Cochrane (2003) suggests that fire modelling in tropical forests must incorporate feedbacks between fire and forest. Tropical trees with large tap roots access moisture deep into the soil profile and can maintain high humidity throughout the dry season. Moisture increases the amount of heat needed to reach fuel ignition (Cochrane, 2003), thus generally reducing the probability of forest fires in humid tropical rainforests. In addition, higher moisture content of fuel typically keeps fire intensities low and spread rates slow.

With that said, certain regions of the humid tropical rainforest in Amazonia and Central America have become unexpectedly susceptible to fire (Siegert et al. , 2001; Nepstad et al. , 2004). The combination of dry years promoted by El Niño Southern Oscillation (ENSO) climate events and the ever increasing area of open forest edges following deforestation, can result in substantial loss of forest biomass and release of CO 2 into the atmosphere. Comparison of area burned in the Brazilian Amazon during ENSO and non- ENSO years indicates a 13-fold increase in understory forest fire during drought-prone ENSO events (Alencar et al. , 2006). Roman-Cuesta et al. (2003) observed that in non- ENSO years, the pine-oak forest was preferentially burned; however, during dry ENSO- years, wet tropical forest burned despite many tree species having low flammability properties. If this trend continues (which is likely the case in light of continued demand for wood products in the tropics and fragmentation of lowland forest) predictive models

35 might have to reconsider the flammability of wet tropical forests. One can foresee future regional models having to replicate a complex cycle of feedbacks between ENSO, forest edges and fire.

It was expected that the inclusion of fire would increase the coverage of savanna in South America; but it did not (Table 2-5). Frequent fires are integral to maintaining savanna ecosystems such as those observed in South Africa (Bond et al. , 2005). Simulated low rates of fire occurrence in savanna regions (Figure 2-3), combined with the fact that anthropogenic ignition sources are not modelled in LPJ-GUESS, resulted in an underestimation of savanna cover to the benefit of tropical dry forest.

LPJ-GUESS currently incorporates a mechanistic fire module based on fire requirements for boreal and temperate regions. A new fire module has recently been incorporated into LPJ-GUESS (Lehsten et al. , 2009) and was able to successfully simulate the fire regime in Africa, but it was not available for this study. Severe forest fires in the temperate and boreal zones are intense surface or crown fires. Tropical forest fires are usually slow moving, low intensity, surface fires (Cochrane, 2003). Understanding that fire behaves differently around the globe and incorporating these differences into regional models will increase our understanding of fire-ecology-vegetation-interactions and may improve our predictions under altered climate.

Soil type and texture

LPJ-GUESS uses the FAO soils map (FAO & UNESCO, 1974) which describes soils in terms of texture and includes categories such as organic, fine, medium and coarse soils. This soil map provides broad-scale global patterns and very coarse soil categories. Regional models may require more details in order to capture landscape variability that may arise from soil heterogeneity. In this study, a poorly described soil layer may have affected the ability of the model to represent savannas. Savannas typically occur on deeply weathered, nutrient poor, ancient land surfaces (Cole, 1986). Low nutrient availability is thought to slow down the growth of trees after a disturbance. The slow

36 recovery rate of trees would favour grasses and the development of a savanna (Bond, 2008). The feedback between frequent fires and the volatilization of nutrients, would also promote a savanna.

Incorporating a dynamic soil layer would also improve the ability of the model to distinguish between somewhat unique biomes. Savanna grasslands in Venezuela and Columbia are predominantly located in a major drainage basin, the Orinoco basin (Cole, 1986). Much of this area floods annually, and it is the variation in soil and drainage that determines if the area is dominated by trees or grasses. The simulation of other types of flooded forests would also require a dynamic soil layer, such as mangroves or várzea. Mangroves are located along the coast (Figure 2-1a), have highly saline soils and are regularly flooded with salt water. Várzea are located next to rivers and lakes and are permanently/seasonally flooded with fresh water. In the current vegetation-climate models, these forest types are indistinguishable from a tropical broadleaf evergreen forest.

Conclusions

Despite the low degree of similarity between the simulated versus observed vegetation cover across Central America, we believe that the exercise helped to clarify critical research priorities that will facilitate improved representation of tropical vegetation in regional models. These priorities are summarized as follows: (1) improve parameterization of PFTs that exist outside the mixed, temperate and boreal zones of the world (i.e. semi-arid shrubs, CAM succulents, cacti), (2) adapt fire regime models intended for non-tropical latitudes to better represent the role of fire in tropical ecosystems, (3) develop a more sophisticated soil module that allows for semi-arid and arid processes of hydraulic redistribution, facilitation and root growth strategies to be better integrated in simulated plant-plant competition, (4) move towards modelling and mapping vegetation as functional units (PFTs) rather than biomes, (5) collaborate more effectively between modellers and field ecologists so that the parameters measured in the field (i.e. average tree height, canopy density, fire burn frequency, gross primary

37 productivity, carbon biomass, diameter at breast height) can be used as a direct tool to evaluate the predictive capacity of a model, and (6) develop more sophisticated statistical techniques that are flexible to different model grid-cell sizes and can provide an index of small-scale and large-scale similarity. It is necessary to establish reliable, reproducible and unbiased validations methods, so models can be applied to future and historical climate scenarios with ever increasing confidence.

Table 2-1. Parameter values that were used to describe the two new plant functional types, Tropical needleleaf evergreen and Desert/xeric shrub. All other parameter values can be found in Appendix 1, Table A-1.

TrNE - Tropical needleleaf evergreen Parameter Value Source Fire resistance 0.5 Martin et al. (2007) Kennedy & Horn (2008)

Root distribution (upper/lower) 0.3/0.7 Minimum temperature of coldest month for 5 Thompson et al. (1999) survival (C°)

Minimum temperature of coldest month for 5 Thompson et al. (1999) establishment (C°)

Max temperature of coldest month for 1000 no upper limit establishment (C°)

DeSh – Desert/xeric shrub Parameter Value Source Fire resistance 0.5 Parmenter (2008) Sapwood turnover (fraction/year) 0.015 Wolf et al. (2008) Sapwood and heartwood density (kgC/m 3) 250 Wolf et al. (2008) Maximum tree crown area (m 2) 1.5 Brisson & Reynolds (1994) Parmenter (2008) k_allom1 (Constant in allometry equations) 10 Parmenter (2008) k_allom2 (Constant in allometry equations) 4 Brisson & Reynolds (1994) Parmenter (2008) k_allom3 (Constant in allometry equations) 0.67 standard value k_rp (Constant in allometry equations) 1.6 standard value Tree leaf to sapwood area ratio 500 Wolf et al. (2008) Root distribution (upper/lower) 0.2/0.8 Minimum temperature of coldest month for 2 Thompson et al. (1999) survival (C°)

Minimum temperature of coldest month for 2 Thompson et al. (1999) establishment (C°)

Max temperature of coldest month for 1000 No upper limit establishment (C°)

Table 2-2. Biome classification scheme from Haxeltine & Prentice (1996). The boreal and arctic biomes are not included since they are not present in the study area. Used to compare the modeled results to the Haxeltine & Prentice (1996) biome map. Acronyms are as follows: TeBS – temperate broadleaf summergreen, TeBE – temperate broadleaf evergreen, TrBE – tropical broadleaf evergreen, TrBR – tropical broadleaf raingreen, TrNE – tropical needleleaf evergreen, NPP – net primary productivity.

Biome type Dominant PFT Leaf Area Index (LAI) Coniferous forest TrNE LAI > 1.5

Temperate deciduous forest TeBS LAI > 2.5

Temperate broadleaf evergreen TeBE LAI > 3.0 forest Tropical rain forest TrBE LAI > 2.5

Tropical deciduous forest TrBR LAI > 2.5

Tall grassland C3 grass LAI > 3.0 C4 grass (& grass NPP/woody NPP > 1.8) LAI > 3.0

Short grassland C3 grass LAI > 0.4 C4 grass (& grass NPP/woody NPP > 1.8) LAI > 0.4

Moist savanna C4 grass (& grass NPP/woody NPP < 1.8) LAI > 1.5

Dry savanna C4 grass (& grass NPP/woody NPP < 1.8) LAI > 0.6

Xeric woodland/scrub TeBE or TrBE or TrBR LAI > 1.0 TrNE or TeBS LAI > 1.5

Arid shrubland Any LAI > 0.2 Desert Any Any

Table 2-3. Biome classification scheme, based on a combination from Hély et al. (2006) and Haxeltine & Prentice (1996). Classification used to compare the modeled results to the Olson et al. (2001) map of biomes. Acronyms are as follows: TeBS – temperate broadleaf summergreen, TeBE – temperate broadleaf evergreen, TrBE – tropical broadleaf evergreen, TrBR – tropical broadleaf raingreen, TrNE – tropical needleleaf evergreen, DeSH – desert shrub, NPP – net primary productivity.

Biome type Classification rules Leaf Area Index (LAI) Tropical evergreen forest TrBE LAI ≥ 66% total LAI LAI > 2.5

Tropical seasonal forest TrBE LAI ≥ 33% total LAI LAI > 2.5 and TrBR LAI ≥ 33% total LAI

Tropical dry forest TrBR LAI ≥ 66% total LAI LAI > 2.5

Montane forest TeBE LAI > 10% total LAI LAI > 2.5 and TrNE LAI < 25% total LAI

Mixed pine-oak forest TeBE LAI > 10% total LAI LAI > 2.5 and TrNE LAI ≥ 25% total LAI

Tropical coniferous forest TrNE LAI ≥ 66% total LAI LAI > 1.5

Savanna ratio of grass NPP/woody NPP < 1.8 and C4 > C3 LAI > 1.5

Grassland ratio of grass NPP/woody NPP > 1.8 and C4 > C3 LAI > 1.5 OR C3 > 66% LAI > 3.0

Desert Any LAI < 0.2

Xeric shrubland DeSh biomass > 50% total biomass Any

Source Aggregated biomes Original biomes H&P Wet Forest Tropical rain forest Moist savanna Temperate broadleaf evergreen forest

Dry Forest Tropical deciduous forest Temperate deciduous forest Coniferous forest Dry savanna

Grassland Tall grassland Short grassland

Xeric Shrubland Xeric woodland/scrub Arid shrubland Desert

Olson Wet Forest Tropical evergreen forest Tropical seasonal forest Tropical montane forest Dry Forest Tropical dry forest Mixed Pine-Oak forest Coniferous forest Savanna

Grassland Grassland

Xeric Shrubland Desert

Table 2-5. Overall and individual Kappa values for the five simulations, shown when compared to (a) the Olson et al. (2001) biome map at 0.166° resolution [designated by "Olson"] and (b) the Haxeltine & Prentice (1996) biome map at 0.5° resolution [designated by "H&P"]. The five simulations are 1) original PFTs without fire, 2) original PFTs with fire, 3) original PFTs plus the tropical needleleaf evergreen (TrNE) without fire, 4) original PFTs plus TrNE with fire, and 5) original PFTs, TrNE and the desert shrub (DeSh).

Original PFTs with TrNE with TrNE + DeSh No fire Fire No fire Fire Fire (a) Olson biomes Overall 0.335 0.299 0.276 0.340 0.301

Tropical evergreen forest 0.307 0.360 0.307 0.366 0.368 Tropical seasonal forest 0.007 0.030 0.015 0.035 0.029 Tropical dry forest 0.121 0.121 0.124 0.117 0.103 Montane forest 0.049 0.025 0.098 0.034 0.008 Mixed pine-oak forest 0.078 0.000 0.158 0.325 0.300 Tropical coniferous forest -0.006 -0.004 -0.019 -0.003 -0.001 Savanna 0.033 0.038 0.066 0.038 0.123 Grassland 0.121 0.009 0.059 0.009 0.020 Desert 0.506 0.485 0.412 0.486 0.620 Xeric Shrublands ------0.055

(b) H&P biomes Overall 0.214 0.213 0.241 0.270 0.284

Coniferous forest 0.000 0.000 0.259 0.461 0.446 Temperate deciduous forest 0.000 0.000 -0.004 -0.002 -0.001 Temperate broadleaf evergreen forest 0.029 0.047 0.147 0.062 0.040 Tropical rain forest 0.239 0.304 0.244 0.307 0.328 Tropical deciduous forest 0.117 0.141 0.123 0.143 0.175 Tall grassland 0.000 -0.013 -0.008 -0.013 -0.011 Short grassland 0.025 0.157 0.043 0.194 0.145 Moist savanna 0.000 -0.013 -0.009 -0.011 -0.008 Dry savanna 0.000 0.000 -0.001 0.000 0.000 Xeric woodland/scrub 0.146 0.158 -0.007 0.100 0.032 Arid shrubland 0.312 0.052 0.399 0.256 0.319 Desert 0.000 0.000 0.000 0.000 0.000

Map Source Original PFTs With TrNE With TrNE + DeSH Olson 0.420 0.538 0.543 H&P 0.299 0.399 0.428

(a)

Tr Broadleaf Evergreen Forest Tr Seasonal Forest Mangrove Tr Dry Forest Savanna Tr Montane Forest Grassland Mixed Forest Desert Coniferous Forest Xeric Shrubland

(b)

(c)

Figure 2-2. (a) Haxeltine & Prentice (1996) biome map for the study area. (b) LPJ- GUESS simulated distribution of biomes using the global PFT parameterization and (c) including the two new PFTs (tropical needleleaf evergreen tree and xeric shrub). Both simulations shown include fire as a disturbance. The small inset maps show the distribution of prediction errors (red indicates a difference between the Haxeltine & Prentice biome and the predicted biome from LPJ-GUESS). Figure shown on next page.

(a) (a)

Coniferous Forest Temp Deciduous Forest Temp Broadleaf Evergreen Forest Tr Broadleaf Evergreen Forest Moist Savanna Tr Deciduous Forest Dry Savanna Tall Grassland Xeric Woodland Short grassland Arid Shrubland

(b) (b )

(c )(c)

(a) Small fire frequency Number of years with fire 0 1-100 101-200 201-300 301-400 401-500 501-600 601-700 701-800 801-900 901 -1000

(b) Large fire frequency Number of years with fire 0 1-5 6-10 11-15 16-27

Figure 2-3. Annual carbon flux to atmosphere from burnt vegetation and litter. LPJ- GUESS was run for 1000 years, shown are the number of years which had (a) small fires (≥ 0.1 kg C/m 2 and < 1.0 kg C/ m2) and (b) large fires ( ≥ 1.0 kg C/m 2). Note the difference in scale.

Figure 2-4. (a) Comparison of simulated leaf area index (LAI) values from LPJ-GUESS to satellite-derived LAI value from MODIS. The LAI values from LPJ-GUESS are from the simulation which included fire and the new PFTs (tropical needleleaf evergreen and xeric shrub). The 1:1 line is shown. The LAI values from MODIS are for July 2005, the maximum annual LAI. (b) The spatial representation of simulated LAI from LPJ-GUESS and (c) satellite-derived LAI from MODIS. 49 49

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Chapter 3

3 Simulating long distance seed dispersal in a Dynamic Global Vegetation Model

3.1 Abstract

Predicting the migration of vegetation in response to climate change is often done with a vegetation-climate model, however the lack of seed dispersal in these models is a common criticism. Previous efforts to incorporate seed dispersal limitations have occurred exclusively in bioclimatic envelope models. This paper describes how I included seed dispersal limitations into a physiologically based vegetation-climate model (LPJ-GUESS). LPJ-GUESS already simulates carbon assimilation, allocation to growth and reproduction, competition, and establishment. I used a generic seed dispersal kernel to determine the probability of moving between grid cells, and a modified logistic growth curve to determine the probability of moving between patches within a grid cell. PFTs were parameterized to represent three temperate tree species (maple, pine and hemlock), by using their published dispersal kernels and life history measurements. Following climate warming, the model was able to simulate dispersal and vegetation migration across an idealized landscape. Simulated rates for Acer (141 m year -1) and Pinus (76 m year -1) matched closely with the genetic and pollen reconstructed rates, although Tsuga migration (85 m year -1) was considerably slower than pollen reconstructions. Possible explanations for the difference between simulated migration and past migrations are discussed, as well as the implications for future climate change.

3.2 Introduction

As atmospheric CO 2 continues to rise over the next century, future climate change scenarios predict a rapid shift in temperature and precipitation (IPCC, 2007). The northern latitudes will likely experience the most extreme change, with a minimum warming of 5°C and a 20% increase in precipitation (IPCC, 2007). One goal of climate change research is to anticipate how these

56 shifts in climate will affect the distribution and functioning of species (Thomas et al. , 2004; Lawler et al. , 2006; Morin et al. , 2008; Loarie et al. , 2009; Doxford & Freckleton 2011). Plants are of particular interest, not only because of the potential feedbacks between climate and vegetation (Cramer et al. , 2001; Purves & Pacala, 2008; Sitch et al. , 2008) but also due to the unique challenges plants face in being able to track climate change (Clark, 1998; Malcolm et al. , 2002; Midgley et al. , 2006). Animals are already moving in response to climate change (Thomas & Lennon, 1999; Parmesan & Yohe, 2003) however plant migration is not expected to occur as quickly. This is because plant migration occurs across generations, starting with long distance seed dispersal, seedling establishment in new habitats, growth, and eventually producing seeds of their own (Pitelka et al. , 1997). Although there are a variety of models that can predict plant migration in response to climate change, none of the current models include all of these necessary processes.

Most of the current vegetation-climate models assume full migration , where plants have the ability to migrate into any suitable habitat regardless of barriers or seed dispersal limitations (Cramer et al. , 2001; Guisan & Thuiller, 2005). Correcting this assumption has mostly occurred in species distribution models, by imposing a predetermined maximum distance on vegetation migration (e.g. Midgley et al. , 2006; Fitzpatrick et al. , 2008) or using a cellular automata to determine dispersal between cells (e.g. Iverson et al. , 2004) . This does curtail some of the more extreme estimates of population spread, but still overestimates migration potential by not considering the impacts of dispersal mechanisms, establishment success, growth and competition. Dynamic global vegetation models (DGVMs) currently don’t impose any limitations on dispersal. DGVMs do simulate other processes important for vegetation migration such as establishment, carbon assimilation, vegetation growth and reproduction (Cramer et al. , 2001). Hybrid models, which incorporate a forest gap model within a DGVM framework, also simulate competition between plants for space, light and resources (Smith et al. , 2001; Sato et al. , 2007; Fisher et al. , 2010). Adding seed dispersal into a hybrid model is a logical step, since so many of the processes important for simulating vegetation migration are already included (Figure 1-2).

One such hybrid model, LPJ-GUESS, is particularly suited for simulating seed dispersal due to the way it represents vegetation within a grid cell. Most DGVMs have one average individual for each PFT (Figure 1-1). This means that new PFTs would arrive and establish as one large

57 individual that immediately travels the length of the grid cell (55 km for most models). LPJ- GUESS simulates a number of replicate patches within each grid cell, where each patch contains several individuals for each PFT at different ages (Figure 1-1). By simulating multiple patches within each grid cell, new PFTs would arrive and establish in just one patch. PFTs would then be forced to disperse between patches to move all the way through a grid cell. Simulating plant migration could be achieved in hybrid models by allowing communication between grid cells, using seed dispersal kernels to predict the probability of dispersing between grid cells, and placing limitations on patch-to-patch movements within a grid cell.

Predictions about future climate change are based on vegetation-climate models which assume either no dispersal or full migration. The reality is likely somewhere between these two extremes. To improve our predictions on how climate change will affect vegetation distributions, this paper describes how long distance seed dispersal was incorporated into the hybrid dynamic vegetation-climate model, LPJ-GUESS. The success of the new dispersal module was determined by comparing simulated migration rates with pollen and genetic reconstructed migration rates for three temperate tree species.

3.3 Development of the dispersal module

3.3.1 The model, LPJ-GUESS

LPJ-GUESS is a generalized ecosystem model that combines the dynamic global vegetation model LPJ with a forest gap model (Smith et al. , 2001). LPJ-GUESS simulates the growth and composition of vegetation through a suite of physiological and biogeochemical processes. LPJ- GUESS was run in cohort mode, where each grid cell contains a number of replicate patches. In the present study, I chose to represent 400 patches per grid cell. This was the minimum number of patches that would allow the model to simulate dispersal between grid cells (see section 3.3.5, one needs a certain number of patches located close to the edge of the grid cell to provide seeds to their neighbours). Since each age cohort has different properties (i.e. height, LAI, biomass), the model can successfully simulate intra- and inter-specific competition for light, space and resources. The herbaceous layer is simulated as one individual for each patch. All patches

58 within a grid cell have the same climate and environmental properties. The variability between patches results from stochastic processes such as age-related mortality and disturbance.

Additional details on LPJ-GUESS can be found in Smith et al. (2001), Sitch et al. (2003) and Chapter 1. To distinguish between LPJ-GUESS with and without dispersal, LPJ-DISP refers to the new version which includes dispersal.

3.3.2 Communication between cells

The first step was to fundamentally change the way the program runs, from isolated single cells to a two-dimensional landscape. Originally, LPJ-GUESS would simulate one grid cell at a time, discarding the grid cell object after it had reached the total number of simulation years (Figure 3-1a). This makes it impossible to transfer seeds between neighbouring grid cells as they don’t exist in memory at the same time.

I chose to distinguish between a spin up period and a migration period. During the spin up period (Figure 3-1b), the grid cells are simulated independently with full migration capabilities for all PFTs. This allows the PFTs which are in equilibrium with the current climate to establish and stabilize. The major distinction is that after the spin up period, the grid cell objects (and all patch and vegetation objects contained within) are retained in memory. This causes a considerable increase in computer memory usage while the program is running, which limits the number of cells that can be simulated at one time. Although 80 grid cells were sufficient for my purposes, larger simulations would need to be run on a parallel system with memory sharing between processors.

During the migration period, each year is simulated across all grid cells before moving onto the next year (Figure 3-1b). For example, year 1000 is simulated for all grid cells, then year 1001 ... and so on. At the end of every year, vegetation composition (i.e. the proportion of patches that contain each type of PFT) for each grid cell is written to an output file. At the start of each year, each grid cell reads in the vegetation composition for its neighbours from the previous year. I chose to define a neighbour as sharing one side of the grid cell (i.e. horizontal or vertical neighbours), thus excluding diagonal movement and setting the maximum number of neighbours to four.

3.3.3 Dispersal between grid cells

In this study, each grid cell is 0.166° or approximately 18 km. Although this is significantly smaller than the traditional resolution in vegetation-climate models (Cramer et al. , 2001), most dispersal events are still going to occur within a grid cell. However, to simulate vegetation migration over a landscape it is still necessary to estimate the occurrence of rare dispersal events between cells. The number of seeds arriving from distance x, is a product of the number of seeds produced in neighbouring grid cells, seed n, and the probability of those seeds traveling that distance, k(x) ,

seed (x) = seed n ∗ k(x) . (3.1)

3.3.4 Seed production ( seed n)

Seed production in LPJ-GUESS is represented by the variable, cmass_repr . This variable represents the total carbon allocated to reproduction for each PFT, from all the patches in a grid cell. This needs to change as not every patch will contribute seeds for long distance dispersal. Patches close to the edge of the grid cell and which contain the PFT in question, are most likely to have seeds disperse into neighbouring grid cells. Seed production for each PFT within that grid cell (pft.cmass_repr ) was scaled by the proportion of patches close to the edge of the grid cell ( pPFT ),

seed n = pft .cmass _ repr ∗ pPFT . (3.2)

3.3.5 Number of patches close to the edge of the cell ( pPFT )

Patches in LPJ-GUESS are not assigned to a concrete location within the grid cell making it impossible to identify the actual patches within a certain distance from the edge. To generate a formula to describe the relationship between patch number, distance and probability of containing the PFT in question, it is assumed that the patches are randomly located throughout the grid cell.

Using the spatial statistical package spatstat within the R program ( www.r-project.org ), 100 random points were generated with a Poisson distribution within an 18 km square. Each point represents one patch, and the square represents a grid cell in LPJ-GUESS using a resolution of

0.166°, or approximately 18 km. The 100 random points were generated 1000 times to determine that on average 0.0028% of the patches are within 500 meters from one of the edges. Given that long distance dispersal can occur over distances greater then 500 meters (Cain et al. , 2000), the proportion of patches within 1 km, 2 km, 3 km, 4 km and 5 km from the edge were also calculated (Figure 3-2).

Using 100 points assumes that the PFT of interest can be found growing in 100% of the patches. What if only 65% of the patches have the PFT? What percent of patches will be close to the edge and contain the PFT? I repeated the random point generation using 90 points (assumes that 90% of the 100 patches contain the PFT), 80, 70, 60 … and so on (Figure 3-2). The resulting formula is:

pPFT (x) = (( /1.0 cell _ size )∗ x)∗ nPFT , (3.3)

where x is distance, cell_size is the size of the grid cell in kilometres, and nPFT is the number of patches within the grid cell that contain the PFT in question.

Combining equations 3.1 through 3.3 results in the following formula:

seed (x) = [pft .cmass _ repr ∗ ((( /1.0 cell _ size ∗ x))∗ nPFT )]∗ k(x) . (3.4)

3.3.6 Seed dispersal kernels ( k(x) )

The probability of a seed traveling a specific distance, x, is known as the dispersal kernel. A generalized dispersal kernel has been described by Clark (1998),

   c   c   x  k(x) =  exp −  (3.5)  2αΓ()/1 c   α  where Γ( ) is the gamma function, c is a shape parameter and α is a distance parameter. By choosing different values for c and α, the same formula can be used to describe different kernels that best reflect the different dispersal mechanisms. For example, c = 2.0 is the Gaussian kernel, c = 1.0 is the exponential, and c < 1.0 is leptokurtic. A leptokurtic dispersal kernel describes a distribution which has a higher peak around the mean (i.e. most seeds are clustered around the parent tree) and a ‘fat-tail’ which captures rare long-distance seed dispersal. Equation 3.5

61 generally fits local or long distance dispersal well, but not both (Clark et al. , 1999). As this equation is only used to describe long distance dispersal, a poor fit of local dispersal is not a concern.

Since different dispersal vectors operate on different spatial scales, I chose to use an increasing distance function, as opposed to a predetermined value for distance. The minimum distance evaluated was 500 m. Distance was increased in 500 m steps until the dispersal probability became too small to consider (see Appendix 2).

3.3.7 Dispersal within a grid cell

Just as there were no limitations to dispersal between cells, LPJ-GUESS also had no restrictions on dispersal between patches within a cell. Each grid cell had a common propagule pool which every patch contributed seedlings to and took seedlings from (Figure 1-2). Theoretically, a new PFT could travel all the way across the cell (i.e. 18 km) in one year. More realistically, incoming seeds from neighbouring cells should only arrive in the patches closest to the edge, establish, spend a few years growing before reproducing, and then disperse to near by patches. It should take years for a new PFT to travel all the way through the cell.

The first step was to eliminate the common seed bank within each grid cell (Figure 1-2). PFTs only contribute seedlings to their own patch and are unable to access seedlings from different patches (except through dispersal).

The second step was to restrict where seeds coming in from neighbouring cells land. Since the actual patches which are closest to the edge can’t be identified, it is enough to know how many patches are likely to be close enough to receive seeds. Using equation 3.3 and a fixed distance of 500 meters, there would likely be three patches within 500 meters from an edge. These three patches remain constant throughout the simulation and will be the only patches that can receive seeds from a neighbouring grid cell. In other words, patch_1, patch_2 and patch_3 will receive seeds from the southern neighbour. Patch_4, patch_5 and patch_6 will receive seeds from the eastern neighbour … and so on.

The third step was to add a new variable, age_repr . This parameter prevents a PFT from allocating carbon to reproduction until it reaches a minimum age. Maturation age is a commonly

62 measured parameter (Clark, 1998) and when used with the already present variable reprfrac (the fraction of net primary productivity allocated to reproduction), it can represent a specific life history for each PFT. For example, Cherry Birch trees delay reproduction for many years but have a very high fecundity once it does start producing seeds, compared to Flowering dogwood trees which start reproducing much younger but have lower fecundity (Clark, 1998).

Adding a minimum age for reproduction delays the rapid migration through the cell, but only by the set number of years (i.e. the minimum age). The final step was to limit patch-to-patch dispersal within a cell. Again, this is made more complicated since patches don’t have real locations within the grid cell. However, knowing the proportion of patches containing the PFT, we can calculate the probability of having at least one neighbouring patch that also contains the PFT. For example, if only one patch within the cell contains the PFT then we would expect only one or two patches to be close enough for seed dispersal. If more than 50% of the patches contain the PFT then we could expect most patches to have at least one neighbour with the PFT. The logistic growth curve, a relatively common function in ecology, can be used to describe this relationship:

rt KP 0e P(t) = rt , (3.6) K + P0 (e − )1 where P is the population size at time t, r is the growth rate, and K the carrying capacity or the largest size the population can reach given unlimited time. To suit my purpose, the formula was modified as follows:

Ke rp P( p) = , (3.7) K + (erp − )1

where P is the population of available patches for receiving seeds (i.e. have at least one neighbouring patch that contains the PFT) when there are p patches that contain reproducing adults for that PFT. The carrying capacity, K, is the total number of patches in one grid cell (i.e.

400 in my simulations). The initial population size ( P0) is always set to 1 since this formula was only used if the PFT was already present in the grid cell. The growth rate ( r) was set to 0.1 and kept constant for all simulations. Choosing a value for r was more difficult since there is no

63 published correlation between population spread and growth rate, but see Chapter 4 for a sensitivity analysis and discussion about this parameter.

Using equation 3.7 this way means that there is not necessarily any growth each year, as in the traditional population growth model. It is used to calculate the number of new patches which have the potential for receiving seeds from neighbouring patches, however seeds may not establish upon arrival due to competition for space and resources. It may take several years for a PFT to successfully establish in a new patch. The growth rate ( r) is not intended to represent any other processes which influence seed success, such as dormancy, disease or seed predation.

Calculating the probability of dispersal between grid cells and between patches within a grid cell is done every year. First, LPJ-DISP determines if any seeds will disperse into the grid cell from neighbouring cells (equation 3.4). Typically, about 70% of the patches in a neighbouring grid cell need to contain the PFT before seed dispersal can occur. Then, seed dispersal within a grid cell and within a patch is calculated. To see how equations 3.1 – 3.7 were used in LPJ-DISP, the full C++ code is provided in Appendix 2.

3.3.8 Simulation protocol

LPJ-DISP was tested using an imaginary landscape, eight rows of ten grid cells across. The top five rows were assigned a boreal climate (mean annual temperature 4.68°C ± 0.45°C) and the bottom three rows were assigned a warmer, temperate climate (mean annual temperature 15.19°C ± 0.41°C). The climate data was extracted from actual boreal and temperate regions in North America from the Climatic Research Unit global gridded data set (New et al. , 2002). The CRU data are composed of mean monthly surface climate from 1961 – 1990, at a resolution of 0.166° or 18km.

I used three boreal PFTs (a shade intolerant, intermediate shade tolerant and shade tolerant tree), three temperate PFTs (a shade intolerant, intermediate shade tolerant and shade tolerant tree) and one C3 grass (Table A-2). Their temperature ranges were modified to ensure complete separation between the warm and cool PFTs, until after the climate started to warm. This was done to make plant migration easier to track.

The model was run for 1000 years with a stable climate and no restrictions on dispersal (spin up period). Over the next 200 years, the boreal climate was warmed by an average of 9.51°C ± 0.35°C and the temperate climate was warmed by an average of 1.74°C ± 0.06°C. The temperature increases were chosen based on the climatic tolerances for the warm PFTs (i.e. the boreal climate needed to warm by ~10°C to reach the minimum temperature requirements for temperate PFTs to establish and grow (Table A-2)). Although the degree of warming in the boreal cells is more extreme than future climate change predictions (IPCC, 2007), the goal of this study was to test migration of plants based on dispersal limitations alone. If the boreal cells were given a more moderate warming (i.e. 2 – 5°C), climate would have been the limiting factor preventing temperate PFTs from establishing. The model continued to run at the new warmer temperatures for 1000 – 2000 years, until the test species had migrated through all the grid cells.

3.3.9 Test species

To test how well the model simulates dispersal, I parameterized the warm tolerant PFT to represent three different species; Acer rubrum , Tsuga canadensis, and Pinus rigida (Table 3-1). The tree species were selected since they had published dispersal kernels (Clark, 1998) for equation 3.5 and reconstructed migration rates following the retreat of the last glacier in North America (Davis, 1981; Delcourt & Delcourt, 1987; McLachlan et al. , 2005). The published dispersal kernels were used to parameterize the model and the reconstructed migration rates were used as an independent comparison with the simulated migration rates. Since individual species are usually not distinguished in the pollen record, simulated rates were compared with the appropriate genus (i.e. Acer rubrum with Acer , Tsuga canadensis with Tsuga ). Migration rates for Pinus rigida were compared to the values reported for southern pine by Delcourt & Delcourt (1987) since that is where they included it. The three species also represent different life history strategies (Table 3-1) which should impact how quickly they migrate across a landscape. For example, A. rubrum is a deciduous tree which reproduces early, has high fecundity and a short lifespan. T. canadensis is a needleleaf, evergreen tree which can live up to 500 years, but also reaches reproductive maturity later in life.

3.3.10 Calculating migration

LPJ-DISP was run for each of the test species twice, once with the assumption of full migration and once with the new limited dispersal described above. Once the runs were finished, the

65 average migration rate (time to move through each grid cell – 18 km) and the overall migration rate (time to move the entire distance – 90 km) were calculated. A PFT was considered to have entered a grid cell after evidence of establishment, which was once a reproducing adult could be found in at least one patch. I chose not to consider the establishment of seedlings since other events (i.e. competition, disturbance) might prevent that seedling from reaching reproductive maturity. This is also comparable to how migration is calculated in the pollen record. Only reproducing trees are considered to be present on the landscape since immature trees don’t produce pollen. A PFT was considered to have moved all the way through a grid cell after mature PFTs were found in more than 80% of the patches. Due to the random patch destroying events, PFTs almost never occupied 100% of the patches.

Migration rates for the first row of grid cells (i.e. the most southerly row) were much slower since both climatic and dispersal limitations were in effect. Thus, an average migration rate was calculated for the first row (n = 10) and another average migration rate was calculated for the next four rows (n = 40). The overall migration rate was the shortest amount of time it took to travel across all five rows. This was the years between the initial establishment in the first row and the earliest time it traveled all the way through a grid cell in the last row.

3.4 Results

Under the traditional assumption of full migration, all five rows were colonized at the same time (Figure 3-3), just after the 200 year warming period. This is the equivalent of moving 383 m year -1 for Acer , 273 m year -1 for Pinus and 360 m year -1 for Tsuga . With the assumption of full migration, it is important to keep in mind that this overall migration rate might change if the area simulated was smaller or larger. The only limiting factor is climate, not distance. If the climate was suitable across the entire area simulated then the rate would be slower if fewer rows were simulated and faster if more rows were simulated.

Simulations with limited dispersal had more moderate overall migration rates. The simulated migration rates for Acer (110 m year -1) were consistent with phylogenetic reconstructed migration rates (80-90 m year -1; Table 3-2). Simulated Pinus migration (60 m year -1) was also comparable to pollen reconstructed rates for Pinus (81 m year -1; Table 3-2). Tsuga was the only

66 species where simulated migration rates were considerably slower than the pollen record indicates (simulated rates 80 m year -1, pollen reconstructed rates 200 m year -1; Table 3-2).

Stochastic processes and random gap forming events caused considerable variability between grid cells at the same latitude (Figure 3-3). For Pinus , there was ~300 years between the first and last grid cell to be colonized in the same row (Figure 3-3b). However, this is perhaps a more appropriate representation of migration across a landscape, as opposed to one unified front spreading over the landscape (as described by simple diffusion models).

Using the logistic growth curve to describe movement through a grid cell produced a consistent pattern. The initial stage, where the PFT was maintained in only a few patches for a long period of time, followed by the rapid spreading stage, once the PFT had established in ~30% of the patches (Figure 3-3).

3.5 Discussion

LPJ-DISP was able to simulate the movement of vegetation across a theoretical landscape at a rate that is approximately consistent with historical vegetation migrations (Table 3-2). Acer had the fastest average and overall migration rates. This was expected considering it had the youngest maturation age, highest fecundity and largest distance parameter (Table 3-1). The overall migration rate was a little lower than the pollen-reconstructed rate from Delcourt & Delcourt (1987), and a little higher than the genetic-reconstructed rate from McLachlan et al. (2005), but reasonably close to both values. That the model was able to simulate migration rates similar to reconstructed rates is a very exciting outcome, considering the values used to parameterize the model are completely independent from paleo and genetic migration rate estimates.

Pinus was the slowest moving of the three test species, with an overall migration rate of just 60 m year -1. Delcourt & Delcourt (1987) also estimated slower migration for the southern pine group (Table 3-2), and is comparable to the simulated rate from LPJ-DISP. It is interesting to compare the range of migration rates, from both the simulated and pollen record. Simulated migration rates were two to three times slower in the first row (Table 3-2), when plants were

67 limited by dispersal as well as climate. Reconstructed migration rates also had a range of values, as slow as 22 m year -1 for Pinus up to 174 m year -1. Delcourt & Delcourt (1987) also believed that the slower migration rates were due to climatic or other environmental constraints, and the fastest migration rates occurred when the only limiting factor was dispersal.

Tsuga was the only test species where there was a large difference between the simulated and pollen reconstructed rates (Table 3-2). Both Davis (1981) and Delcourt & Delcourt (1987) estimated Tsuga migrated more than 200 m year -1, which is more than twice as fast as the simulated rate. The simulated migration rates in LPJ-DISP are slower since they are constrained by the life history parameters for Tsuga canadensis . This is potentially another example illustrating Reid’s paradox (Clark et al. , 1998), the conflict between the pollen record which has multiple examples of incredibly rapid plant migrations following the retreat of the last glacier in North America and Europe (Davis, 1981; Birks, 1989), versus measurements from modern day vegetation which estimate migration rates at least an order of magnitude slower (Clark, 1998). Part of the explanation is evolving from recent phylogeographic studies. Genetic work has been able to indentify refugia populations that persisted close to the edge of the retreating glacier (Anderson et al. , 2006; Hu et al. , 2009). Refugia populations are too small to appear in the pollen record, but factoring in their existence drastically lowers our estimates of historical migration rates (Anderson et al. , 2006). Of the three test species, migration rates based on genetic evidence were only available for Acer rubrum (McLachlan et al. , 2005), which incidentally matched quite well to the simulated rates (Table 3-2). A phylogeographic study for Tsuga would confirm the reconstructed migration rates and discern how well the model simulates dispersal for Tsuga . One way to achieve rapid migration rates similar to those observed in the pollen record is by increasing the proportion of long-distance seeds (Clark, 1998). For all three species, I used a ‘fat’ tailed dispersal kernel (equation 3.5, c = 0.5) with different values for α (Table 3-1). This ensured that there was some long distance dispersal, but didn’t specify how much. To reproduce the rapid migration rates observed in the paleo-record, Clark (1998) used a ‘fat’ tail and allocated up to 10% of the seeds to the tail. It would be possible to perform a similar study with LPJ-DISP, where an increasing proportion of seeds are assigned to the tail until we can simulate the rapid migration observed for Tsuga . In reality, it is highly unlikely that 10% of seeds would be part of this tail but it would help to identify if long distance dispersal alone could account for rapid plant migration observed in the past.

Dispersal within a grid cell

Using the logistic growth curve to describe the probability of patch-to-patch dispersal in LPJ- GUESS was a novel approach and does produce migration rates that are consistent with historical vegetation migration rates (Table 3-2). This is in spite of an unconventional spread pattern within a grid cell (Figure 3-3). Even though the logistic growth curve limits dispersal between patches when occupancy is low (i.e. only 5% of the patches have the PFT), there comes a point when it ‘jumps’ from about 30% to 80% within a few years. This is an unfortunate artifact of the patches not having real locations within the grid cell. Once the occupancy reaches a specific threshold, then all patches are assumed to be within receiving distance of a neighbouring patch. The size of the grid cell does influence the size of the ‘jump’ (Appendix 3). In order to maintain the relationship across scales, the logistic growth rate ( r) needs to be adjusted. For example, reducing the grid cell resolution to 9 km 2 requires a doubling of r to maintain the same migration rate (Table A-3). I believe it is important evaluate the simulation of vegetation migration at the landscape scale. Despite the spread within an individual grid cell resembling a logistic growth curve (Figure 3-3), the overall migration rates across the entire landscape are not unreasonable (Table 3-2).

Wind- versus animal-dispersal

The three species used in this study all use wind as their primary method for seed dispersal (Clark et al. , 1999). This is interesting since the assumption of full migration has been argued to be a reasonable representation for wind-dispersed trees (Higgins & Richardson, 1999). This study clearly shows that full migration is not the same as long distance dispersal, even for wind- dispersal (Figure 3-3).

To date, most of the effort towards developing a generic model for seed dispersal has focused heavily on wind dispersed seeds (e.g. Govindarajan et al. , 2007; Nathan et al. , 2011). This may be a northern hemisphere research bias, since wind dispersal is a common strategy in boreal and temperate trees. Alternatively, the focus on wind dispersal may be because animal dispersed seed shadows are so complex and rely heavily on disperser behaviour (Gomez, 2003). A

69 mechanistic model for animal dispersal needs to account for many additional factors such as animal movement, seed detachment, gut throughput, landscape heterogeneity, interactions with predators or competing species, and the spatial distribution and abundance of food sources (Gomez, 2003; Levey et al. , 2008; Cousens et al. , 2010). Although animal dispersal is usually studied at a more local scale (Godoy & Jordano, 2001; Clark et al. , 2005), I believe that modeling animal dispersal at a large scale may work really well for several reasons. First, animals have the potential for frequent and significant long distance dispersal (Levey et al. , 2008; Campos-Arceiz & Blake, 2011). Second, most of the complexity when simulating local or daily movements can effectively be ignored since all of these processes would occur within a patch. Using the framework outlined in this paper, the only information that would be needed to simulate dispersal between grid cells is the amount of long distance dispersal. Finally, studies that track animal movement and seed dispersal between patches (Gomez, 2003; Levey et al. , 2008) could be modified to describe patch-to-patch dispersal within a grid cell. Animal dispersal is an important dispersal strategy in both temperate and tropical forests (Jordano, 2000). Being able to simulate range shifts in response to climate change for plants with all modes of dispersal would be an enormous improvement for our future climate change scenarios.

Competition among vegetation types

A strength of LPJ-DISP is that plants participate in intra- and inter-specific competition, a common deficiency in species distribution models (Hampe, 2004). Although the climate was suitable, the progression of the warm PFTs was slower since they were competing with the existing cold-tolerant PFTs for space. Even at the end of the Acer simulation (year 2199), there were still 12 of the 50 grid cells that contained at least one patch with the cold-tolerant PFT.

However, a limitation of this model is that incoming vegetation does not compete with other migrating species (i.e. other warm PFTs). The warm shade-intolerant PFTs were unable to migrate since they could never establish in the first row. First, they were out-competed by the existing cool shade-tolerant PFTs. Then, Acer/Pinus/Tsuga replaced the cool forest and continued to block out the shade-intolerant PFTs. The pollen record has multiple examples of shade intolerant species, such as Larch and Jack pine, migrating after the retreat of the glacier

(Davis, 1981; Delcourt & Delcourt, 1987). To simulate the movement of these species, the landscape would need to be modified to include natural open spaces, or increase the frequency and size of disturbance events, creating more gaps in the forest and more opportunities for shade- intolerant species to have a competitive edge.

Simulating dispersal at larger spatial scales

Although most studies of seed dispersal focus on events occurring within populations at local scales (Godoy & Jordano, 2001), dispersal events that occur beyond the population limits into new habitat is what will determine range shifts and plant migrations. Previous efforts to simulate dispersal at a large scale have taken existing mechanistic models representing local dispersal, and scaled them up to represent larger areas (e.g Govindarajan et al. , 2007; Nathan et al., 2011). Govindarajan et al. (2007) argued their model allowed them to simulate large-scale phenomenon like migration as well as the small-scale population dynamics within a forest. However, I am proposing that is not necessary to accurately describe the small-scale dynamics in order to simulate the large-scale effects. Factors which are important for local regeneration and population dynamics aren’t necessarily relevant at larger spatial scales. This includes information like the spatial arrangement of individual species within a forest, the variability of seed production between individuals, or the variability in dispersal processes. My model assumes that long distance seed dispersal, maturation age and fecundity are the most important factors and most likely to have an effect on migration rates. Although it is a broad generalization of a very complex process, the model results seem to support this. Additional reproductive processes may also have an impact and could be incorporated into LPJ-DISP in the future (see Chapter 6).

Conclusions

The lack of seed dispersal is a major criticism in all vegetation-climate models. This is the first time seed dispersal limitations have been incorporated into a physiological vegetation-climate model, at a spatial and temporal scale which is suitable for simulating vegetation migration. The

71 model was tested with three temperate tree species, illustrating the approximate agreement between simulated migration rates and reconstructed migration rates. Future work on this model can address questions about future climate change and potential range shifts and extinctions, the selection and location of migration corridors, the need for human-assisted migration and the rate of extinction at the retreating edge of the populations. Adding seed dispersal to vegetation- climate models will ultimately help us to develop more realistic expectations for how vegetation will respond to future climate change.

Table 3-1. Values used to parameterize the three test species (additional parameter values are listed in the Appendix, Table A-2). αdisp is a distance parameter used in the dispersal kernel. reprfrac is the fraction of carbon allocated to reproduction and kest_repr is a constant in the equation for seed production.

maturation age αdisp reprfrac kest_repr longevity Other

Acer rubrum 8 30.8 0.1 5000 80 temperate, broadleaf, deciduous Pinus rigida 12 15.1 0.1 1097 100 temperate, needleleaf, evergreen Tsuga canadensis 15 22.8 0.1 2317 500 temperate, needleleaf, evergreen

Table 3-2. Simulated migration rates for each of the test species. The first row is the most southerly row, subsequent rows calculates the migration rate from all rows excluding the first. Shown is the average ± standard deviation (minimum – maximum values). The reconstructed migration rates are either from pollen records (Davis, 1981; Delcourt & Delcourt, 1987) or phylogenetic methods (McLachlan et al ., 2005).

Species Simulated migration rates (m year -1) Reconstructed migration rates (m year -1)

First row Subsequent Overall rows Acer rubrum 47.90 ± 8.30 140.98 ± 9.47 110.97 200 Davis (1981) (34 – 64) (122 – 162) 126 Delcourt & Delcourt (1987) (80 – 172)

80 – 90 McLachlan et al. (2005)

Pinus rigida 29.63 ± 4.36 76.20 ± 12.23 59.76 81 Delcourt & Delcourt (1987) (24 – 37) (55 – 101) (22 – 174)

Tsuga 47.41 ± 4.56 85.40 ± 16.06 78.95 200 – 250 Davis (1981) canadensis (40 – 53) (25 – 100) 202 Delcourt & Delcourt (1987) (113 – 278)

(a) Original scheme, one cell at a time Time Time Time

Latitude Latitude Latitude

Longitude Longitude Longitude

(b) New scheme, independent spin up followed by one-year-at-a-time for all cells Time Time Time

ts ts ts Latitude Latitude Latitude

Longitude Longitude Longitude Time Time Time

ts+1 ts+1 ts Latitude Latitude Latitude

Longitude Longitude Longitude

one year at a time. ts represents the spin up period.

Figure 3-3. Simulated migration in LPJ-DISP for the three test species. Each line represents one grid cell and there are 10 grid cells in every row. The grey lines represent the simulation with the traditional assumption of full migration. The dotted line indicates the end of the warming period (i.e climate is now suitable for species in all grid cells). Each grid cell was ~18 km 2 (0.166°). For graphing purposes, distance was calculated by multiplying the proportion of occupied patches within a grid cell by 18 km. For example, if 30% of the patches were occupied in year 2150 then it had moved 5.4 km through that grid cell.

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Gerten, D., Schaphoff, S., Haberlandt, U., Lucht, W., & Sitch, S. (2004) Terrestrial vegetation and water balance - hydrological evaluation of a dynamic global vegetation model. Journal of Hydrology , 286 , 249-270. Godoy, J.A. & Jordano, P. (2001) Seed dispersal by animals: exact identification of source trees with endocarp DNA microsatellites. Molecular Ecology , 10 , 2275-2283. Gomez, J.M. (2003) Spatial patterns in long-distance dispersal of Quercus ilex acorns by jays in a heterogeneous landscape. Ecography , 26 , 573-584. Govindarajan, S., Dietze, M.C., Agarwal, P.K., & Clark, J.S. (2007) A scalable algorithm for dispersing population. Journal of Intelligent Information Systems , 29 , 39-61. Guisan, A. & Thuiller, W. (2005) Predicting species distribution: offering more than simple habitat models. Ecology Letters , 8, 993-1009. Hampe, A. (2004) Bioclimatic envelope models: what they detect and what they hide. Global Ecology and Biogeography , 13 , 469-471. Haxeltine, A. & Prentice, I.C. (1996) BIOME3: An equilibrium terrestrial biosphere model based on ecophysiological constraints, resource availability, and competition among plant functional types. Global Biogeochemical Cycles , 10 , 693-709. Hély, C., Bremond, L., Alleaume, S., Smith, B., Sykes, M.T., & Guiot, J. (2006) Sensitivity of African biomes to changes in the precipitation regime. Global Ecology and Biogeography , 15 , 258-270. Hickler, T., Smith, B., Sykes, M.T., Davis, M.B., Sugita, S., & Walker, K. (2004) Using a generalized vegetation model to simulate vegetation dynamics in northeastern USA. Ecology , 85 , 519-530. Higgins, S.I. & Richardson, D.M. (1999) Predicting plant migration rates in a changing world: the role of long-distance dispersal. American Naturalist , 153 , 464-475. Hu, F.S., Hampe, A., & Petit, R.J. (2009) Paleoecology meets genetics: deciphering past vegetational dynamics. Frontiers in Ecology and the Environment , 7, 371-379. IPCC (2007). Climate Change 2007: Synthesis report. Contribution of working groups I, II and III to the fourth assessment report of the Intergovernmental Panel on Climate Change. (eds R.K. Pachauri & A. Reisinger), pp. 104, Geneva, Switzerland. Iverson, L.R., Schwartz, M.W., & Prasad, A.M. (2004) Potential colonization of newly available tree-species habitat under climate change: an analysis for five eastern US species. Landscape Ecology , 19 , 787-799. Jordano, P. (2000). Fruits and frugivory. In Seeds: The ecology of regeneration in plant communities (ed M. Fenner), pp. 125-165. CABI Publishing, New York. Lawler, J.J., White, D., Neilson, R.P., & Blaustein, A.R. (2006) Predicting climate-induced range shifts: model differences and model reliability. Global Change Biology , 12 , 1568-1584. Levey, D.J., Tewksbury, J.J., & Bolker, B.M. (2008) Modelling long-distance seed dispersal in heterogeneous landscapes. Journal of Ecology , 96 , 599-608. Loarie, S.R., Duffy, P.B., Hamilton, H., Asner, G.P., Field, C.B., & Ackerly, D.D. (2009) The velocity of climate change. Nature , 462 , 1052-U111.

Malcolm, J.R., Markham, A., Neilson, R.P., & Garaci, M. (2002) Estimated migration rates under scenarios of global climate change. Journal of Biogeography , 29 , 835-849. McLachlan, J.S., Clark, J.S., & Manos, P.S. (2005) Molecular indicators of tree migration capacity under rapid climate change. Ecology , 86 , 2088-2098. Midgley, G.F., Hughes, G.O., Thuiller, W., & Rebelo, A.G. (2006) Migration rate limitations on climate change-induced range shifts in Cape Proteaceae. Diversity and Distributions , 12 , 555-562. Morin, X., Viner, D., & Chuine, I. (2008) Tree species range shifts at a continental scale: new predictive insights from a process-based model. Journal of Ecology , 96 , 784-794. Nathan, R., Horvitz, N., He, Y.P., Kuparinen, A., Schurr, F.M., & Katul, G.G. (2011) Spread of North American wind-dispersed trees in future environments. Ecology Letters , 14 , 211- 219. New, M., Lister, D., Hulme, M., & Makin, I. (2002) A high-resolution data set of surface climate over global land areas. Climate Research , 21 , 1-25. Parmesan, C. & Yohe, G. (2003) A globally coherent fingerprint of climate change impacts across natural systems. Nature , 421 , 37-42. Pitelka, L.F., Gardner, R.H., Ash, J., Berry, S., Gitay, H., Noble, I.R., Saunders, A., Bradshaw, R.H.W., Brubaker, L., Clark, J.S., Davis, M.B., Sugita, S., Dyer, J.M., Hengeveld, R., Hope, G., Huntley, B., King, G.A., Lavorel, S., Mack, R.N., Malanson, G.P., McGlone, M., Prentice, I.C., & Rejmanek, M. (1997) Plant migration and climate change. American Scientist , 85 , 464-473. Purves, D. & Pacala, S. (2008) Predictive models of forest dynamics. Science , 320 , 1452-1453. Sato, H. (2009) Simulation of the vegetation structure and function in a Malaysian tropical rain forest using the individual-based dynamic vegetation model SEIB-DGVM. Forest Ecology and Management , 257 , 2277-2286. Sato, H., Itoh, A., & Kohyama, T. (2007) SEIB-DGVM: A new dynamic global vegetation model using a spatially explicit individual-based approach. Ecological Modelling , 200 , 279-307. Sitch, S., Huntingford, C., Gedney, N., Levy, P.E., Lomas, M., Piao, S.L., Betts, R., Ciais, P., Cox, P., Friedlingstein, P., Jones, C.D., Prentice, I.C., & Woodward, F.I. (2008) Evaluation of the terrestrial carbon cycle, future plant geography and climate-carbon cycle feedbacks using five Dynamic Global Vegetation Models (DGVMs). Global Change Biology , 14 , 2015-2039. Sitch, S., Smith, B., Prentice, I.C., Arneth, A., Bondeau, A., Cramer, W., Kaplans, J.O., Levis, S., Lucht, W., Sykes, M.T., Thonicke, K., & Venevsky, S. (2003) Evaluation of ecosystem dynamics, plant geography and terrestrial carbon cycling in the LPJ dynamic global vegetation model. Global Change Biology , 9, 161-185. Smith, B., Prentice, I.C., & Sykes, M.T. (2001) Representation of vegetation dynamics in the modelling of terrestrial ecosystems: comparing two contrasting approaches within European climate space. Global Ecology and Biogeography , 10 , 621-637.

Thomas, C.D., Cameron, A., Green, R.E., Bakkenes, M., Beaumont, L.J., Collingham, Y.C., Erasmus, B.F.N., de Siqueira, M.F., Grainger, A., Hannah, L., Hughes, L., Huntley, B., van Jaarsveld, A.S., Midgley, G.F., Miles, L., Ortega-Huerta, M.A., Peterson, A.T., Phillips, O., & Williams, S.E. (2004) Extinction risk from climate change. Nature , 427 , 145-148. Thomas, C.D. & Lennon, J.J. (1999) Birds extend their ranges northwards. Nature , 399 , 213- 213.

Chapter 4

4 A sensitivity analysis of dispersal and climate change related migration in a dynamic ecosystem model

4.1 Abstract

I performed a sensitivity analysis of LPJ-DISP, the new seed dispersal functionality recently added into the hybrid dynamic vegetation climate model, LPJ-GUESS. The five parameters which relate to plant fecundity and seed dispersal were examined in a sensitivity study. Parameter values and combinations were chosen based on a Latin hypercube sampling design and the model was run 60 times. Average migration rates ranged from 37 – 162 m year -1. The sensitivity analysis identified three parameters as being important to the simulation of vegetation

migration. The distance parameter ( αdisp ) in the dispersal kernel determined if seed dispersal between grid cells occurred or not. Even with a leptokurtic distribution, the average dispersal distance had to be greater than 7 m in order for there to be any dispersal between grid cells. The migration rate was determined mostly by maturation age (trees that started reproducing at younger ages had faster rates of spread) and a parameter describing the shape of the logistic growth curve ( r_log ). The logistic growth curve is used to describe the probability of spread between patches within a grid cell. In general, fecundity was the least important parameter. This study highlights how a robust sensitivity analysis can be performed on complex ecological models with relatively few sample runs, provides confidence in the model results and identifies areas for further research.

4.2 Introduction

Future climate scenarios predict rapid environmental changes, which will result in significant habitat shifts for plants and animals alike (Parmesan & Yohe, 2003; Fitzpatrick et al. , 2008). The ability of a species to respond to climate change may depend on its adaptability (Morin et

83 al. , 2008; Kuparinen et al. , 2010), intraspecific competition (Best et al. , 2007), landscape heterogeneity (del Barrio et al. , 2006; Luoto et al. , 2007) or migration capacity (Midgley et al ., 2006; Fitzpatrick et al ., 2008). Long-lived, sessile organisms like trees are of particular interest since lengthy generation times limit opportunities for rapid adaptation (Kuparinen et al. , 2010) and migration rates are constrained by rare, long-distance seed dispersal events (Clark et al. , 2001). Predicting how plants will respond to future climate change is often investigated using a variety of vegetation-climate models (e.g. Morin et al. , 2008; Wolf et al. , 2008), even though most vegetation-climate models don’t explicitly include seed dispersal.

In general, vegetation-climate models take one of two approaches with regards to seed dispersal: full dispersal, where plants can travel to any climatically suitable location regardless of absolute distance, physical barriers or even the presence of parent trees (e.g. Thuiller, 2004; Malcolm et al. , 2006; Weng & Zhou, 2006), or limited dispersal , where plants are allowed to move a predetermined maximum distance at each time step (e.g. Midgley et al. , 2006; Morin et al. , 2008). Species distribution models which assume full or even limited dispersal, predict migration rates that over-estimate the ability of plants to track future climate change. However for the first time, seed dispersal limitations were successfully added into a dynamic vegetation- climate model (LPJ-DISP, Chapter 3). Including seed dispersal will provide more realistic estimates for how quickly vegetation will respond to climate change and migrate to new habitats. Since this is a relatively new and untested model, performing a sensitivity analysis is an important step towards reducing model uncertainty, improving the confidence in model predictions, and identifying areas that require further research.

LPJ-GUESS has already been the subject of several comprehensive sensitivity analyses (Cramer et al. , 2001; Zaehle et al. , 2005; Wramneby et al. , 2008), which allows this study to focus soley on the parameterization of the new seed dispersal functionality in LPJ-DISP. Several new parameters were added to simulate seed dispersal (see Chapter 3 for a full description) and values were chosen based on published data when available. There is one variable in particular for which there was no known value ( r_log ). This parameter is part of the logistic growth curve that describes the probability of spread between patches within a grid cell. As there is no known analog between population growth rate and population spread across a landscape, a default value was chosen. The descriptions of semi-empirical processes in models often have parameter

84 values which are not easily measured, and it is these values in particular which benefit from a rigorous sensitivity analysis.

Choosing the right sampling design is very important for computationally expensive programs, such as dynamic global vegetation models (DGVMs). The goal is to maximize the range of input values while minimizing the number of simulations. A simple grid design is a common strategy where a few parameter values are chosen and each parameter combination is tried once (Sato, 2009). The issue with a full factorial design is the number of potential combinations grows exponentially and quickly reaches unreasonable numbers. For example, a 3 parameter grid space with 3 values each is 27 (3 3) runs. Testing LPJ-DISP with 3 values for each of the 5 parameters, is 243 (3 5) simulations. Even if the model was run 243 times, large regions of the parameter space remain unsampled which can be problematic if the relationships are complex or non-linear (Saltelli et al. , 2008). There is also the potential for a significant proportion of those combinations to be ‘wasted’ runs. Presumably, the model will be more sensitive to some of the parameters than others. The runs which only vary the insensitive parameter(s) are essentially wasted since there won’t be any change in the output. These runs would be better spent exploring different values for those parameters which are influential to the model.

Alternatively, a random sample design draws input values from the entire distribution range for each of the uncertain parameters. A purely random design requires hundreds to thousands of repetitions (Saltelli et al. , 2008) to ensure the entire space is sampled and to generate almost every input combination, thus improving the accuracy of the results. Constrained by a limited number of runs, a stratified random approach ensures the entire input space is sampled and runs are not wasted. A Latin hypercube sampling design is an example of a forced stratified design (Figure 4-1), and results obtained are generally considered robust even with small sample sizes (Saltelli et al. , 2008). The Latin hypercube approach starts by dividing the range of each input

variable Xn into m contiguous intervals. One value is selected randomly from each interval.

Then, the m values for X1 are combined at random with the m values for X2. The X1X2 pairs are then randomly combined with the chosen values for X3, and so on (McKay et al. , 1979). This method ensures each variable is represented in a fully stratified design, prior to any knowledge of which variables will be most significant. The Latin hypercube sampling design has also been used in the previous sensitivity studies for LPJ-GUESS (Zaehle et al. , 2005; Wramneby et al. , 2008).

The goal of this paper is to present the results of a sensitivity analysis of LPJ-DISP, which simulates seed dispersal and vegetation migration. It is important to identify how sensitive vegetation migration predictions are to the various unknown and known parameters to quantify model uncertainty and direct future research. This study also supports previous research (McKay et al., 1979; Seaholm et al., 1988; Helton & Davis, 2003; Urban & Fricker, 2010) which illustrates the effectiveness of Latin hypercube designs for computationally large programs.

4.3 Methods

4.3.1 The model, LPJ-DISP

LPJ-DISP is a new version of LPJ-GUESS, a physiological-based model which incorporates a forest gap model within an existing dynamic global vegetation model (LPJ-DGVM, Smith et al ., 2001). LPJ-DISP also includes a mechanistic representation of seed dispersal to better represent vegetation migration in response to climate change (Chapter 3). The model uses environmental data as input (i.e. temperature, precipitation, solar radiation and soil characteristics) to simulate biogeochemical cycles, growth and competition between potential vegetation types. Vegetation is represented as plant functional types (PFTs), functionally similar plants grouped together based on life-history characteristics, growth form, phenology, shade tolerance, and bioclimatic limits for growth, survival and establishment. Stochastic processes such as disturbance and age- based mortality allow for different dynamics in each patch, creation of canopy gaps and succession.

A complete description of LPJ-GUESS is provided by Smith et al. (2001). Elements which are shared with the global model LPJ-DGVM, such as biogeochemical cycling and plant physiology, are described in Sitch et al. (2003).

4.3.2 Testing the sensitivity of simulated migration rates

LPJ-DISP requires a large number of input parameters, which includes four environmental data sets, 18 model parameters and 53 parameters which are PFT-specific. Previous sensitivity analyses for LPJ-DGVM (Zaehle et al. , 2005) and LPJ-GUESS (Wramneby et al. , 2008) identified the most important parameters for simulating growth, productivity and PFT

86 composition. I chose to test only those variables that would have a direct impact on simulating seed dispersal and migration rates (Table 4-1).

4.3.2.1 Maturation age ( age_repr ) age_repr is a new variable which represents the maturation age for a tree, or the minimum age when a PFT can start allocating a portion of its carbon to reproduction. Previous versions of LPJ-GUESS had no age-related restrictions on reproduction and allowed PFTs to start producing seeds the year after establishment. There remains no restriction on grass reproduction. This variable is considered a basic life history parameter and is often included in seed dispersal studies since it is important for determining rates of spread (Clark, 1998; Nathan et al. , 2011).

4.3.2.2 Distance parameter in dispersal kernel ( αdisp )

To determine the probability of a seed moving between grid cells, I used the generic dispersal kernel proposed by Clark (1998) which describes a probability distribution for a seed travelling a specific distance, x,

   c   c   x  k(x) =  exp −  , (4.1)  2αΓ()/1 c   α  where c is a shape parameter, Γ( ) is the gamma function and α is a distance parameter. Although c can be set to different values (e.g. c = 1.0 is the exponential curve, c = 2.0 is the Gaussian curve, and c < 1.0 is leptokurtic), I chose a value of 0.5 for all PFTs for all simulations. This created a ‘fat-tail’ and ensured that at least some long distance dispersal would occur. Each

PFT could have different values for α (referred to as αdisp to distinguish it from other parameters in LPJ-GUESS). In the literature, α values are found by fitting a curve to measured seed dispersal distances (Clark et al. , 2005). Those values are used to parameterize this kernel such that each PFT can represent a unique tree species.

4.3.2.3 Spread rate between patches within a grid cell ( r_log )

To simulate seed dispersal between patches within a grid cell, I used the logistic growth curve,

Ke rp P( p) = + rp − K (e )1 , (4.2)

87 where P is the population of available patches for receiving seeds (i.e. have at least one neighbouring patch that contains the PFT) when there are p patches that contain reproducing adults for that PFT. The carrying capacity, K, is the total number of patches in one grid cell (400 in this study). The initial population size ( P0) is always set to 1 since this formula was only used if the PFT was already present in the grid cell. Refer to section 3.3.7 for the full description of this step. The growth rate, r (referred to as r_log in LPJ-DISP), was given a default value of 0.1. Choosing a value for r_log is difficult since this is the first time, that I am aware of, where the logistic growth curve has been used to describe population spread between patches. Since there are no published values to draw upon, I tested a 20% range around the default value (Table 4-1).

4.3.2.4 Fecundity ( kest_repr and reprfrac )

Once a tree has reached reproductive maturity, resources are allocated to seed production. The proportion of net primary productivity (NPP) which goes to reproduction is determined by the parameter reprfrac , which is typically set to 0.1 (Sitch et al. , 2003; Wramneby et al. , 2008).

cmass repr = npp * reprfrac . (4.3)

It is important to distinguish that carbon allocated to reproduction in LPJ-DISP ( reprfrac ) is not the same as “reproductive allocation” (all the resources allocated to reproductive structures (Thomas, 2011)). It is an unfortunate word choice, since reprfrac actually represents “reproductive effort” (the resources used for reproduction instead of vegetation growth (Thomas, 2011)).

The parameters cmass repr and kest_repr are used to calculate the number of seeds that will establish in a patch. There are three scenarios to consider; arriving from a patch in a neighbouring grid cell, arriving from a patch within the same grid cell, and from reproductively mature plants within the patch. The number of seeds that arrive from neighbouring grid cells uses equations 4.1 and 4.3,

seeds = kest _ repr * cmass repr _ neighbour * pPFT * k(x) , (4.4)

where kest_repr is a PFT-specific constant, cmass repr_neighbour is carbon allocated to reproduction from that PFT from the neighbouring grid cell, pPFT is the proportion of patches in the neighbouring grid cell that contain the PFT, and k(x) is the dispersal kernel (equation 4.1).

If the PFT is not present in the patch but is present in the grid cell, then the probability of a patch receiving seeds from neighboring patches is determined by equation 4.2. If a patch is considered eligible to receive seeds from nearby patches, then the number of new seeds is based on the “spatial mass effect” (Smith et al. , 2001). This is where the carbon allocated to reproduction from all PFTs in the grid cell ( cmass repr_gridcell ) is used to calculate seedling establishment,

seeds = cPAR * kest _ repr *cmass repr _ gridcell , (4.5)

where cPAR describes available space and light at the forest floor within the patch, and PFT- specific light requirements. Thus, PFTs which have a higher density in the grid cell have an advantage and will contribute more seeds.

If the PFT is already present in the patch, then the number of seeds is determined by the reproductive carbon from the PFTs within the patch,

seeds = cPAR * kest _ repr *cmass repr _ patch . (4.6)

Since fecundity, usually measured as the number of seed produced per area of tree, is not

explicitly included in LPJ-DISP, I thought to generate a similar effect with kest_repr and reprfrac . Published values for fecundity from different tree species don’t fit the model requirements.

Thus, fecundity values were scaled between 1000 – 5000 and assigned to kest_repr . Although it is a compromise, it does maintain the relationship that trees with high fecundity do produce a greater number of seeds in the model, and trees with low fecundity produce fewer seeds. Different reproductive strategies can be represented with these two parameters. For example, plants that produce bigger seeds and fewer of them can be represented by a higher value for reprfrac and a lower value for kest_repr .

4.3.3 Sampling design

I chose to use a Latin hypercube sampling design (McKay et al. , 1979) with 60 simulations. The number of simulations was chosen a priori based on time constraints. The range of potential

89 values for each of the five parameters was developed from the literature (Table 4-1) and a uniform distribution was assumed. This means that for each parameter, the range was divided into 60 equal segments (e.g. maturation age ranged from 6 to 50, so there would have been segments from 6 – 6.73, 6.73 – 7.46 .... 49.27 – 50). Within each segment, a value was randomly selected. The randomly selected values for all five parameters were then combined to create 60 unique input combinations (Figure 4-1c). Each value is only used once. I used the ‘lhs’ package in R ( http://cran.r-project.org/ ) to generate the input combinations with the “maximinLHS” function. This function selects input points that maximize the minimum distance between them (Stein, 1987; Figure 4-1c) to ensure the entire parameter space is sampled.

4.3.4 Simulation protocol

The sensitivity analysis for LPJ-DISP used an artificial landscape, eighty grid cells arranged in eight rows of ten columns. The top five rows had a cold climate and the bottom three rows had a warm climate. The climate data was extracted from actual boreal and temperate regions in North America from the Climatic Research Unit global gridded data set (New et al. , 2002) which has a resolution of 0.166° or 18km. A total of seven PFTs were included: one grass which could grow in both the warm and cold climates, three trees which preferred the cold climate (a shade intolerant, an intermediate shade tolerant and a shade tolerant tree), and three warm trees (also one of each shade-intolerant/intermediate/tolerant). Additional details about the climatic input and PFTs can be found in Chapter 3 and Appendix 1 (Table A-2).

The model was allowed 1000 years of spin up (i.e. stable climate, no restrictions on dispersal), followed by 200 years of warming, then another 1000 years at the new temperatures (same climatic input as in Chapter 3). Using the original temperatures, there was complete separation between cold and warm PFTs. Approximately 50 years into the warming period, the warm- shade tolerant PFT started to establish in the first row of cold grid cells. The different combinations of input parameters as chosen by the Latin hypercube sampling design were modified for the warm shade tolerant PFT only. Values for the other PFTs stayed constant for each simulation.

4.3.5 Output measures

The sensitivity analyses were based on five different measurements that were calculated from the model output.

Dispersal – this is a dichotomous variable which indicates whether seed dispersal occurred (1) or seed dispersal did not occur (0). Evidence that the warm PFT had arrived in previously unoccupied cold grid cell (i.e. leaf area index > 0) was taken as proof of dispersal. The success of the seedling after establishment was not considered in this measure. Those simulations which had no dispersal were excluded from the remaining calculations.

Migration – this dichotomous variable indicates whether the PFT was able to migrate through the first grid cell. The PFT is considered to have moved all the way through a grid cell once >80% of the patches contain the PFT. Simulations which had no migration were excluded from the rate measures below.

Overall migration rate (m year -1) – the shortest amount of time to travel the greatest distance in the time allowed. Each grid cell is 18 km 2, so the maximum vertical distance is 90 km. However, not every combination of input parameters allowed for trees to move fast enough to cover the entire distance. For example, if the PFT was only able to travel through a grid cell in the 4 th row and it reached that distance 900 years after it started moving, the overall rate would be 72000 m / 900 years = 80 m year -1. This metric does not consider variability between grid cells within a simulation, it merely reflects the fastest migration path that was achieved for each simulation.

Average migration rate, first row (m year -1) – vertical distance of one grid cell (18 km) divided by the number of years to migrate through each grid cell in the first row (i.e. the most southerly row). The first row was analyzed separately from the rest of the rows since climate, in addition to dispersal, was a limiting factor.

Average migration rate, rest (m year -1) – vertical distance of one grid cell (18 km) divided by the number of years to migrate through each grid cell in all subsequent rows.

4.3.6 Sensitivity analysis

Measuring the sensitivity of model output to input values can be quantified by several different sensitivity measures, all of which are based on regression or correlation analyses between the original input parameters and output measures. The two dichotomous measures (dispersal and migration) were analyzed with a logistic regression, using all five parameters as predictor variables. The three rate measurements were analyzed a few different ways, using the correlation coefficient (CC), the standardized regression coefficient (SRC), and the partial correlation coefficient (PCC).

The CC is the linear correlation between input parameter Xn and output Y (i.e. Pearson’s r). The larger the value, the stronger the degree of correlation between input and output. A negative value signifies an inverse relationship between Xn and Y. If the relationship between X and Y is linear and there is no correlation between the input parameters, then the CC should be mostly equal to the SRC (Manache & Melching, 2004).

The SRC starts with a standard linear regression model. Given that the resulting regression coefficients are dependant on the units of the input parameters, it can be difficult to compare their effects. Standardizing them (between 0 and 1) removes the effect of units and makes it easier to identify the parameters with the most impact on the output. The SRC measures the contribution of each input parameter to the linear uncertainty in the output. However, it does not consider correlation between the input parameters. As all five parameters were included in the regression, the adjusted R 2 value was reported since it accounts for the increase in R 2 as the number of parameters increases.

The PCC is a useful measurement since it does account for potential correlations between input parameters. The PCC measures the correlation between input parameter X1 and output Y, while

eliminating the effect of other input parameters X2, X 3 ... X n (Hamby, 1994). If no correlations exist between input parameters, the sensitivity rankings based on the linear correlation coefficients (CC) will remain the same.

The CC, SRC and PCC all assume a linear relationship between input and output, which is not necessarily true. Ranking the data (i.e. replace the value with their rank, 1 for the smallest value and n for the largest value) reduces the effects of non-linearity. If the relationship between X and

Y is monotonic, rank transformation will also reduce the effect of outliers and transforms the relationship into a linear one (Hamby, 1994). I calculated the CC, SRC and PCC on the rank- transformed data as well.

4.4 Results

LPJ-DISP simulated a range of migration rates by varying the five parameters. For example, the overall migration rate ranged from 15 – 108 m year -1, the average migration rates ranged from 16 – 49 m year -1 for the first row and 37 – 162 m year -1 for all subsequent rows.

The logistic regression identified αdisp as the most important parameter for determining if

dispersal occurred or not, followed by kest_repr (Table 4-2). There was a clear threshold value

(αdisp ≥ 7) which needed to be surpassed in order for dispersal between grid cells to take place (Figure 4-2). The success of migration was mostly influenced by maturation age (Table 4-2), although this model had a much lower predictive value (R 2 = 0.27).

In general, the multiple regressions fit the data well (overall migration rate R 2 = 0.82, average migration rate first row R 2 = 0.88, average migration rate rest of rows R 2 = 0.88). Ranking the data resulted in a small improvement in model fit (overall migration rate R 2 = 0.93, average migration rate first row R 2 = 0.90, average migration rate rest of rows R 2 = 0.95). Overall migration rate and average migration rates through each grid cell were the most sensitive to maturation age ( age_repr ), as this parameter was consistently ranked first under all the various sensitivity measures (Figure 4-3). The second most important parameter was most often r_log , which is important for overall and average migration rates since it describes dispersal between patches within a grid cell.

Fecundity (represented by kest_repr and reprfrac ) had a weaker effect on migration rates (Figure 4-3) and were correlated, as seen by the different values of PCC, CC and SRC. In general, reprfrac had a negative relationship with migration rates where a higher proportion of carbon allocated to reproduction resulted in slower migration.

4.5 Discussion

Performing a sensitivity analysis on complex and computationally intense ecosystem models can be a challenge since the long running time of these programs limits the number of simulations. Latin hypercube sampling has been shown to produce more robust results with lower errors than a full factorial or random sampling design (McKay et al ., 1979; Helton & Davis, 2003; Urban & Fricker, 2010) when using the same number of limited runs (typically less than 100). Latin hypercube sampling designs can also produce comparable results to a full factorial design, with 14 times fewer runs (Seaholm et al ., 1988). The results from this paper illustrate this point. With just 60 simulations, the Latin hypercube sampling design was able to draw from the entire parameter space and identify which of the input parameters are important for determining migration rates in LPJ-DISP. The distance parameter used in the seed dispersal kernel ( αdisp ) determined if dispersal between grid cells occurred or not, and maturation age had a strong, negative correlation on migration rates. Both of these input parameters are known or can be measured precisely which increases our confidence in model results. However, migration rates were also sensitive to the parameter used to determine the rate of spread between patches within a grid cell ( r_log ). This is a parameter for which there is no known value, and this uncertainty in the input parameter carries through to cause uncertainty in the output. A closer examination of both the known and unknown parameters would benefit the model.

Movement between patches

It is not surprising that the model is sensitive to the parameter which describes the probability of movement between patches in a grid cell ( r_log , equation 4.2). Using the logistic growth curve may be a novel approach for describing seed dispersal between patches, but it has long been used in epidemiology to describe the spread of diseases (Berger, 1981). It may be possible to use some of the epidemiological research for quantifying r_log , if we consider humans to be patches and viruses to be seeds. Another area of on-going research which might prove to be useful is metapopulation theory, which describes the movement of organisms between discreet populations (Hanski, 1998). Although the usefulness of metapopulation theory for plants is still open to debate (Freckleton & Watkinson, 2002; Ehrlen & Eriksson, 2003) there are similarities

94 to our current situation and may provide another way for LPJ-DISP to describe dispersal between patches. Finally, there are already data on the movement of birds between patches (Gomez, 2003; Levey et al. , 2008) which could be incorporated into the model as a value for r_log or as an alternative function, especially when the simulated tree species had bird-dispersed seeds.

Exploring any one of these avenues may provide the answers for r_log or present alternatives for simulating dispersal between patches. It would be ideal to choose a value for r_log that describes movement between patches based on their dispersal vector (i.e. wind, mammal, bird). However in the interim, I suggest keeping this value constant for all PFTs. Although this may not be as realistic, it would ensure the simulated migration rates are based on known life history parameters which would reduce uncertainty.

Life history strategies

The sensitivity analysis identified maturation age as the most influential parameter for simulating migration rates in LPJ-DISP. Maturation age is an important component in tree life history strategies (Loehle, 1988; Clark, 1991) and can impact biodiversity, community composition and population spread (Clark & Ji, 1995; Nathan et al. , 2011). Life history theory assumes that plants have a finite amount of resources and competing interests (Loehle, 1998; Obeso, 2002; Thomas, 2011). Should they invest in growth for competitive advantages, defensive measures for protection against herbivory, or reproduction for the survival of their genes? Delaying reproduction to invest in growth is a common strategy for trees in stable environments. However, if trees delay reproduction too long they may be unable to respond quickly to climate change and migrate to new locations.

The sensitivity analysis also illustrates another potential trade-off for trees, the cost of reproduction (Obeso, 2002). It was interesting that a higher reproductive effort (represented in the model by reprfrac ) resulted in slower migration rates. One might have expected that producing more seeds would result in faster migration rates. However, allocating more carbon to reproduction means there is less carbon available for growth which puts trees at a disadvantage when competing for light and resources.

Reproductive effort had a relatively weak effect on migration rates, usually ranked 4 th or 5 th (Figure 4-3). This may be because the range of values tested was fairly small, from 0.08 – 0.12 (although it is important to note that the exact same range was tested for r_log and there was a significant effect of r_log on migration rates) or because the model results are truly insensitive to this parameter. This is the first time reprfrac has ever been changed in LPJ-GUESS because reproduction, and how it relates to vegetation migration, has not been studied in DGVMs. In reality, reproductive effort is a function of size and/or age in trees ( reviewed in Thomas, 2011). It can range from 0% in immature trees, anywhere from 20 – 40% for mature beech trees (Genet et al. , 2010), and 100% in monocarpic trees. Simulated migration rates may be more sensitive to changes in reprfrac when a broader range is tested or when reprfrac is allowed to change over the lifespan of a tree (see section 6.2.2).

One parameter that was not included in the sensitivity analysis was longevity. Although longevity may not directly impact migration rates (Nathan et al. , 2011), there is a linear relationship between longevity and maturation age (Loehle, 1988): trees that start reproducing younger have shorter life-spans. In addition, Kuparinen et al. (2010) showed mortality to be the most important factor for regulating the speed of adaptation to climate change. The death of established trees allowed more adapted seedlings the opportunity to establish faster. The same argument might be applied to migration rates where the death of established trees opens up space for new seedlings to migrate into. In LPJ-DISP, mortality is stochastic and can be caused by patch-destroying events, shade intolerance or aging (Smith et al. , 2001). Each PFT has a non- stressed maximum longevity, and the probability of mortality increases as the PFT approaches this maximum life span. If plant longevity or the frequency of disturbances were shown to be sensitive to climate change, migration rates might be affected and a sensitivity analysis which focused on these parameters would be useful.

How much trees allocate to reproduction is another decision which impacts their life history strategy. Trees which reproduce younger also tend to invest more towards reproduction over a shorter life-span (Sakai et al. , 2003). The fact that fecundity didn’t impact migration rates in these simulations is likely an issue of scale or the small range of values tested. Fecundity has been shown to be important at smaller scales (Clark & Ji, 1995), but long-distance dispersal is likely the most important factor at the landscape level (Clark et al. , 1998). It doesn’t matter how many seeds a tree produces, only that one of those seeds travels a significant distance from the

96 parent. However, there are scenarios where reproductive effort might have an impact at a larger scale (see Chapter 5 and 6 for a discussion on masting).

Life history strategies and future climate change

In light of future climate change and the importance of being able to predict vegetation migration, it is interesting that many of the life history parameters are flexible and can be influenced by environmental stress and elevated CO 2 levels. Abies mariesii trees growing at high altitudes are under considerable environmental stress. This caused A. mariesii trees to reach reproductive maturity at smaller sizes, younger ages and to allocate more resources to reproduction (Sakai et al. , 2003). Red mangrove trees started reproducing at a much younger

age when exposed to elevated CO 2, a full two years before seedlings typically start reproducing

(Farnsworth et al. , 1996). Pinus taeda trees growing under elevated CO 2 levels also reached reproductive maturity at younger ages, smaller sizes and produced more cones (Ladeau & Clark, 2006). Climate change may cause modifications to life-history parameters that result in faster migration rates (i.e. younger maturation age and higher fecundity). However, these changes may come at a cost of shorter life spans (Sakai et al. , 2003) and reduced competitive abilities.

Conclusion

Sensitivity analyses are an integral step in model development. Using a Latin hypercube design was an effective method to test the sensitivity of migration rates in LPJ-DISP with a limited number of simulations. The analyses identified r_log as a parameter which would benefit from additional research, and illustrated the importance of various life history parameters. How plants will respond to climate change often focuses on dispersal and their ability to migrate to new locations. It is also important to recognize how climate change may alter the timing of their life cycles and partitioning of resources. Dynamic global vegetation models can provide some of these answers by making life history parameters dynamic and sensitive to carbon levels and climate.

Table 4-1. Parameters tested in the sensitivity analysis for LPJ-DISP. The range of values was used for generating the input parameters for the Latin hypercube sampling design.

Parameter Description Standard value Range tested Reference age_repr Maturation age 6 – 50 Clark (1998) Nathan et al. (2011)

αdisp Distance parameter in 3.52 – 34.2 Clark (1998) dispersal kernel kest_repr Constant in equation for seed 1000 – 5000 Clark et al. (1999)* production r_log Rate of spread between 0.1 0.08 – 0.12 ± 20% patches in a grid cell reprfrac Fraction of carbon allocated to 0.1 0.08 – 0.12 ± 20% reproduction

* original values were 0.145 – 1024, but were scaled between 1000 to 5000 for the model.

Table 4-2. Results of a sensitivity analysis for LPJ-DISP. Shown are the dichotomous outcomes; whether or not seeds entered the first row of grid cells (Dispersal), and whether or not trees were able to migrate through the first row (Migration).

Parameter Logistic Regression Dispersal R2 = 0.94

distance parameter in dispersal kernel p = 0.0007 ( αdisp ) odds = 5.05 constant in equation for seed production p = 0.40 (kest_repr ) odds = 1.00 maturation age p = 0.63 (age_repr) odds = 1.03 spread rate through a grid cell p = 0.73 (r_log) odds = 2.5 x 10 12 fraction of carbon allocated to reproduction p = 0.93 (reprfrac) odds = 240

Migration R2 = 0.27

maturation age p = 0.014 (age_repr) odds = 1.14 fraction of carbon allocated to reproduction p = 0.15 (reprfrac) odds = 5.34 x 10 31 spread rate through a grid cell p = 0.16 (r_log) odds = 8.17 x 10 30 distance parameter in dispersal kernel p = 0.66

( αdisp ) odds = 1.03 constant in equation for seed production p = 0.24 (kest_repr ) odds = 1.00

(a) Full factorial (b) Random

X 2 X 2

X 1 X 1

X 2 X 2

X 1 X 1

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Figure 4-2. Logistic regression for probability of dispersal (whether or not seeds entered the

first row of grid cells). αdisp is the distance parameter used in the dispersal kernel. Values below 7 have no dispersal.

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Figure 4-3. Results from a sensitivity analysis for LPJ-DISP. (a) overall migration rate – shortest amount of time to travel the greatest distance, (b) average migration rate, first row only – average number of years to travel through one grid cell in the first row, and (c) average migration rate for the rest of the grid cells. SRC –standardized regression coefficient, LCC – linear correlation coefficient, PCC – partial correlation coefficient, SRRC – standardized ranked regression coefficient, LRCC – linear ranked correlation coefficient, PRCC – partial ranked correlation coefficient.

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Farnsworth, E.J., Ellison, A.M., & Gong, W.K. (1996) Elevated CO 2 alters anatomy, physiology, growth, and reproduction of red mangrove ( Rhizophora mangle L). Oecologia , 108 , 599- 609. Fitzpatrick, M.C., Gove, A.D., Sanders, N.J., & Dunn, R.R. (2008) Climate change, plant migration, and range collapse in a global biodiversity hotspot: the Banksia (Proteaceae) of Western Australia. Global Change Biology , 14 , 1337-1352.

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Freckleton, R.P. & Watkinson, A.R. (2002) Large-scale spatial dynamics of plants: metapopulations, regional ensembles and patchy populations. Journal of Ecology , 90 , 419-434. Genet, H., Breda, N., & Dufrene, E. (2010) Age-related variation in carbon allocation at tree and stand scales in beech ( Fagus sylvatica L.) and sessile oak ( Quercus petraea (Matt.) Liebl.) using a chronosequence approach. Tree Physiology , 30 , 177-192. Gerten, D., Schaphoff, S., Haberlandt, U., Lucht, W., & Sitch, S. (2004) Terrestrial vegetation and water balance - hydrological evaluation of a dynamic global vegetation model. Journal of Hydrology , 286 , 249-270. Gomez, J.M. (2003) Spatial patterns in long-distance dispersal of Quercus ilex acorns by jays in a heterogeneous landscape. Ecography , 26 , 573-584. Hamby, D.M. (1994) A review of techniques for parameter sensitivity analysis of environmental- models. Environmental Monitoring and Assessment , 32 , 135-154. Hanski, I. (1998) Metapopulation dynamics. Nature , 396 , 41-49. Helton, J.C. & Davis, F.J. (2003) Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems. Reliability Engineering & System Safety , 81 , 23-69. Kuparinen, A., Savolainen, O., & Schurr, F.M. (2010) Increased mortality can promote evolutionary adaptation of forest trees to climate change. Forest Ecology and Management , 259 , 1003-1008.

Ladeau, S.L. & Clark, J.S. (2006) Elevated CO 2 and tree fecundity: the role of tree size, interannual variability, and population heterogeneity. Global Change Biology , 12 , 822- 833. Levey, D.J., Tewksbury, J.J., & Bolker, B.M. (2008) Modelling long-distance seed dispersal in heterogeneous landscapes. Journal of Ecology , 96 , 599-608. Loehle, C. (1988) Tree life-history strategies - the role of defenses. Canadian Journal of Forest Research , 18 , 209-222. Luoto, M., Virkkala, R., & Heikkinen, R.K. (2007) The role of land cover in bioclimatic models depends on spatial resolution. Global Ecology and Biogeography , 16 , 34-42. Malcolm, J.R., Liu, C., Neilson, R.P., Hansen, L., & Hannah, L. (2006) Global warming and extinctions of endemic species from biodiversity hotspots. Conservation Biology , 20 , 538-548. Manache, G. & Melching, C.S. (2004) Sensitivity analysis of a water-quality model using Latin hypercube sampling. Journal of Water Resources Planning and Management , 130 , 232- 242. McKay, M.D., Beckman, R.J., & Conover, W.J. (1979) A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics , 21 , 239-245. Midgley, G.F., Hughes, G.O., Thuiller, W., & Rebelo, A.G. (2006) Migration rate limitations on climate change-induced range shifts in Cape Proteaceae. Diversity and Distributions , 12 , 555-562.

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Morin, X., Viner, D., & Chuine, I. (2008) Tree species range shifts at a continental scale: new predictive insights from a process-based model. Journal of Ecology , 96 , 784-794. Nathan, R., Horvitz, N., He, Y.P., Kuparinen, A., Schurr, F.M., & Katul, G.G. (2011) Spread of North American wind-dispersed trees in future environments. Ecology Letters , 14 , 211- 219. New, M., Lister, D., Hulme, M., & Makin, I. (2002) A high-resolution data set of surface climate over global land areas. Climate Research , 21 , 1-25. Obeso, J.R. (2002) The costs of reproduction in plants. New Phytologist , 155 , 321-348. Parmesan, C. & Yohe, G. (2003) A globally coherent fingerprint of climate change impacts across natural systems. Nature , 421 , 37-42. Sakai, A., Matsui, K., Kabeya, D., & Sakai, S. (2003) Altitudinal variation in lifetime growth trajectory and reproductive schedule of a sub-alpine conifer, Abies mariesii . Evolutionary Ecology Research , 5, 671-689. Saltelli, A., Chan, K., & Scott, E.M. (2008) Sensitivity Analysis. Wiley & Sons, Ltd., Chichester. Sato, H. (2009) Simulation of the vegetation structure and function in a Malaysian tropical rain forest using the individual-based dynamic vegetation model SEIB-DGVM. Forest Ecology and Management , 257 , 2277-2286. Seaholm, S.K., Ackerman, E., & Wu, S.C. (1988) Latin hypercube sampling and the sensitivity analysis of a Monte-Carlo epidemic model. International Journal of Bio-Medical Computing , 23 , 97-112. Sitch, S., Smith, B., Prentice, I.C., Arneth, A., Bondeau, A., Cramer, W., Kaplans, J.O., Levis, S., Lucht, W., Sykes, M.T., Thonicke, K., & Venevsky, S. (2003) Evaluation of ecosystem dynamics, plant geography and terrestrial carbon cycling in the LPJ dynamic global vegetation model. Global Change Biology , 9, 161-185. Smith, B., Prentice, I.C., & Sykes, M.T. (2001) Representation of vegetation dynamics in the modelling of terrestrial ecosystems: comparing two contrasting approaches within European climate space. Global Ecology and Biogeography , 10 , 621-637. Stein, M. (1987) Large sample properties of simulations using Latin hypercube sampling. Technometrics , 29 , 143-151. Thomas, S.C. (2011). Age-related changes in tree growth and functional biology: the role of reproduction. In Size- and Age-Related Changes in Tree Structure and Function (eds F.C. Meinzer, B.J. Lachenbruch & T. Dawson), pp. 33-64. Springer. Thuiller, W. (2004) Patterns and uncertainties of species' range shifts under climate change. Global Change Biology , 10 , 2020-2027. Urban, N.M. & Fricker, T.E. (2010) A comparison of Latin hypercube and grid ensemble designs for the multivariate emulation of an Earth system model. Computers and Geosciences . Weng, E. & Zhou, G. (2006) Modeling distribution changes of vegetation in China under future climate change. Environmental Modeling and Assessment , 11 , 45-58. Wolf, A., Callaghan, T.V., & Larson, K. (2008) Future changes in vegetation and ecosystem function of the Barents Region. Climatic Change , 87 , 51-73.

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Wramneby, A., Smith, B., Zaehle, S., & Sykes, M.T. (2008) Parameter uncertainties in the modelling of vegetation dynamics - Effects on tree community structure and ecosystem functioning in European forest biomes. Ecological Modelling , 216 , 277-290. Zaehle, S., Sitch, S., Smith, B., & Hatterman, F. (2005) Effects of parameter uncertainties on the modeling of terrestrial biosphere dynamics. Global Biogeochemical Cycles , 19 , GB3020.

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Chapter 5 5 Simulating vegetation migration and landscape colonization with northerly refugia populations

5.1 Abstract

According to the palynological record, rapid plant migrations following the retreat of the last glacier were common in North America and Europe. However, providing an explanation for these rapid migration rates has been challenging based on modern seed dispersal distances. I used the newly developed seed dispersal functionality in LPJ-DISP to simulate the two theories that have been proposed to explain rapid plant migrations; long-distance seed dispersal and northerly refugia populations. Vegetation migration for three different species ( Acer rubrum , Fagus grandifolia , and Picea glauca ) was simulated in response to climate change, on an idealized landscape. For all three species, the colonization rates were faster when there was a northerly refugia population present. Increasing the number of refugia locations further increased the rate of landscape colonization, and this was most effective when refugia populations were separated. The implications for pollen-reconstructed migration rates are significant, since refugia populations are too small to appear in the pollen record. The perceived migration rates (defined as the time it took to move the maximum distance) were twice as fast when refugia were present. For example, A. rubrum had a perceived migration rate of 119 m year -1 without refugia and a perceived migration rate of 204 m year -1 with refugia. If northerly refugia populations were more common than previously thought, historical plant migration rates were likely much slower than current estimatations based on palynological reconstructions.

5.2 Introduction

Predicting how plants will respond to future anthropogenic climate change is informed by our understanding of how plants reacted to past climatic fluctuations. One critical component is the plants ability to migrate into new, climatically suitable habitats as they become available. Paleo-

108 reconstructions show the Earth has experienced multiple episodes of rapid climate change; most recently the glacial-interglacial cycles during the Quaternary (Petit et al. , 1999). According to the palynological record, trees did respond to these climatic fluctuations with rapid range contractions and expansions. After the last glacial maximum (LGM), there are multiple examples of trees moving hundreds to thousands of meters per year in North America (Delcourt & Delcourt, 1987; Yansa, 2006) and Europe (Huntley & Birks, 1983). However, modern-day seed dispersal studies find the vast majority of seeds travel less than 100 m from their parent tree (e.g. Clark et al. , 2005). This has caused speculation that paleo-reconstructed migration rates are gross overestimates (Anderson et al ., 2006; Pearson, 2006).

Two hypotheses have been proposed to explain the inconsistency between known seed dispersal distances and the rapid migration rates observed in the paleo record: long distance seed dispersal (LDD) and northern refugia populations (Clark et al. , 1998). Long distance seed dispersal events are very rare and consequently almost impossible to observe in the field. However, even the smallest number of LDD events have a disproportionally large influence on migration rates and theoretically can create spread rates that are consistent with the paleo record (Clark, 1998). Alternatively, the existence of northerly refugia populations could also account for the discrepancy.

Paleobotanical evidence confirms that most trees survived the glacial periods in southern refugia locations, such as the southern coastal plains in North America and Mediterranean peninsula locations in Europe (Davis, 1983; Delcourt & Delcourt, 1987; Hewitt, 1999; Provan & Bennett, 2008). As climate warmed and glaciers melted, trees migrated north and expanded into their current distributions. Traditional estimates for postglacial vegetation spread assume all trees originated from the southern refugia populations. If northerly refugia populations existed, they would have done so in locations with favorable climatic conditions, outside of the expected longitudes and latitudes (Stewart et al. , 2010). These small, disconnected groups would not have produced enough pollen to be detected in the palynological record, but these higher latitude populations would have acted as additional nuclei for populations spreading north. Thus, trees appear to move very quickly (i.e. trees “arrive” at a new location even though they were already present). In reality, trees may have spread at a more moderate pace, perhaps closer to migration rates that would be expected from modern seed dispersal measurements.

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Identifying the existence and location of northerly refugia populations is difficult using pollen alone (Birks & Willis, 2008). Pollen data reflect the broad-scale forest composition on the landscape and can miss species which are present at very low levels. Plant macrofossils, macroscopic charcoal, and stomata data are the only way to actually confirm species presence at a minimum age (Birks & Willis, 2008; Valiranta et al. , 2011); however, these data are rare. Recent breakthroughs towards identifying refugia locations have been made by using fossil data in combination with phylogeography, which uses genetic markers to reconstruct population history (McLachlan et al. , 2005; Anderson et al. , 2006; Shepherd et al. , 2007; Provan & Bennett, 2008; Willner et al. , 2009; Parducci et al. , 2012). In general, two types of northerly refugia have been identified: those located north of the major southern refugia (Figures 5-1a – 5-1d), and those located north of the glacial ice-sheet (Figure 5-1e).

Combining fossil and genetic data for European beech ( Fagus sylvatica ) demonstrated several refugia (Magri et al. , 2006), including a refugia in the eastern Alps which was solely responsible for the colonization of central and northern Europe (Magri et al. , 2006; Brus, 2010). In North America, northerly refugia populations for red maple ( Acer rubrum ) and American beech ( F. grandifolia ) have also been confirmed using pollen and genetics (McLachlan et al. , 2005). The northern-most populations of red maple descend from trees in the Appalachian Mountains, located significantly further north than the traditional southern refugia. A Berigian refugia for white spruce ( Picea glauca ) has also been confirmed using phylogeography, pollen and macrofossils (Anderson et al. , 2006; Zazula et al. , 2006; Wetterich et al. , 2012). The Berigian refugium is interesting because it means spruce survived on the north side of the glacier. Recently, a northern refugium for white spruce was discovered on the north side of the glacier in northern Scandinavia, parts of which are believed to have remained ice-free during the LGM (Anderson et al. , 2006; Parducci et al. , 2012). Thus, spruce moved into its current distribution by colonizing the land from both the north and south.

As the existence and locations of northerly refugia are being uncovered, questions about plant migration and future climate change appear more uncertain. Understanding how climate change, refugia locations, long-distance seed dispersal, and plant life history interact requires integrating processes that occur across very different spatial and temporal scales. Computer simulation modelling can be an invaluable tool since it allows us to combine processes and create scenarios that would be unobservable in the real world. This paper illustrates how a newly developed seed

110 dispersal module within a DGVM (LPJ-DISP, Chapter 3), can be used to test these theories about rapid plant migration in response to climate change. LPJ-DISP uses published seed dispersal kernels from modern day plants to simulate vegetation migration across a landscape. LPJ-DISP is a hybrid dynamic global vegetation model, which means vegetation growth will respond to simulated climate change. Simulating landscapes with and without northerly refugia locations addresses the question, is long-distance dispersal alone sufficient for plants to track rapid climate change? Or, is the presence of small, distributed, refugia populations necessary for plants to rapidly colonize a landscape?

5.3 Methods

5.3.1 The model, LPJ-DISP

LPJ-GUESS is a hybrid model, combining a forest gap model with a dynamic global vegetation model (Smith et al. , 2001; Sitch et al. , 2003). Bioclimatic interactions determine plant functional type (PFT) composition, by simulating physiological responses to temperature, precipitation, atmospheric CO 2, soil type, and photosynthetically active radiation. Vegetation growth and success is also influenced by intra- and inter-specific competition for light and resources. LPJ-DISP refers to the version of LPJ-GUESS which includes the new seed dispersal functionality described in Chapter 3.

LPJ-DISP was run in cohort mode, with 400 replicate patches within each grid cell. Stochastic patch-destroying events create variability within a grid cell, simulating gap-formation and plant succession. The generalized dispersal kernel described by Clark (1998) is used to describe the probability of a seed travelling a specific distance, x (see Chapter 3, equation 3.5). The distance parameter, c, was set to 0.5 for all PFTs. This describes a leptokurtic distribution. Values for α, a distance parameter, were selected from published values (Table 5-2). Additional details on how dispersal is simulated can be found in Chapter 3.

5.3.2 Simulation protocol

Two theoretical landscapes were used to test how the presence/absence of northerly refugia populations impact vegetation colonization (Figure 5-1). The bottom row of the temperate

111 landscape (Figures 5-1a – 5-1d) was assigned a warm, temperate climate to create a southern refugia. The next seven rows had a cooler, boreal climate. One to three grid cells in the middle were selected to be the location for the northerly refugia population, and were assigned a slightly warmer climate than the surrounding cells. This resulted in the temperate species being present at low levels (% of total LAI: Boreal PFTs = 85%, Temperate PFTs = 4%, Herbaceous PFT = 11%), mimicking the conditions of a refugium. The boreal landscape (Figure 5-1e) had a boreal climate in the south-east corner and a cooler, drier tundra climate in the rest of the grid cells. One grid cell in the north-west corner was selected to be the northerly refugia location, and was also given a boreal climate.

Climate data were extracted from temperate, boreal and tundra regions in North America using the Climatic Research Unit global gridded data set (New et al. , 2002). LPJ-DISP uses the resolution of the climatic input, which was available at 0.166° (approximately 18km). LPJ-DISP was run for 1000 years with the original climate and no restrictions on dispersal (spin up period). After the spin up period, seed dispersal is limited by distance and reproductive output. Climate change occurred over the next 200 years. For the temperate landscape , climate change was in the form of temperate increases only (Table 5-1). For the boreal landscape , an increase in both temperature and precipitation was required before trees could establish (Table 5-1). The change in temperature and precipitation were not based on paleo-climate reconstructions, but rather were chosen based on the climatic tolerances for the migrating trees. The ~10°C warming in the boreal climate was necessary to reach the minimum temperature requirements for Acer and Fagus (Table A-2). Since precipitation in the tundra climate is too low to support trees, an increase in temperature as well as rainfall was necessary for Picea to establish in the new climate. The goal of this study was to illustrate the migration of trees based on refugia populations and long distance dispersal. The rapid and extreme changes in temperature and precipitation were chosen to minimize the impact of climate change on migration rates (Delcourt & Delcourt 1987). The model continued to run at the new climate until the test species had migrated through all the grid cells.

5.3.3 Test species

Migration of Acer rubrum and Fagus grandifolia were simulated on the temperate landscape. These two tree species were selected since a phylogeographic study in North America identified

112 the existence of northern refugia populations for both species and provided reconstructed vegetation migration rates (McLachlan et al. , 2005). Picea glauca was simulated using the boreal landscape. P. glauca has also been subject to several phylogeographic studies (Anderson et al. , 2006; de Lafontaine et al. , 2010; Parducci et al. , 2012) and has proven refugia locations on the north side of the Pleistocene glaciers in both Europe and North America.

The three species were also selected because they represent different life history strategies (Table 5-2) which will impact how quickly they colonize the landscape. P. glauca is a pioneer species, being one of the first tree species to arrive on the tundra landscape. Although A. rubrum is a temperate tree species migrating into a landscape that is already occupied by a boreal forest (Davis, 1983), it is similar to an early successional species. For example, A. rubrum has an early maturation age, high fecundity and a short lifespan. Both P. glauca and A. rubrum have wind dispersed seeds and significant potential for long distance seed dispersal. F. grandifolia is a late successional, temperate tree with significantly delayed reproductive maturation (Table 5-2). F. grandifolia nuts are commonly dispersed by barochory (i.e. gravity) with secondary dispersal by small mammals or birds (Wagner et al. , 2010). Beech is also a masting species. This is a population-level phenomenon where trees have a coordinated, increase in reproduction every few years (Koenig & Knops, 2005). To simulate F. grandifolia , masting was added to LPJ-DISP. Every three years was a mast year, where reproductive output was greater than the two preceding years. This was simulated by changing the fraction of carbon allocated to reproduction and the number of seeds produced (Table 5-2).

The model was run for each of the test species twice, once without northern refugia and once with the presence of northerly refugia. A. rubrum had a few additional simulations, where the location and number of northerly refugia populations were tested (Figures 5-1b – 5-1d).

5.3.4 Vegetation movement metrics

Evidence of establishment was the first year a reproducing adult was present in a grid cell. The earlier presence of saplings was not considered, since competition or disturbance may prevent saplings from reaching reproductive maturity. The palynological record also makes this distinction, since trees only appear to be present on the landscape once they start producing pollen. A tree had moved all the way through a grid cell once mature trees occupied 80% (or more) of the patches within a grid cell.

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To determine how quickly trees colonized the landscape, several metrics were calculated. The average migration rate is the mean number of years to move through each grid cell, divided by distance (18 km). Unlike Chapter 3, the average migration rate includes all the grid cells (i.e. grid cells in the first row as well as subsequent rows). The average migration rate should remain fairly constant for each species, regardless of the presence of northerly refugia. This is because the average migration rate is not a landscape-level measurement, it is simply the time it takes to move through one grid cell.

The perceived migration rate is the amount of time it takes for a species to move the greatest distance (i.e. the minimum number of years to move all the way through a grid cell in the last row). The perceived migration rate is similar to pollen-reconstructed migration rates, as it only makes use of the start location/time and the end location/time. Anything that occurs on the landscape in between is not considered. Given that the boreal simulation already has a northerly refugium located in the last row, the perceived migration rate was only calculated for A. rubrum and F. grandifolia .

Colonization rates were also calculated for each simulation. This was done by regressing the total number of colonized grid cells (i.e. had > 80% of the patches within a grid cell occupied by that species) against the simulation year. A simple linear regression was tried first. If it failed to meet the assumptions (i.e. linearity, normal distribution of errors) then non-linear models were tried. Specifically, logistic and exponential models were tested since they seemed to best suit the shape of the curve (Figure 5-5). The most appropriate model was determined by examining the R2 value and the Akaike Information Criterion (AIC). The AIC measures the goodness of fit for statistical models, where a lower value indicates a better fit. I used the AICc as it adds an extra penalty for each additional parameter (models with more parameters will generally provide a better fit).

5.4 Results

5.4.1 Migration

Similar to previous simulations with A. rubrum (Chapter 3), the average migration rate was 132.7 m year -1 (39.6 – 163.6 m year -1) without refugia and 125.4 m year -1 (43.1 – 163.6 m year -1)

114 with refugia. As expected, the average migration rates were not significantly different in the simulations with or without refugia ( t-test: t = 1.1572, df = 137, p = 0.25). Expanding from the southern refugia only, it took A. rubrum 1062 years to arrive at the last row (Figure 5-2a). This was a perceived migration rate of 119 m year -1. With the presence of just one northerly refugium, A. rubrum reached the maximum distance in 618 years (Figure 5-2b), which makes the perceived migration rate 203.9 m year -1.

The average migration rate for F. grandifolia was very slow, just 21.3 m year -1 (7.8 – 35.9 m year -1) without refugia and 21.1 m year -1 (4.7 – 31.5 m year -1) with refugia. Average migration rates did not significantly differ between simulations ( t-test: t = 0.150, df = 136, p = 0.88). Without a northerly refugia population, F. grandifolia had a perceived migration rate of 17.5 m year -1 (it took 5129 years after warming to travel the maximum distance). When the northerly refugia population was present, the perceived migration rate was almost double; 34.9 m year -1 (travelled maximum distance in 2578 years) (Figure 5-3).

The average migration rate for P. glauca was 41.4 m year -1 (27.1 – 54.4 m year -1) without refugia, and 38.9 m year -1 (21.8 – 51.7 m year -1) with refugia. This time, the difference in migration rates was significantly different between simulations ( t-test: t = 2.355, df = 138, p = 0.02). Spreading from the southern population only, P. glauca travelled the maximum distance in 4898 years (Figure 5-4a).

5.4.2 Landscape colonization

All of the calculated colonization rates had very high R 2 values (Table 5-3) and could be described with one of two models. From a single source population in the south, the rate of landscape colonization was mostly linear (Table 5-3, Figure 5-5). When the refugia populations were located in the middle of the landscape, as in the Acer and Fagus simulations, the colonization rate was exponential (Table 5-3, Figures 5-4a, 5-4b, 5-4c). The Picea simulation was unique since the location of the refugium was in the north-west corner. The presence of a refugium population in that location didn’t change the shape of the curve, but did double the rate of landscape colonization (Figure 5-5d).

Adding additional refugia locations (Figure 5-5b) increased the colonization rate. The rate was maximized when the locations were separated. Compare the simulations with three separate

115 refugia and one large refugium (Figures 5-1c and 5-1d, Figure 5-5b); both had northerly refugia populations in three grid cells, however the simulation with the large refugium was more similar to the simulation with a single refugium in a single grid cell (Table 5-3, Figure 5-5). In addition, the entire landscape was colonized almost 200 years later when the three refugia were located side by side, compared to the simulation with three separate refugia.

5.5 Discussion

LPJ-DISP allows the flexibility to simulate landscape colonization, with and without northerly refugia populations. These small test cases used scaled-down landscapes reflective of actual refugia locations, which permits us to draw several conclusions about the importance of northern refugia and how this model can be applied to its full advantage in future applications.

Long distance dispersal and northerly refugia hypotheses

Explaining rapid vegetation migration rates seem to focus on either long distance dispersal (Clark et al. , 1998; Clark et al. , 2003; Nathan et al. , 2011) or northerly refugia (Magri et al. , 2006; Valiranta et al. , 2011; Parducci et al. , 2012), but not both. As it is likely that both mechanisms are important, LPJ-DISP offered the rare opportunity to combine theories. Simulating dispersal at the large scale LPJ-DISP uses, the model assumes that at least some LDD occurs for all trees (equation 3.5, c = 0.5). Choosing an exponential (c = 1.0) or Gaussian (c = 2.0) dispersal kernel results in no movement at all. However, migration rates can still be very slow even with long distance dispersal. Spruce moved at a moderate rate of ~40 m year -1 and beech was slower, moving an average of ~20 m year -1. This slow migration rate for beech corresponds well to the updated migration rates from McLachlan et al. (2005). For these slow moving species, both long distance dispersal and northerly refugia populations were necessary to explain their colonization of the landscape since the last glacial maximum.

The case study of A. rubrum offers an interesting example. Migration rates with long distance dispersal alone (106 – 113 m year -1) were consistent with reconstructed rates from McLachlan et

116 al. (2005). McLachlan et al. (2005) included the location of the northerly refugia populations when calculating past migration rates for A. rubrum , ~90 m year -1. In LPJ-DISP, including the northern refugium caused the perceived migration rate to double (~200 m year -1) which is remarkably similar to migration rates for Acer using pollen alone (Davis, 1981). Obviously, the location of refugia populations will impact the perceived migration rate. It will be interesting to see how this study compares when simulating the migration of A. rubrum across the actual North American landscape.

As the case with A. rubrum illustrates, there are some species for which northerly refugia might not have been necessary. Even without northerly refugia, A. rubrum had fairly fast migration rates. Species which share characteristics with A. rubrum , such as short generation times, small seeds, wind dispersal and significant long-distance dispersal, are likely to have faster migration rates (Nathan et al. , 2011; Chapter 4). Interestingly, the characteristics which preclude the necessity for northerly refugia are also the characteristics which tend to be associated with species which had northern refugia (Bhagwat & Willis, 2008). The species that really need northerly refugia (i.e. thermophilous, animal dispersed, long generation times) are the ones least likely to have them.

The significance of masting for beech and oak

How do we explain rapid postglacial plant expansions for species with minimal long distance dispersal and no known northerly refugia locations? Neither genetic nor fossil evidence supports northerly refugia for oak in Europe (Brewer et al. , 2002; Petit et al. , 2002; Bhagwat & Willis, 2008). Yet pollen-based estimates for oak indicate they migrated hundreds of meters per year (Huntley & Birks, 1983).

Even though there is evidence of beech having northerly refugia (Magri et al. , 2006), oak and beech trees have several similarities. Both are slow growing, deciduous trees, with delayed reproductive maturation. Oaks and beech trees produce large, gravity-dispersed seeds with secondary dispersal by birds and small mammals. And they are both masting species.

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Masting is a group phenomenon that occurs when trees synchronize the quantity of their reproduction to create certain years with exceptionally large seed crops (Koenig & Knops, 2005). Masting is thought to provide several advantages to trees, including predator satiation and higher seed survival, saving reproduction for when resources are plentiful and taking advantage of non- mast years to allocate carbon to growth or protection. I would propose that masting also has a positive effect on vegetation migration. Adding masting into LPJ-DISP was the only way to get beech to move. With delayed maturation, low fecundity and short dispersal distances, beech never produced enough seeds that could travel long distances.

In LPJ-DISP, fecundity was increased during mast years but the underlying seed dispersal kernel remained the same. Measuring dispersal distances during mast and non-mast years would identify if different dispersal kernels are needed for different years (Martínez & González- Taboada, 2009). Is there a greater probability of LDD during mast years? Interestingly, it may be the opposite effect. Moran & Clark (2012) found that there was greater long distance dispersal by rodents in forests with low acorn density. Changing the dispersal kernel in mast/non-mast years may also increase the simulated migration rates which could help explain rapid migration rates for these species.

No evidence for refugia or absence of refugia?

There are known difficulties when using pollen analysis alone to detect small, refugia populations (Birks & Willis, 2008). Some tree species don’t produce much pollen (especially animal-pollinated trees), whereas other species produce a lot of pollen (Lisitsyna et al. , 2011). Low levels of tree pollen are also notoriously difficult to interpret; are these small, nearby populations or is this long-distance pollen transported from populations far away? Pollen is often identified to genus only, which can be problematic when several species within the genus posses different tolerances or life histories (e.g. compare A. rubrum and A. saccharum in North America). Reconstructing tree migration using pollen requires a network of lakes, evenly distributed across the region. This is a limiting factor for northern, central and eastern Europe (Birks & Willis, 2008). Pollen production is also related to climate (Birks & Willis, 2008). Boreal species, such as Picea spp . and Betula spp . can tolerate extremely low temperatures but

118 will stop producing pollen and reproduce vegetatively during cold or dry periods (Bhagwat & Willis 2008). Thus, trees may be present on the landscape yet remain undetected in the pollen record. Finally, pollen production may be reduced under low CO 2 levels, common during the glacial periods (Jackson & Williams, 2004). It may be that the increase in CO 2 levels that preceded the last deglaciation (Shakun et al. , 2012) may have given migrating species an initial advantage.

Using phylogeographic methods to identify refugia also has limitations. The basic assumption is that populations that persisted in refugia during the glacial maxima are older and should have higher levels of genetic diversity than populations that arose during the post-glacial phase (Provan & Bennett, 2008). In addition, populations separated between different refugia will be genetically distinct, due to long-term isolation. Genetics can distinguish between refugia populations and postglacial expansion populations (Petit et al. , 2002; Magri et al. , 2006; de Lafontaine et al. , 2010) however the patterns are not always clear (Potter et al. , 2012). Issues such as contact zones between separate refugia, effective long-distance pollen dispersal and human transportation of seeds (Provan & Bennett, 2008; Hu et al. , 2009) can obscure the results.

Ideally, confirming the existence and location of refugia populations would occur through plant macrofossils (i.e. seeds, twigs, leaves, wood) which can be precisely identified to species and dated. However, plant macrofossils are rare and non-uniformly distributed, most often preserved in wetlands (Jackson et al. , 1997; Binney et al. , 2009). This makes it difficult to unequivocally determine that certain species did not have northerly refugia populations. An absence of evidence may not necessarily mean absence of refugia.

Future implications and conclusions

Migration rates under future climate change are not necessarily going to equal past migration rates, particularly due to land use change, potential migration barriers or lack of available habitat patches. However, finding an explanation for how rapid plant migrations were achieved in the past will improve predictions for future tree populations. As more fossil and genetic data confirm, many tree species achieved postglacial rates of spread through small populations acting as multiple point sources for spread. Trees may not be able to track future climate change

119 through long distance dispersal alone. If future climate is going to change as quickly as predicted, human-assisted migration will need to be considered (Bernazzani et al. , 2012). Even for pioneer species which can migrate relatively quickly, land-use change and landscape fragmentation may limit their success. Past vegetation migrations and simulation models assume an uninterrupted landscape. Clearly, this is no longer the case.

Simulation modeling should be part of the paleo-ecological toolbox and used to bring data from multiple sources together to test different theories or generate new ideas. The next step for LPJ- DISP is to use a real landscape (i.e. eastern North America or Europe) and simulate known refugia locations. Actual landscapes would present different challenges to migration, such as a heterogeneous surface with variable climates, or physical barriers like mountains and water. An alternative approach would be to simulate hypothesized but unconfirmed refugia locations and see if simulated rates of spread match fossil data. Results of this model could be used to direct exploratory research in an effort to find fossil evidence and confirm species presence.

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Table 5-1. Original climate data used and the degree of climate change applied (shown by ∆Temperature and ∆Precipitation) for the different simulations described in section 5.3.2 and Figure 5-1.

Temperate scenario (for Acer and Fagus )

Mean Annual ∆Temperature Total Annual ∆Precipitation Temperature Precipitation

Temperate 14.69°C ± 0.09°C 1.71°C ± 0.05°C 1163.43 mm ± 51.17 mm --

Boreal 5.05°C ± 0.45°C 9.54°C ± 0.37°C 786.36 mm ± 38.13 mm --

Boreal scenario (for Picea )

Mean Annual ∆Temperature Total Annual ∆Precipitation Temperature Precipitation

Boreal -4.34°C ± 0.07°C 7.60°C ± 0.21°C 462.95 mm ± 3.91 mm 5.78 mm ± 2.76 mm

Tundra -13.90°C ± 0.30°C 10.28°C ± 0.39°C 183.80 mm ± 8.92 99.22 mm ± 15.53 mm

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Table 5-2. Values used to parameterize the three test species (additional parameters are listed in the Appendix, Table A-2). αdisp is a distance parameter used in the dispersal kernel. There was no published value for αdisp for F. grandifolia . Since it has very short dispersal distances, the smallest value the model accepts was chosen (Chapter 4). reprfrac is the fraction of carbon

allocated to reproduction and kest_repr is a constant in the equation for seed production. F.

grandifolia is a masting species, so the higher values for reprfrac and kest_repr were used during mast years and the lower values were used during non-mast years. Data sources (Clark, 1998; McEuen & Curran, 2004; Prasad et al., 2007; Wagner et al. , 2010; Nathan et al. , 2011)

maturation age αdisp reprfrac kest_repr longevity Other

Acer rubrum 8 30.8 0.1 5000 80 temperate, broadleaf, deciduous

Fagus grandifolia 40 7.5 0.08 1000 300 temperate, 0.12 4000 broadleaf, deciduous

Picea glauca 25 15 0.1 1500 200 boreal, needleleaf, evergreen

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Table 5-3. Colonization rates (defined as the cumulative number of occupied grid cells regressed against the simulation year), with and without refugia. For the linear model, a = intercept and b = slope. For the exponential model, a = asymptote, b = scale and r = growth rate. Equations are plotted in the corresponding graphs in Figure 5-5. Best model Model parameters R2 AICc Acer No refugia Linear a = -113.4 0.9978 196.66 y = a + bx b = 0.0836

One refugium Exponential a = 99.71 0.9899 300.36 y = a + br*x b = -1030.89 r = -0.001712

One large refugium Exponential a = 81.51 0.9929 235.07 y = a + b r*x b = -1669.84 r = -0.002232

Two refugia Exponential a = 90.37 0.9832 309.42 y = a + b r*x b = -3129.58 r = -0.002578

Three refugia Exponential a = 87.91 0.9879 291.10 y = a + b r*x b = -4572.06 r = -0.002926

Fagus No refugia Exponential a = 138.38 0.9967 227.69 y = a + b r*x b = -166.17 r = -0.000107

One refugium Exponential a = 90.60 0.9954 245.43 y = a + b r*x b = -141.35 r = -0.000238

Picea No refugia Linear a = -17.73 0.9977 204.19 y = a + bx b = 0.01310

One refugium Linear a = -34.22 0.9942 278.98 y = a + bx b = 0.02233

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(a) One refugium (b) Two refugia (e) Boreal refugium

Figure 5-1. Theoretical locations of refugia populations. Light green grid cells are the southern refugia, dark green grid cells are the northerly refugia, and blue is the glacier. Configuration (a) was used for Acer rubrum and Fagus grandifolia simulations, and configuration (e) was used for Picea glauca . Additional simulations testing the number and location of refugia (b – d) were done using Acer rubrum .

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Figure 5-3. Simulation of Fagus grandifolia migration across a landscape, (a) from the southern refugia only and (b) with the addition of a northerly refugia population. The colour represents the year after climate warming (in 200 year steps) when Fagus moved all the way through the grid cell.

Figure 5-4. Simulation of Picea glauca migration across a landscape, (a) from the southern refugia only and (b) from both a southern and northern refugia. The colour represents the year after warming (in 200 year steps) when Picea moved all the way through the grid cell. 126 126

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Figure 5-5. Landscape colonization rate, calculated as the cumulative number of colonized grid cells (i.e. > 80% of the patches within a grid cell occupied by that species) regressed against the simulation year. The northerly refugia location was located in the middle of the landscape for (a) Acer rubrum and (c) Fagus grandifolia , and in the top corner for (d) Picea glauca. (b) shows the effect of changing the number and location of refugia for Acer rubrum . See Figure 5-1 for a diagram of the landscape and refugia locations.

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Stewart, J.R., Lister, A.M., Barnes, I., & Dalen, L. (2010) Refugia revisited: individualistic responses of species in space and time. Proceedings of the Royal Society B-Biological Sciences , 277 , 661-671. Valiranta, M., Kaakinen, A., Kuhry, P., Kultti, S., Salonen, J.S., & Seppa, H. (2011) Scattered late-glacial and early Holocene tree populations as dispersal nuclei for forest development in north-eastern European Russia. Journal of Biogeography , 38 , 922-932. Wagner, S., Collet, C., Madsen, P., Nakashizuka, T., Nyland, R.D., & Sagheb-Talebi, K. (2010) Beech regeneration research: From ecological to silvicultural aspects. Forest Ecology and Management , 259 , 2172-2182. Wetterich, S., Grosse, G., Schirrmeister, L., Andreev, A.A., Bobrov, A.A., Kienast, F., Bigelow, N.H., & Edwards, M.E. (2012) Late Quaternary environmental and landscape dynamics revealed by a pingo sequence on the northern Seward Peninsula, Alaska. Quaternary Science Reviews , 39 , 26-44. Willner, W., Di Pietro, R., & Bergmeier, E. (2009) Phytogeographical evidence for post-glacial dispersal limitation of European beech forest species. Ecography , 32, 1011-1018. Yansa, C.H. (2006) The timing and nature of Late Quaternary vegetation changes in the northern Great Plains, USA and Canada: a re-assessment of the spruce phase. Quaternary Science Reviews , 25 , 263-281. Zazula, G.D., Telka, A.M., Harington, C.R., Schweger, C.E., & Mathewes, R.W. (2006) New spruce ( Picea spp.) macrofossils from Yukon Territory: Implications for Late Pleistocene refugia in Eastern Beringia. Arctic , 59 , 391-400.

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Chapter 6

6 Conclusion 6.1 Summary of results

The overall objective of this thesis was to improve representations of vegetation and ecological processes in vegetation-climate models. I addressed two major concerns for dynamic global vegetation models; developing more specific plant functional types to better represent tropical vegetation and integrating seed dispersal to better predict vegetation migration in response to climate change.

In Chapter 2, I illustrated that the globally defined plant functional types (PFTs) are not appropriate for representing tropical and arid ecosystems in Central America. LPJ-GUESS has been extensively validated with boreal and temperate ecosystems (e.g. Badeck et al. , 2001; Hickler et al. , 2004; Gritti et al. , 2006; Wolf et al. , 2008) however there has been a real lack of applications which use hybrid models on tropical regions. Developing PFTs which are more reflective of tropical ecosystems helped to improve the results, to a limited degree. Ecological processes, unique to tropical ecosystems likely need to be incorporated. Including certain processes, such as CAM photosynthesis, may allow the model to simulate a succulent CAM PFT which will help to represent tropical dry ecosystems and distinguish between them (i.e. xeric shrubland, savanna and dry tropical forest).

Assuming full migration results in unrealistically fast migration rates, as shown in Chapter 3. Under this paradigm, the only limiting factor is the rate of climate change. Chapter 3 describes how I incorporated seed dispersal into LPJ-GUESS, creating the new version LPJ-DISP. The first thing to do was to represent the landscape as a true, two-dimensional surface where grid cells were aware of what was happening in the neighbouring grid cells. Seed dispersal between grid cells was determined by using published seed dispersal kernels, which describe the probability of seeds travelling a specific distance. Dispersal between patches within a grid cell was simulated using the logistic growth curve, appropriate for determining the probability of having a seed source nearby since patches are not assigned real locations within the cell. I

133 simulated vegetation migration in LPJ-DISP using three temperate tree species with different life history strategies, which resulted in three different migration rates. Acer rubrum had the fastest migration rates, followed by Tsuga canadensis , and then Pinus rigida . From the sensitivity analysis in Chapter 4, most of this variation can be explained by maturation age. The age when trees start reproducing was the single most important parameter for determining migration rates. The growth rate ( r_log ) used in the logistic growth curve was also important for migration rates, but since it was kept constant for all three species it would have no impact on the difference between these simulated migration rates.

The sensitivity analysis in Chapter 4 also identified the distance parameter (αdisp ) in the dispersal kernel as being important in determining if there was any seed dispersal between grid cells. This is significant, since the dispersal kernel is a measurable trait that differs among species.

Parameters such as maturation age and αdisp can be measured and known exactly, which provides confidence in the model results. The fact that parameter to describe movement between patches within a grid cell ( r_log ) was also significant means future research should focus on quantifying this parameter more exactly to reduce uncertainty.

In Chapter 5, I illustrated how LPJ-DISP could be used to address hypotheses that are difficult to answer without simulation models, such as explaining rapid migration rates for trees following the last glacial maximum in North America and Europe. If northern refugia populations existed, their presence would help to explain the rapid post-glacial spread rates for trees. However, the only way to confirm their existence is with rare macrofossils, which can be dated exactly. Using LPJ-DISP, I simulated a hypothetical landscape with and without northern refugia populations and re-created landscape colonization for three tree species ( Acer rubrum , Fagus grandifolia and Picea glauca ). The presence of even just one northerly refugia location significantly increased the rate landscape colonization. Phylogenetic studies confirm Picea glauca survived through the last glacial period in northerly refugia on the northern side of the glacier in North America and Europe (Anderson et al. , 2006; Parducci et al. , 2012). Simulating landscape colonization for P. glauca with a northerly refugia population doubled the colonization rate. In light of these results, pollen-reconstructed migration rates for P. glauca of 300 m year -1 (Yansa, 2006), may be overestimates.

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In general, the simulated migration rates in all the studies were considerably slower than pollen- reconstructed rates. The simulated rates were much more conservative, closer to what modern day seed dispersal distances would suggest. With long distance dispersal and fast generation times, LPJ-DISP was able to produce migration rates close to 170 m year -1 which is relatively fast for a tree. However, this is still significantly slower than historical estimated migration rates of 500 m year -1 or more (Davis 1983; Huntley & Birks, 1983).

6.2 Future work

The next step would be to use LPJ-DISP to simulate an actual case study, such as the post-glacial spread of beech in Europe (Magri et al. , 2006) or the response of vegetation in North America to future climate change scenarios (IPCC, 2007). Currently, computer memory limits the number of grid cells to ~100 for one simulation. Representing larger regions, such as Europe or North America would require thousands of grid cells. LPJ-DISP currently runs on a single processor. I plan to parallelize the code to run on multiple processors, dividing up the grid cells and allowing information to be shared between them. Using a UNIX cluster, such as SciNet at the University of Toronto, I will be able to simulate a much larger area much faster.

In addition to parallelizing the existing code, there are also several processes that could be modified in the model itself, which would improve representation of vegetation reproduction and migration.

6.2.1 Masting

The importance of masting has already been introduced in Chapter 5. Although I initially intended to add masting at a later date, I had to incorporate a simplified version of masting to simulate seed dispersal and vegetation migration for Fagus grandifolia (Chapter 5). I have begun a small sensitivity analysis for masting, where I alter the frequency of mast years and the allocation of carbon during mast and non-mast years ( reprfrac ). The frequency of mast years makes a large difference in migration rates, although it does not appear to be a linear relationship. Masting every 2 or 4 years have the slowest rates, whereas masting every 3 or 5 years produce faster migration rates. I am not sure why. I am hoping that additional tests which alter mast frequency beyond 5 years may indicate a larger pattern. Higher carbon allocation to

135 reproduction during mast years caused a slight increase in migration rates. Strangely, there was a much stronger increase in migration rates when I increased carbon allocation during non-mast years. To understand these patterns, I intend to examine when seedlings are most likely to establish (during mast or non-mast years) and why. It may be related to the parameter, k est_repr . I have used this parameter to represent fecundity, set to 1000 during non-mast years and 4000 during mast years. Perhaps a lower value for k est_repr results in higher seedling establishment success.

My initial representation of masting is fairly simple, and there are several improvements that should be made. I represent the frequency of mast years as a constant (e.g. every 3 years). In nature, masting is related to larger, environmental cues (Kelly & Sork, 2002; Koenig & Knops, 2005) which results in mast frequency being more variable. One strength of LPJ-DISP is that it already uses climatic data as input. It would be possible to simulate mast frequency based upon temperature and/or precipitation cues. This would also allow us to simulate the potential effect of climate change on mast frequency (Koenig & Knops, 2005). As the temperature warms or precipitation changes, it will alter the frequency of mast years. Increasing the temperature will lead to more frequent mast events (Schauber et al. , 2002) which ultimately comes with a tradeoff of reduced growth for plants. Decreasing precipitation, which is predicted for dry regions such as the Mediterranean, will reduce the investment in large seed crops causing fewer mast years (Perez-Ramos et al. , 2010). Either situation will ultimately change the composition of the plant community and impact those ecosystems where masting vegetation plays an important role.

I would also like to change the underlying seed dispersal kernel between mast and non-mast years. Masting changes the reproductive effort between years which also has consequences for disperser behaviour (Moran & Clark, 2012). Two recent studies on beech (Martínez & González-Taboada, 2009) and oak (Moran & Clark, 2012) both found that mean seed dispersal distances were further when seed density was lower. This would cause more long distance dispersal events during non-mast years. Thus, it may be that vegetation migration rates for masting trees are primarily determined during their non-mast years. This would be really interesting considering one explanation of masting is predator satiation. During non-mast years, most seeds would be eaten even though these are the seeds which may determine migration and the success of the population at the landscape scale.

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6.2.2 Reproductive effort

As identified in Chapter 4, reproductive effort ( reprfrac ) has a negative impact on migration rates due to the tradeoff between higher reproduction and reduced vegetative growth, which can lead to reduced competitive abilities. The variable reprfrac was only varied between 0.08 – 0.12, a 20% range around the default value but still considerably less than the natural variation that exists in trees (Thomas, 2011). Most of the variation in reproductive effort occurs as tree age and grow, with trees allocating more and more resources to reproduction as they approach their maximum lifespan. Currently, reproductive effort in LPJ-DISP is represented as a static value (reprfrac ). An interesting avenue for future research would be to replace this parameter with a function, where reproductive effort changes based on the size and/or age of the tree. This would allow the model to test larger ranges of carbon allocated to reproduction and to simulate monocarpic trees, which it is currently unable to do.

6.2.3 Dispersal kernels

All of the test species (with the exception of Fagus grandifolia ) have wind dispersed seeds. Similar to plant functional types, seed dispersal kernels can be grouped into functional types based on their dispersal vector (Vittoz & Engler, 2007). Different dispersal vectors may have different dispersal kernels, fundamentally different in shape than Clark’s (1998) kernel used in the model (equation 3.5). It would be relatively simple to include different kernels into LPJ- DISP and let the user select the one that best fits their data.

I also wanted to discuss the choice of seed dispersal kernels, instead of realized dispersal kernels (i.e. describes the probability of finding a seedling at a specific distance, instead of a seed). I chose to represent the dispersal of seeds in LPJ-DISP, as it is closest to what LPJ-DISP actually simulates. The argument could be made for representing seedlings instead. The main issue is that LPJ-DISP doesn’t include many of the processes which are important for determining the success of seeds becoming seedlings (i.e. dormancy, cold tolerance, seed predation, disease). Using a dispersal kernel for seedlings only considers the successful seedlings, which is not exactly congruent with LPJ-DISP either. Not every seed in LPJ-DISP is successful. Seedlings can only establish in available spaces, when the PAR reaches a minimum threshold, and they out-compete other vegetation. Perhaps the solution would be to add some level of stochasticity to seed success, which might broadly represent some of the obstacles seeds are exposed to.

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6.2.4 Simulating the trailing population

Predicting species extinctions and range shifts in response to climate change depends not only on simulating the leading edge of the migrating population, but also on simulating the fate of the trailing population (Thuiller et al. , 2008). Species distribution models predict an immediate range shift for vegetation and assume populations remaining outside the new climatic envelope will go extinct (Thomas et al. , 2004; Fitzpatrick et al. , 2008). Reduced fitness, inbreeding depression and environmental stress can all cause small and isolated populations at the retreating edge to eventually go extinct (Thuiller et al. , 2008). However, how quickly that will happen is not known. Long life spans, reproductive output, phenotypic plasticity, and the ability to adapt will all influence population persistence (Thuiller et al. , 2008; Hampe & Jump, 2011). Interestingly, in the Pinus and Tsuga simulations in Chapter 3, the cold-tolerant PFT survived until the year 2515, more than 1300 years after the increase in temperature. There is also the possibility that populations won’t go extinct. Relic populations have been found in protected and isolated locations with suitable climate conditions, even though the surrounding area is considered climatically inhospitable (Hampe & Jump, 2011). These population remnants are important for genetic diversity, local population dynamics and understanding historical range shifts (Hampe & Jump, 2011). It is important to understand what influences population persistence, and how this will affect the impact of future climate change.

It would be possible to use LPJ-DISP to address this issue of trailing populations and persistence. Each PFT has an optimal temperature range for photosynthesis, and a maximum/minimum temperature for establishment. Plants which are already established will continue to grow and reproduce, but at a lower fitness level. LPJ-DISP offers a process based modeling solution, as opposed to prescribing changes in demography to simulate the same effect in SDMs (Thuiller et al. , 2008). In this thesis, the goal was to test dispersal limitations only. To ensure the leading edge of the population had a constant seed supply for dispersal, the temperature in the warm region was modified only slightly (not enough to cause environmental stress for the warm PFTs). However, it would be relatively easy to apply the same degree of warming across all the grid cells in order to create a retreating edge that is under extinction pressure.

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6.2.5 Tropical plants and migration

Ultimately, it would be great to use LPJ-DISP to simulate tropical vegetation and their response to climate change. As Chapter 2 illustrated, there are still ecological processes that need to be included first to accurately capture the current vegetation. After this occurs, LPJ-DISP could be adapted to represent seed dispersal in the tropics. Animals would represent the dominant seed disperser type (Jordano, 2000), which could translate into more long distance dispersal depending on the animal (i.e. bird versus large or small mammal). Future climate change also predicts an expansion of dry habitats (Neelin et al. , 2006). The ability of dry-adapted plants to expand into new habitats may be limited by their dispersal ability. Yet, LPJ-GUESS had the most difficulty in simulating the dry ecosystems, which serves to reinforce the importance of correctly simulating the current ecosystem processes before addressing future climate change.

6.2.6 Arid PFTs

As mentioned in Chapter 2, it would be great to add a PFT that used the CAM photosynthetic pathway. At the global scale, CAM photosynthesis likely represents a very small proportion of total CO 2 assimilated, which is likely why it hasn’t been considered before. At the regional scale, especially in semi-arid to arid regions, CAM photosynthesis could represent a much more significant component of carbon sequestration. In Mexico, CAM plants reached productivity levels (> 40 Mg C/ha/year) matching those of high-biomass C 3 crops (Nobel et al. , 1992; Davis et al. 2011). Furthermore, double CO 2 experiments with Agave deserti show that CAM productivity can increase by over 88 percent resulting from a corresponding increase in water- use efficiency by 110 percent relative to control CO 2 treatments (Graham & Nobel, 1996).

Considering future climatic change and the anticipated rise in CO 2, CAM plants may have an important role to play in ecosystem function and carbon cycling.

6.3 Significance of Ph.D. research

My Ph.D. dissertation contributes to two areas of research. First, the results from Chapter 2 should help improve vegetation-climate modelling in the neotropics. This was the first application of a regional dynamic vegetation-climate model for Central America. Unfortunately, the model was unable to fully capture the distribution and ecosystem functioning of several

139 important regions. I provide a detailed discussion of the processes that need to be improved including fire, soil, alternative photosynthetic pathways (i.e. CAM) and other adaptations for arid vegetation. Future work should focus on improving the representation of these processes in models, aided by research which collects the appropriate field data. Accurate regional models can be an important tool for determining the appropriate management strategies, maximizing ecosystem services and mitigating future climate change effects. My work identifies the necessary steps towards achieving this goal.

Secondly, my Ph.D. dissertation adds to the ongoing discussion about the ability of plants to migrate fast enough to track future, rapid climate change (Clark et al ., 2003; Pearson, 2006; Hampe, 2011; Nathan et al. , 2011). Answering questions about range expansions and climate change requires synthesizing work from multiple disciplines across a variety of temporal and spatial scales (Hampe, 2011). This is not always easy to do, but vegetation-climate models offer an opportunity to tackle this.

Previously, incorporating seed dispersal limitations into vegetation-climate models occurred exclusively in species distribution models (SDMs). Various cellular automata models or demographic models have been linked to habitat suitability from SDMs, to generate range predictions that consider dispersal limitations (e.g. Iverson et al. , 2004; Engler & Guisan, 2009; van Loon et al. , 2011; Conlisk et al ., 2012). It is interesting to see the evolution of distribution modelling. To improve the prediction of migration potential of vegetation under future climate change scenarios, SDMs have started to include different ecological processes such as seed dispersal, reproduction and competition. One of the benefits of SDMs was their simplicity and specificity (i.e. predictions at the species level). Adding in these extra processes has increased the amount of information required for each species, which can be difficult to find. One model, BioMOVE (Midgley et al ., 2010), addresses this information requirement by adopting the PFT approach. BioMOVE simulates community dynamics within an SDM using functional traits to predict regeneration and population demographics, instead of species-specific population demography.

Before this study, there were no seed dispersal limitations in dynamic vegetation-climate models. My Ph.D. research illustrates how I was able to include seed dispersal into a dynamic vegetation- climate model, and provide more realistic estimates for vegetation migration in response to

140 climate change. One of the challenges when including dispersal limitations in a DGVM is the issue of scale. LPJ-DISP has a grid cell size of 18 km. This may be small compared to global scale models, but consider that most dispersal models use grid cells that are measured in meters (e.g. 20 m 2 – Caplat et al ., 2008; 5 m 2 to 25 m 2 – Engler & Guisan, 2009; 1.5 m 2 – Merow et al ., 2011). The difference in scale also makes it difficult to draw from previous seed dispersal modelling studies. However, simulating seed dispersal at this scale in a DGVM has advantages. First, we can apply past or future climate change scenario and simulate the dynamic response of vegetation and how dispersal limitations influence their ability to migrate into new habitat. We can also simulate limitations due to climate or competition with existing vegetation. Second, SDMs assume species outside of the ‘climate envelope’ go extinct. As demonstrated in Chapter 3, LPJ-DISP does not make that assumption and could be used to simulate the trailing edge of the population, an area which has been overlooked in range shift research (Thuiller et al ., 2008). Third, we can test theories about rapid historical vegetation migration rates based on pollen data. As illustrated in Chapter 5, LPJ-DISP offer an explanation for how pollen data could have been misinterpreted and corroborates the mounting phylogeographic and macrofossil evidence (McLachlan et al. , 2005; Anderson et al. , 2006; Zazula et al. , 2006; Brus, 2010; Parducci et al. , 2012) for the presence of northern refugia populations and their impact on historical migration rates.

So, is it possible to make any conclusions about the response of vegetation to future climate change? Will plants be able to keep up with the projected rates of rapid climate change? Although LPJ-DISP did produce fairly rapid migration rates (up to ~170 m year -1), actual migration under future climate change may be slower. In my simulations, climate was not a limiting factor. The rate of climate change was fairly rapid and essentially all of the grid cells had climate which was suitable for the temperate tree species. In Chapter 3, migration rates through the first row were much slower than subsequent rows due to climate. Depending on how quickly climate change occurs, climate change itself may slow down vegetation migration. In addition, real landscapes have potential barriers to migration (e.g. lakes, mountains, landscape fragmentation, lack of suitable habitat patches), which will force plants to migrate around those barriers. This would also cause vegetation migration rates to be slower than simulated. Basically, migration rates simulated in LPJ-DISP probably represent the fastest rates that trees

141 may be able to achieve. In conclusion, plants are not likely to migrate fast enough to track future climate change without some human assistance.

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6.4 References Anderson, L.L., Hu, F.S., Nelson, D.M., Petit, R.J., & Paige, K.N. (2006) Ice-age endurance: DNA evidence of a white spruce refugium in Alaska. Proceedings of the National Academy of Sciences of the United States of America, 103 , 12447-12450. Badeck, F.W., Lischke, H., Bugmann, H., Hickler, T., Honninger, K., Lasch, P., Lexer, M.J., Mouillot, F., Schaber, J., & Smith, B. (2001) Tree species composition in European pristine forests: Comparison of stand data to model predictions. Climatic Change , 51 , 307-347. Brus, R. (2010) Growing evidence for the existence of glacial refugia of European beech ( Fagus sylvatica L.) in the south-eastern Alps and north-western Dinaric Alps. Periodicum Biologorum , 112 , 239-246. Clark, J.S., Lewis, M., McLachlan, J.S., & HilleRisLambers, J. (2003) Estimating population spread: What can we forecast and how well? Ecology , 84 , 1979-1988. Conlisk, E., Lawson, D., Syphard, A.D., Franklin, J., Flint, L., Flint, A., & Regan, H.M. (2012) The roles of dispersal, fecundity, and predation in the population persistence of an oak (Quercus engelmannii ) under global change. Plos One , 7. Davis, M.B. (1983) Quaternary history of deciduous forests of eastern North-America and Europe. Annals of the Missouri Botanical Garden , 70 , 550-563. Davis, S.C., Dohleman, F.G., Long, S.P. (2011) The global potential for Agave as a biofuel feedstock. Global Change Biology Bioenergy, 3, 68-78. Engler, R. & Guisan, A. (2009) MIGCLIM: Predicting plant distribution and dispersal in a changing climate. Diversity and Distributions , 15 , 590-601. Fitzpatrick, M.C., Gove, A.D., Sanders, N.J., & Dunn, R.R. (2008) Climate change, plant migration, and range collapse in a global biodiversity hotspot: the Banksia (Proteaceae) of Western Australia. Global Change Biology , 14 , 1337-1352.

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Appendix 1. Parameter values for plant functional types

Table A-1. Plant functional type (PFT) parameterization implemented in LPJ-GUESS (Smith et al. 2001; Sitch et al. 2003) including the new parameters introduced in LPJ-DISP (this thesis). The abbreviations refer to the following PFTs: TeBE–Temperate broad-leaf evergreen, TeBS– Temperate broad-leaf summergreen, TrBE–Tropical broad-leaf evergreen, TrBR–Tropical broadleaf raingreen, TrNE–Tropical needle-leaf evergreen, TeH–Temperate herbaceous, TrH–Tropical herbaceous

The parameters are described below: parameter name, description (units when appropriate) age_repr Maturation age for trees (years) alphar Shape parameter for recruitment-juvenile growth rate relationship crownarea_max Maximum tree crown area (m 2) cton_leaf Leaf C:N mass ratio cton_root Fine root C:N mass ratio cton_sap Sapwood C:N mass ratio disp_alpha Distance parameter used in seed dispersal kernel (m) disp_c Shape parameter used in seed dispersal kernel emax Maximum evapotranspiration rate (mm/day) est_max Max sapling establishment rate (indiv/m 2/year) fireresist Fire resistance (0-1) gdd5min_est Min GDD on 5 C° base for establishment gmin Canopy conductance not assoc with photosynthesis (mm/s) greff_min Threshold for growth suppression mortality (kgC/m 2 leaf/year) intc Interception coefficient k_allom1 Constant in allometry equations (equation 4 in Sitch et al. (2003)) k_allom2 Constant in allometry equations (equation 3 in Sitch et al. (2003)) k_allom3 Constant in allometry equations (equation 3 in Sitch et al. (2003)) k_chilla Constant in equation for budburst chilling time requirement k_chillb Coefficient in equation for budburst chilling time requirement k_chillk Exponent in equation for budburst chilling time requirement k_latosa Tree leaf to sapwood area ratio k_rp Constant in allometry equations (equation 4 in Sitch et al. (2003)) kest_bg Constant in equation for background tree establishment rate (turned off in dispersal mode) kest_repr Constant in equation for tree establishment rate lambda_max Non-water-stressed ratio of intercellular to ambient CO 2 pp leaflong Leaf longevity (years) litterme Litter moisture flammability threshold (fraction of AWC) log_r Growth rate in logistic growth curve to describe dispersal between patches within a grid cell

146 longevity Expected longevity under lifetime non-stressed conditions (years) ltor_max Non-water-stressed leaf:fine root mass ratio parff_min Min forest floor PAR for grass growth/tree establishment (J/m 2/day) pathway Biochemical pathway (C3 or C4) phengdd5ramp GDD on 5 C° base to attain full leaf cover pstemp_high Approx higher range of temp optimum for photosynthesis (C°) pstemp_low Approx lower range of temp optimum for photosynthesis (C°) pstemp_max Maximum temperature limit for photosynthesis (C°) pstemp_min Approximate low temp limit for photosynthesis (C°) reprfrac Fraction of NPP allocated to reproduction respcoeff Respiration coefficient (0-1) rootdist(lower) Fraction of roots in lower soil layer rootdist(upper) Fraction of roots in upper soil layer tcmax_est Max 20-year coldest month mean temp for establishment (C°) tcmin_est Min 20-year coldest month mean temp for establishment (C°) tcmin_surv Min 20-year coldest month mean temp for survival (C°) turnover_leaf Leaf turnover (fraction/year) turnover_root Fine root turnover (fraction/year) turnover_sap Sapwood turnover (fraction/year) twmin_est Min warmest month mean temp for establishment (C°) wooddens Sapwood and heartwood density (kgC/m 3) wscal_min Water stress threshold for leaf abscission (for raingreen PFTs only)

Table A-1. TeBE TeBS TeNE TrBE TrBR TrNE DeSh TeHerb TrHerb lifeform Tree Tree Tree Tree Tree Tree Tree Grass Grass phenology Evergreen Summergreen Evergreen Evergreen Raingreen Evergreen Evergreen Any Any shade? tolerant tolerant intolerant tolerant tolerant intolerant intolerant alphar 3 3 10 3 3 10 10 crownarea_max 27.3 27.3 27.3 27.3 27.3 27.3 2 cton_leaf 29 29 29 29 29 29 29 29 29 cton_root 29 29 29 29 29 29 29 29 29 cton_sap 330 330 330 330 330 330 330 emax 5 5 5 5 5 5 5 5 5 est_max 0.125 0.125 0.25 0.125 0.125 0.25 0.5 fireresist 0.5 0.12 0.12 0.12 0.5 0.5 0.5 1 1 gdd5min_est 1200 1200 900 0 0 900 0 0 gmin 0.5 0.5 0.3 0.5 0.5 0.3 0.2 0.5 0.5 greff_min 0.1 0.1 0.12 0.1 0.1 0.12 0.03 intc 0.02 0.02 0.06 0.02 0.02 0.06 0.02 0.01 0.01 k_allom1 200 200 150 200 200 150 8 k_allom2 40 40 40 40 40 40 2 k_allom3 0.67 0.67 0.67 0.67 0.67 0.67 0.67 k_chilla 0 0 0 0 0 0 k_chillb 100 100 100 100 100 100 k_chillk 0.05 0.05 0.05 0.05 0.05 0.05 k_latosa 4000 4000 3000 4000 4000 3000 500 k_rp 1.6 1.6 1.6 1.6 1.6 1.6 1.6 kest_bg 1 1 1 1 1 1 1 kest_repr 200 200 200 200 200 200 200 lambda_max 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 leaflong 1 0.5 2 2 0.5 2 2 1 1 litterme 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.2 longevity 200 200 300 320 250 300 200 ltor_max 1 1 1 1 1 1 1 0.5 0.5 parff_min 1250000 1250000 2500000 1250000 1250000 2500000 2500000 2500000 2500000 146 146

Table A-1. continued. TeBE TeBS TeNE TrBE TrBR TrNE DeSh TeHerb TrHerb pathway c3 c3 c3 c3 c3 c3 c4 c4 c3 phengdd5ramp 200 0 50 50 pstemp_high 30 25 30 30 30 30 30 45 30 pstemp_low 20 20 20 25 25 20 20 20 10 pstemp_max 42 38 42 55 55 42 55 55 45 pstemp_min -4 -4 -4 2 2 -4 -4 6 -4 reprfrac 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 respcoeff 1.2 1.2 1.2 0.2 0.2 0.4 0.2 1 1 rootdist(lower) 0.3 0.2 0.3 0.15 0.3 0.3 0.2 0.1 0.1 rootdist(uppper) 0.7 0.8 0.7 0.85 0.7 0.7 0.8 0.9 0.9 tcmax_est 18.8 15.5 22 1000 1000 1000 1000 1000 15.5 tcmin_est 3 -17 -2 15.5 15.5 5 2 15.5 -1000 tcmin_surv 3 -17 -2 15.5 15.5 5 2 15.5 -1000 turnover_leaf 1 1 0.5 0.5 1 0.5 0.5 1 1 turnover_root 1 1 0.5 0.5 1 0.5 0.5 0.5 0.5 turnover_sap 0.05 0.05 0.1 0.05 0.05 0.1 0.015 twmin_est -1000 -1000 -1000 -1000 -1000 -1000 -1000 -1000 -1000 wooddens 200 200 200 200 200 200 250 wscal_min 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35

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Table A-2. Parameter values for the plant functional types (PFT) used in the simulations for Chapter 3, 4 and 5. Simulations in Chapter 3 included the CoolIntol, CoolInterm, CoolTol, WarmIntol, WarmInterm, Grass, and one of either Acer, Pinus or Tsuga . The parameters outlined in the black box relate to seed dispersal. The two numbers for kest_repr and reprfrac for Fagus represent masting (low and high years). Abbreviations are described in Table A-1. CoolIntol CoolInterm CoolTol WarmIntol WarmInterm Grass Acer Pinus Tsuga Picea Fagus lifeform Tree Tree Tree Tree Tree Grass Tree Tree Tree Tree Tree phenology a B,S B,S B,S B,S B,S Any B,S N, E N, E N, E B,S b age_repr 10 10 10 10 10 0 8 12 15 25 40 disp_alpha b 40 40 40 40 40 30.8 15.1 22.8 15 7.5 disp_c 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 kest_repr c 2000 2000 2000 3000 3000 5000 1097 2317 1500 1000/4000 log_r 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 reprfrac 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.08/0.12 alphar 30 20 10 30 20 10 25 10 10 10 crownarea_max 27.3 27.3 27.3 27.3 27.3 27.3 27.3 27.3 27.3 27.3 cton_leaf 29 29 29 29 29 29 29 29 29 29 29 cton_root 29 29 29 29 29 29 29 29 29 29 29 cton_sap 330 330 330 330 330 330 330 330 330 330 emax 5 5 5 5 5 5 5 5 5 5 5 est_max 0.4 0.3 0.2 0.4 0.3 0.2 0.35 0.2 0.2 0.2 gdd5min_est 600 600 600 1200 1200 0 1200 900 900 600 1200 gmin 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.3 0.3 0.3 0.5 greff_min 0.17 0.153 0.136 0.17 0.153 0.136 0.161 0.136 0.136 0.136 intc 0.02 0.02 0.02 0.02 0.02 0.01 0.02 0.06 0.06 0.06 0.02 k_allom1 200 200 200 200 200 200 150 150 150 200 k_allom2 40 40 40 40 40 40 40 40 40 40 k_allom3 0.67 0.67 0.67 0.67 0.67 0.67 0.67 0.67 0.67 0.67 k_chilla 0 0 0 0 0 0 0 0 0 0 k_chillb 100 100 100 100 100 100 100 100 100 100 k_chillk 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 148

Table A-2. continued

CoolIntol CoolInterm CoolTol WarmIntol WarmInterm Grass Acer Pinus Tsuga Picea Fagus k_latosa 4000 4000 4000 4000 4000 4000 3000 3000 3000 4000 k_rp 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 kest_bg 1 1 1 1 1 1 1 1 1 1 kest_pres 0 0 0 0 0 0 0 0 0 0 lambda_max 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 leaflong 0.5 0.5 0.5 0.5 0.5 1 0.5 2 2 2 0.5 litterme 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 longevity b 200 300 350 200 300 80 100 500 200 300 ltor_max 1 1 1 1 1 1 1 1 1 1 parff_min 604800 432000 259200 604800 432000 259200 518400 259200 259200 259200 pathway c3 c3 c3 c3 c3 c3 c3 c3 c3 c3 phengdd5ramp 150 150 150 200 200 200 0 0 0 200 pstemp_high 25 25 25 25 25 30 25 25 25 25 25 pstemp_low 10 10 10 15 15 10 15 15 15 10 15 pstemp_max 38 38 38 38 38 45 38 42 42 38 38 pstemp_min -4 -4 -4 -4 -4 -4 -4 -4 -4 -4 -4 respcoeff 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 rootdist(lower) 0.9 0.9 0.9 0.8 0.8 0.8 0.7 0.7 0.9 0.8 rootdist(uppper) 0.1 0.1 0.1 0.2 0.2 0.2 0.3 0.3 0.1 0.2 tcmax_est -2 -2 -2 15.5 15.5 15.5 15.5 22 22 -2 15.5 tcmin_est -32.5 -32.5 -32.5 -8 -8 -1000 -8 -2 -2 -32.5 -8 tcmin_surv -32.5 -32.5 -32.5 -8 -8 -1000 -8 -2 -2 -32.5 -8 turnover_leaf 1 1 1 1 1 1 0.33 0.33 0.33 1 turnover_root 1 1 1 1 1 0.5 1 0.5 0.5 0.5 1 turnover_sap 0.2 0.15 0.12 0.2 0.15 0.12 0.17 0.12 0.12 0.12 twmin_est -1000 -1000 -1000 -1000 -1000 -1000 -1000 -1000 -1000 -1000 -1000 wooddens 200 200 200 200 200 200 200 200 200 200 wscal_min 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35

149 149

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Appendix 2. C++ code used in LPJ-DISP to simulate dispersal

The following code is the implementation of the formulas described in Chapter 3 (i.e. dispersal between grid cells and between patches within a grid cell in LPJ-DISP). This code can be found in the vegdynam.cpp module (simulates vegetation dynamics and disturbance) and was called instead of the establishment_guess function. This code is only a small section of the entire program, thus there are references to functions and parameters outside of this module which are not included. However, the code which illustrates the equations used and described in this thesis are included.

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void dispersal_guess(Stand& stand,Patch& patch,Pftlist& pftlist) {

// DESCRIPTION // Establishment in cohort mode, used to simulate seed dispersal // between grid cells and patches within a grid cell. // New grass PFTs are introduced (any year) if climate conditions // become suitable.

// Equations 2 – 6 from LPJ-GUESS, Smith et al. (2001) // spatial mass effect (stand-level "propagule pool" influences // establishment): // (2) est = c*(kest_repr*cmass_repr+kest_bg) // if no spatial mass effect and propagule pool exists // (cmass_repr non-negligible): // (3) est = c*(kest_pres+kest_bg) // if no spatial mass effect and no propagule pool: // (4) est = c*kest_bg // where // (5) c = mu(anetps_ff/anetps_ff_max)*est_max*patcharea // (6) mu(F) = exp(alphar*(1-1/F)) (Fulton 1991, Eqn 4)

// Equations related to dispersal described in this thesis, will be // refered to by Chapter and number (i.e. 3.5)

const double SAPSIZE=0.1; // coefficient in calculation of initial sapling size and initial // grass biomass bool present; // whether PFT already present in this patch bool gridpresent; // whether PFT already present in this gridcell double c; // constant in equation for number of new saplings (Eqn 5) double est; // expected number of new saplings for PFT in this patch double nsapling; // actual number of new saplings for PFT in this patch double bminit; // initial sapling biomass (kgC) or new grass biomass (kgC/m2) double ltor; // leaf to fine root mass ratio for new saplings or grass int newindiv; // number of new Individual objects to add to vegetation for this PFT double kest_bg; int i,j; int used_stands=0; double new_seedlings, tot_seedlings, distance, pPFT=0.0;

// Obtain reference to Vegetation object

Vegetation& vegetation=patch.vegetation;

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// Loop through PFTs pftlist.firstobj(); while (pftlist.isobj) { Pft& pft=pftlist.getobj();

// For this PFT ...

if (patch.age==0) { patch.pft[pft.id].anetps_ff_est=patch.pft[pft.id].anetps_ff; patch.pft[pft.id].wscal_mean_est=patch.pft[pft.id].wscal_mean;

// initialize patches if this is the first simulation year if (date.year==0) patch.pft[pft.id].anetps_ff_est_initial=patch.pft[pft.id].anetps_ff;

} else { patch.pft[pft.id].anetps_ff_est+=patch.pft[pft.id].anetps_ff; patch.pft[pft.id].wscal_mean_est+=patch.pft[pft.id].wscal_mean; }

if (establish(patch,stand.climate,pft)) {

if (pft.lifeform==GRASS || pft.lifeform==CROP) { // ESTABLISHMENT OF GRASSES // Each grass PFT represented by just one individual in each // patch // Check whether this grass PFT already represented

present=false; vegetation.firstobj(); while (vegetation.isobj && !present) { if (vegetation.getobj().pft.id==pft.id) present=true; vegetation.nextobj(); }

if (!present) {

// ... if not, add it

Individual& indiv=vegetation.createobj(pft,vegetation); indiv.height=0.0; indiv.crownarea=1.0; // (value not used) indiv.densindiv=1.0; indiv.fpc=1.0;

// Initial grass biomass proportional to potential forest // floor. Net assimilation this year on patch area basis

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bminit=SAPSIZE*patch.pft[pft.id].anetps_ff;

if (ifdisturb && patch.disturbed)

bminit=SAPSIZE*patch.pft[pft.id].anetps_ff_est_initial;

// Initial leaf to fine root biomass ratio based on // hypothetical value of water stress parameter

ltor=patch.pft[pft.id].wscal_mean*pft.ltor_max;

// Allocate initial biomass allocation_init(bminit,ltor,indiv);

// Calculate initial allometry allometry(indiv);

// Account for C flux from atmosphere to vegetatio patch.fluxes.acflux_est-=bminit; } }

else if (pft.lifeform==TREE) {

// ESTABLISHMENT OF NEW TREE SAPLINGS

// check if the PFT is present in the patch present=false; if (patch.pft[pft.id].cmass_repr>0.0) present=true;

// check if PFT is present in the stand gridpresent=false; if (stand.veg_pop[pft.id]>0.0) gridpresent=true;

// check if new seedlings will disperse in from neighbouring // cells-will be added to est from within cell reproduction tot_seedlings=0.0; est=0.0; for (j=0;j<4;j++){ if (stand.neighbourStands[j]!=NULL) { if (stand.neighbourStands[j]->veg_pop[pft.id]>0.0 && patch.id==j) { // this neighbour gridcell has this PFT // new PFTs could be added to selected patch (in this // case, assuming patch[j] is closest to neighbourstand[j] used_stands=0; new_seedlings=0.0; distance=500; // start at 500m pPFT=0.0;

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// Calculate disperal kernel (Equation 3.5) while (disperse_prob(distance,pft.disp_c,pft.disp_alpha)>1.0e-15){ // number of stands in neighbouring cell within // distance with PFT in question (Equation 3.3)

pPFT=((0.1/cell_size_km)*distance)* (stand.neighbourStands[j]- >veg_pop[pft.id]*(npatch/100));

// don't want to double count pPFT=pPFT-used_stands;

if (pPFT > 0) { // Equation 3.4

new_seedlings=(pft.kest_repr*stand.neighbourStands[j]-> pft[pft.id].cmass_repr*pPFT* disperse_prob(distance,pft.disp_c,pft.disp_alpha)); tot_seedlings+=new_seedlings; }

used_stands=used_stands+pPFT; distance+=500; // go up in increments of 500m

if (distance>(cell_size_km*1000)) distance=1.0e25; // hit end of grid cell need to exit while loop } } } }

// if PFT is already present in patch, then new individuals // determined spatial mass effect

if (present) { if (patch.pft[pft.id].anetps_ff>0.0 && !negligible(patch.pft[pft.id].anetps_ff)) { c=exp(pft.alphar-pft.alphar/patch.pft[pft.id].anetps_ff* stand.pft[pft.id].anetps_ff_max)*pft.est_max*patcharea; } else c=0.0;

// Background establishment should never be enabled for // dispersal mode. If it is, set it to 0 here. kest_bg=0.0;

// Spatial mass effect enabled? Should always be enabled for // dispersal mode (Eqns 2, 3, 4)

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if (ifsme) est=c*(pft.kest_repr*patch.pft[pft.id].cmass_repr+kest_bg) ; else if (!negligible(stand.pft[pft.id].cmass_repr)) est=c*(pft.kest_pres+kest_bg); else est=c*kest_bg; } else if (!present && gridpresent) {

// PFT is not present in this patch, but is present in the // grid cell. This is also the situation for a patch that // has been destroyed

// Uses the logitistic growth curve to determine the number of // patches within the gridcell that can receive new seeds // (Equation 3.7). Seeds are then distributed by the spatial // mass effect (Eqns 2,3,4)

int K = npatch; // carrying capacity (the number of patches) double r = pft.log_r; // growth rate of patches double P0 = 1.0; // initial 'population' double Pt; // calculated number of new patches double new_patches; // number of new patches est=0.0;

// Equation 3.7 Pt=(K*P0*exp(r*stand.veg_pop[pft.id]*npatch))/(K+P0*(exp(r* stand.veg_pop[pft.id]*npatch)-1));

new_patches=(int)(Pt+0.5); if ((stand.veg_pop[pft.id]*npatch)<5 && patch.id < 5) {

// can add new seeds to this patch if (patch.pft[pft.id].anetps_ff>0.0 && !negligible(patch.pft[pft.id].anetps_ff)) { c=exp(pft.alphar- pft.alphar/patch.pft[pft.id].anetps_ff*

stand.pft[pft.id].anetps_ff_max)*pft.est_max*patcharea; } else c=0.0;

// Background establishment should never be enabled for // dispersal mode. If it is, set it to 0 here. kest_bg=0.0;

// Spatial mass effect should always be enabled for

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// dispersal mode (Eqns 2, 3, 4) if (ifsme)

est=c*(pft.kest_repr*stand.pft[pft.id].cmass_repr+kest_bg); else if (!negligible(stand.pft[pft.id].cmass_repr)) est=c*(pft.kest_pres+kest_bg); else est=c*kest_bg;

} else if ((stand.veg_pop[pft.id]*npatch)+new_patches >= patch.id) {

// can add new seeds to this patch if (patch.pft[pft.id].anetps_ff>0.0 && !negligible(patch.pft[pft.id].anetps_ff)) { c=exp(pft.alphar- pft.alphar/patch.pft[pft.id].anetps_ff*

stand.pft[pft.id].anetps_ff_max)*pft.est_max*patcharea; } else c=0.0;

// Background establishment should never be enabled for //dispersal mode. If it is, set it to 0 here. kest_bg=0.0;

// Spatial mass effect should always be enabled for // dispersal mode (Eqns 2, 3, 4) if (ifsme)

est=c*(pft.kest_repr*stand.pft[pft.id].cmass_repr+kest_bg); else if (!negligible(stand.pft[pft.id].cmass_repr)) est=c*(pft.kest_pres+kest_bg); else est=c*kest_bg; } } est+=tot_seedlings;

// Have a value for expected number of new saplings (est) // Actual number of new saplings drawn from the Poisson // distribution if (ifstochestab || vegmode==INDIVIDUAL) nsapling=randpoisson(est); else nsapling=est; if (vegmode==COHORT) {

if (ifdisturb && patch.disturbed) {

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patch.pft[pft.id].anetps_ff_est= patch.pft[pft.id].anetps_ff_est_initial; patch.pft[pft.id].wscal_mean_est= patch.pft[pft.id].wscal_mean; newindiv=(1.0e-15

} else if (patch.age%estinterval) { // Not an establishment year - save sapling count for // establishment the next establishment year

patch.pft[pft.id].nsapling+=nsapling; newindiv=0;

} else { if (patch.age) {// all except first year after disturbance nsapling+=patch.pft[pft.id].nsapling; patch.pft[pft.id].anetps_ff_est/=(double)estinterval; patch.pft[pft.id].wscal_mean_est/=(double)estinterval; } newindiv=(1.0e-15

// Now create 'newindiv' new Individual objects for (i=0;i

if (!negligible(nsapling/patcharea)) { Individual& indiv=vegetation.createobj(pft,vegetation);

if (vegmode==COHORT) indiv.densindiv=nsapling/patcharea; else if (vegmode==INDIVIDUAL) indiv.densindiv=1.0/patcharea;

indiv.age=0.0;

// Initial biomass proportional to potential forest floor net // assimilation for this PFT in this patch bminit=SAPSIZE*patch.pft[pft.id].anetps_ff_est;

// Initial leaf to fine root biomass ratio based on // hypothetical value of water stress parameter ltor=patch.pft[pft.id].wscal_mean_est*pft.ltor_max;

// Allocate initial biomass allocation_init(bminit,ltor,indiv);

// Calculate initial allometry

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allometry(indiv);

// Account for C flux from atmosphere to vegetation patch.fluxes.acflux_est-=indiv.cmass_leaf+indiv.cmass_root+ indiv.cmass_sap; } } } }

// Reset running sums for next year (establishment years only in // cohort mode) if (vegmode!=COHORT || !(patch.age%estinterval)) { patch.pft[pft.id].nsapling=0.0; patch.pft[pft.id].wscal_mean_est=0.0; patch.pft[pft.id].anetps_ff_est=0.0; }

// ... on to next PFT

pftlist.nextobj(); } }

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Appendix 3. Additional simulations with a smaller grid cell size

To test the effect of grid cell size on simulated migration rates in LPJ-DISP, I ran a small number of tests which modified the patch density and logistic growth rate within 9 km 2 grid cells. The 9 km 2 grid cells were created as follows:

Original grid cell size Smaller grid cell size

18 km

9 km

In the thesis, all grid cells were 18 km 2.

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Table A-3. The effect of cell size on average migration rates (vertical distance in km divided by the number of years to move through a grid cell). Acer rubrum was used as the test species, and the simulation with 18 km 2 grid cells was taken from the thesis (Chapter 3) and included as a comparison. r_log refers to the logistic growth rate used to describe patch-to-patch dispersal within a grid cell (see Chapter 3, section 3.3.8). The migration rates for the first row of grid cells were calculated separately as climate change itself is a limiting factor and migration rates are slower than subsequent rows. The tests with 9 km 2 grid cells used a smaller landscape (6 columns across, 2 rows of warm cells followed by 4 rows of cool cells). Thus, n = 24 for All rows , n = 6 for the First row and n = 18 for All but the first row .

Grid cell size patches patch r_log Average migration rate (m year -1) density All rows First row All but the first row 18 km 2 400 1.23 0.1 121.98 47.90 140.98 9 km 2 400 4.94 0.1 58.08 18.76 71.19 9 km 2 200 2.47 0.1 61.40 27.48 72.70 9 km 2 100 1.23 0.1 61.91 26.21 73.80 9 km 2 100 1.23 0.15 91.17 33.80 110.29 9 km 2 100 1.23 0.2 115.46 35.03 142.27