RESEARCHPAPER

Simulating long-distance seed dispersalin a dynamic vegetation modelRebecca S. Snell*†

Faculty of Forestry, University of Toronto,

Toronto, ON, Canada M5S 3B3

ABSTRACT

Aim Predicting the migration of vegetation in response to climate change is oftendone using a climate-driven vegetation model; however, the assumption of fullmigration (where seeds are not limited by distance or barriers) is a commoncriticism. Previous efforts to incorporate limitations on seed dispersal haveoccurred exclusively in bioclimatic envelope models. This paper describes howlimitations on seed dispersal were integrated into a physiologically based dynamicvegetation model, LPJ-GUESS.

Location An idealized landscape, representative of temperate and boreal forests inNorth America.

Methods LPJ-GUESS already simulates establishment, growth, reproduction andcompetition. I used a generic seed dispersal kernel to determine the probability ofdispersal between grid cells, and a logistic function to determine the spread betweenpatches within a grid cell. Plant functional types were parameterized to representthree temperate tree species, Acer, Pinus and Tsuga, by using published dispersalkernels and life-history measurements. Simulations were run with full and limitedmigration, and compared with past vegetation migration rates.

Results Using the old assumption of full migration, the entire landscape wascolonized at the same time (migration rates of 270–380 m year−1). With the newlimited dispersal, species colonized the landscape one row at a time, at rates whichcorresponded well with independent migration estimates based on genetic orpollen reconstructions (Acer, 141 m year−1; Pinus, 76 m year−1). Tsuga was the onlyspecies where simulated migration rates (85 m year−1) were quite a bit slower thanhistorical migration estimates.

Main conclusions The new model was able to simulate reasonable migrationrates, which is a substantial improvement over previous assumptions of full migra-tion. Migration estimates which include the effects of limitations on dispersal,demography,competition and plant physiology will also improve our understandingof how climate change and various other processes can influence plant range shifts.

KeywordsHemlock, Latin hypercube, long-distance seed dispersal, LPJ-DISP, maple,migration, pine, sensitivity analysis, simulation modelling.

*Correspondence: R. S. Snell, Faculty ofForestry, University of Toronto, Toronto, ON,Canada M5S 3B3.E-mail: rebecca.snell@usys.ethz.ch†Present address: Forest Ecology, Institute ofTerrestrial Ecosystems, Department ofEnvironmental Systems Science, ETH Zürich,8092 Zürich, Switzerland.

INTRODUCTION

As the amount of CO2 in the atmosphere continues to rise over

the next century, future climate change scenarios predict a rapid

shift in temperature and precipitation (IPCC, 2007). The north-

ern latitudes are likely to experience the most extreme change,

with a minimum warming of 5 °C and a 20% increase in pre-

cipitation (IPCC, 2007). One goal of climate change research is

to anticipate how these shifts in climate will affect the distribu-

tion and functioning of species (Thomas et al., 2004; Morin

et al., 2008; Doxford & Freckleton, 2012). Plants are of particu-

lar interest, not only because of the potential feedbacks between

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Global Ecology and Biogeography, (Global Ecol. Biogeogr.) (2013) ••, ••–••

© 2013 John Wiley & Sons Ltd DOI: 10.1111/geb.12106http://wileyonlinelibrary.com/journal/geb 1

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 (Malcolm et al.,

2002; Midgley et al., 2006). Plants shift their distributions

through their offspring, relying on rare long-distance seed dis-

persal events and successful establishment in new habitats

(Pitelka et al., 1997). Predicting plant range shifts or plant

extinctions in response to climate change is an area where simu-

lation modelling can be a powerful tool.

Large-scale vegetation models traditionally assumed either no

migration or full migration, where plants have the ability to

migrate into any suitable habitat regardless of barriers or limi-

tations on seed dispersal (Cramer et al., 2001; Guisan & Thuiller,

2005). In reality, seed dispersal probably occurs somewhere in

between these two extremes. Efforts to correct this assumption

have occurred almost exclusively in species distribution models

(SDMs). SDMs correlate current species distribution with a

variety of climate and landscape variables (Guisan & Thuiller,

2005). Once this climatic niche has been established, future

climate scenarios can be used to test the potential shift in a

species’ distribution. Recent work has focused on incorporating

the effect of dispersal limitations and demography to improve

predictions of species ranges (e.g. Dullinger et al., 2012; Meier

et al., 2012; Pagel & Schurr, 2012). TreeMig, a process-based

forest landscape model, also includes competition between trees

(Lischke et al., 2006), which can influence the rate and success of

species migration. However, there has been very little progress in

adding dispersal limitations into the process-based, dynamic

global vegetation models (DGVMs).

DGVMs are physiologically based models which simulate

vegetation processes, hydrology and biogeochemical cycles in

response to climate change (Cramer et al., 2001). DGVMs are

often coupled with global climate models (GCMs) to simulate

the bi-directional feedback between biosphere and atmosphere;

climate-induced vegetation shifts can affect CO2 and water

exchange between land and air, which influence climate (Quillet

et al., 2010). However, DGVMs seldom impose any limitations

on migration (but see Sato & Ise, 2012). This assumption of full

migration could have significant impacts on predictions of

future climate change, and needs to be addressed within a

DGVM framework.

DGVMs already include many of the processes important for

migration of vegetation, such as establishment, carbon assimila-

tion, vegetation growth, reproduction and competition (Cramer

et al., 2001). LPJ-GUESS is a hybrid model (i.e. it incorporates a

forest gap model within a DGVM framework; Smith et al., 2001)

and is particularly suitable for simulating seed dispersal due to

the way it represents vegetation within a grid cell. Most DGVMs

simulate one average individual for each plant functional type

(PFT) within a grid cell. This means that PFTs arrive and establish

as one large individual that immediately travels the length of the

grid cell. LPJ-GUESS simulates a number of replicate patches

within each grid cell, where each patch contains several individ-

uals for each PFT at different ages. New PFTs could arrive and

establish in just one patch. PFTs would then be forced to disperse

between patches to cross a grid cell.

To improve our predictions on how climate change will affect

vegetation distributions, this paper describes how long-distance

seed dispersal was incorporated into the dynamic vegetation

model LPJ-GUESS. Seed dispersal kernels were used to predict

the probability of dispersing between grid cells, and limitations

were placed on patch-to-patch movements within a grid cell.

The goal of this study was to simulate plant migration based

on dispersal limitations alone, so variations in atmospheric

carbon, precipitation, soil and landscape heterogeneity were

not included. The success of the new dispersal module was

determined with a sensitivity analysis and by comparing simu-

lated migration rates with migration rates for three temperate

tree species reconstructed from pollen and genetic data.

METHODS

The LPJ-GUESS model

LPJ-GUESS is a generalized ecosystem model that combines the

dynamic global vegetation model LPJ with a forest gap model

(Smith et al., 2001). Carbon assimilation is calculated using

a modified Farquhar photosynthesis scheme (Haxeltine &

Prentice, 1996), which is influenced by temperature, atmos-

pheric CO2 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).

LPJ-GUESS was run in cohort mode, where each grid cell

contains a number of replicate patches (400 in the present study,

which was the minimum number of patches required to simu-

late dispersal between grid cells). Since each age cohort has

different properties (i.e. height, leaf area index, biomass), the

model can successfully simulate intra- and interspecific compe-

tition for light, space and resources. The herbaceous layer is

simulated as one individual for each patch. All patches within a

grid cell have the same climatic 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 Gerten et al. (2004). To distin-

guish between LPJ-GUESS with full migration or with limited

migration, LPJ-DISP refers to the new version with limited

migration.

Communication between cells

The first step was to fundamentally change the way the program

runs, from isolated single cells to a two-dimensional landscape.

LPJ-GUESS simulates one grid cell at a time, discarding the grid

cell object after it had reached the total number of simulation

years. This makes it impossible to transfer seeds between neigh-

bouring grid cells as they don’t exist in memory at the same

time.

R. S. Snell

Global Ecology and Biogeography, ••, ••–••, © 2013 John Wiley & Sons Ltd2

I chose to distinguish between a spin-up period and a migra-

tion period. During the spin-up period, the grid cells are simu-

lated independently with full migration capabilities for all PFTs.

This allows the PFTs which are in equilibrium with the current

climate to establish and form stable communities. However,

after the spin-up period, each grid cell (and all patch and veg-

etation information contained within it) is retained in memory.

During the migration period, each year is simulated across all

grid cells before moving forward to the next year. Each grid cell

accesses the vegetation composition for its neighbours from the

previous year.

Dispersal between grid cells

In this study, each grid cell is 0.166° or approximately 18 km.

Although most dispersal events would occur within a grid cell,

long-distance dispersal between cells will determine the migra-

tion of vegetation across a landscape. The number of seeds

arriving from distance x, is a product of the number of seeds

produced in neighbouring grid cells, seedn, and the probability

of those seeds travelling that distance, k(x),

seed seedx k xn( ) = ∗ ( ). (1)

Seed production (seedn)

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.

However, only those patches located close to the edge of the grid

cell are likely to have seeds disperse into neighbouring grid

cells. So seed production for each PFT within a grid cell

(pft.cmass_repr) was scaled by the proportion of patches close to

the edge of the grid cell (pPFT),

seed PFTn pft cmass repr p= ∗. _ . (2)

Number of patches close to the edge of thecell (pPFT)

Patches in LPJ-GUESS do not have locations within the grid cell,

making it impossible to identify the actual patches located close

to 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 (http://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. The 100 random points were generated

1000 times to determine that on average 0.0028% of the patches

are within 500 m from one of the edges. Given that long-

distance dispersal can occur over distances greater than 500 m

(Cain et al., 2000), the proportion of patches within 1, 2, 3, 4 and

5 km from the edge were also calculated.

Using 100 points assumes that the PFT of interest can be

found growing in 100% of the patches. Thus, random point

generation was repeated using 90 points (assuming that 90% of

the 100 patches contain the PFT), 80, 70, 60 . . . and so on. The

resulting formula is:

p x cell size x nPFT PFT( ) = ( )[ ]∗0 1. _ (3)

where x is distance, cell_size is the size of the grid cell in km and

nPFT is the number of patches within the grid cell that contain

the PFT in question. Combining equations 1–3 results in the

following formula:

seed PFTx pft cmass repr cell size x n k x( ) = ( )[ ]∗{ } ( ). _ . _ .0 1 (4)

Seed dispersal kernels (k(x))

The probability of a seed travelling a specific distance, x, is

known as the dispersal kernel. A generalized dispersal kernel has

been described by Clark (1998):

k xc

c

x c

( ) =( )

⎛⎝⎜

⎞⎠⎟ −⎛

⎝⎜⎞⎠⎟2 1α αΓ

exp (5)

where Γ() is the gamma function, c is a shape parameter and αis a distance parameter. By choosing different values for c and α,

the formula can be used to describe different kernels. For

example, c = 2.0 is the Gaussian kernel and c = 1.0 is the expo-

nential. Kernels with c < 1.0 are leptokurtic. A leptokurtic dis-

persal 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.

Since different dispersal vectors operate on different spatial

scales, an increasing distance function was used, as opposed to a

predetermined value for distance. The minimum distance evalu-

ated was 500 m. Distance was increased in 500-m steps until the

dispersal probability became too small to consider.

Spread between patches within a grid cell

Just as there were no limitations to dispersal between cells, LPJ-

GUESS also has no restrictions on dispersal between patches

within a cell. Each grid cell has a common propagule pool which

every patch contributed seedlings to and took seedlings from.

Theoretically, a new PFT could travel all the way across the cell

(i.e. 18 km) in 1 year. Ideally, seeds coming in from neighbour-

ing cells should only arrive in the patches closest to the edge,

establish, spend a few years growing before reproducing, and

then disperse to nearby 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 propagule pool

within each grid cell. PFTs should only contribute seedlings to

Incorporating seed dispersal into a DVM

Global Ecology and Biogeography, ••, ••–••, © 2013 John Wiley & Sons Ltd 3

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. Equation (3) was used to calculate the

number of patches located close enough to an edge to receive

seeds. These patches remain constant throughout the simulation

and are the only patches that can receive seeds from a neigh-

bouring grid cell (e.g. patch1, patch2 and patch3 will receive seeds

from the southern neighbour; patch4, patch5 and patch6 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 reproduc-

tion until it reaches a minimum age. Maturation age is a com-

monly 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 spe-

cific life history for each PFT. For example, cherry birch trees

delay reproduction for many years but have a very high fecun-

dity once they do start producing seeds, compared with flower-

ing dogwood trees which start reproducing at a much younger

age 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 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 the probability of having a neighbouring patch

contain that PFT is very low. If more than 50% of the patches

contain the PFT, the probability of a patch having at least one

neighbour with the PFT is quite high. The logistic growth curve,

a relatively common function in ecology, can be used to describe

this relationship:

P tKP

K P

rt

rt( ) =

+ −( )0

0 1

e

e, (6)

where P is the population size at time t, r is the growth rate and

K is the carrying capacity or the largest size that the population

can reach given unlimited time. To suit my purpose, the formula

was modified as follows:

P pK

K

rp

rp( ) =

+ −( )e

e 1, (7)

where P is the population of patches available for receiving seeds

(i.e. those having 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. The initial population size (P0) is

always set to 1 since this formula is only used if the PFT is

already present in the grid cell. The growth rate (r) was set to 0.1

and kept constant for all simulations (see Appendix S2 in Sup-

porting Information for a sensitivity analysis and discussion

about this parameter).

Using equation 7 in this way means that there is not neces-

sarily any growth each year, unlike in the traditional population

growth model. It is used to calculate the number of new patches

which have the potential to receive 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 influ-

ence the success of seeds, such as dormancy, disease or seed

predation.

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 ± 0.45 °C) and the

bottom three rows were assigned a warmer, temperate climate

(mean annual temperature 15.19 ± 0.41 °C). The climate data

were extracted from actual boreal and temperate regions from

the Climatic Research Unit (CRU) global gridded data set (New

et al., 2002). The CRU data are composed of mean monthly

surface climate from 1961 to 1990, at a resolution of 0.166° or

18 km.

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 were used (Appendix S1). Their

temperature ranges were modified to ensure complete separa-

tion between the temperate and boreal 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 ± 0.35 °C and the temperate climate was warmed by an

average of 1.74 ± 0.06 °C. The temperature increases were

chosen based on the climatic tolerances for the temperate PFTs

(i.e. the boreal climate needed to warm by c. 10 °C to reach the

minimum temperature requirements for temperate PFTs to

establish and grow; Appendix S1). Although the degree of

warming in the boreal cells is more extreme than in future

climate change predictions (IPCC, 2007), the goal of this study

was to test migration of plants based on dispersal limitations

alone. If a more moderate warming was applied, dispersal and

climate would have been limiting factors. The model continued

to run at the new warmer temperatures for 1000–2000 years,

until the species had migrated through all the grid cells.

Test species

To test how well the model simulates dispersal, the temperate

PFT was parameterized to represent three different species: Acer

rubrum, Tsuga canadensis and Pinus rigida (Table 1). These tree

species were selected since they had published dispersal kernels

(Clark, 1998) for equation 5 and reconstructed migration rates

following the retreat of the last glacier in North America (Davis,

R. S. Snell

Global Ecology and Biogeography, ••, ••–••, © 2013 John Wiley & Sons Ltd4

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 inde-

pendent comparison with the simulated migration rates. Since

individual species are not usually distinguished in the pollen

record, simulated rates were compared with the appropriate

genus (Table 2). The three species also represent different life-

history strategies (Table 1) which should have an effect on how

quickly they migrate across a landscape.

Sensitivity analysis

Performance of a sensitivity analysis on LPJ-DISP is important

to reduce model uncertainty, improve confidence in model pre-

dictions and identify areas that require further research. The

analysis identifies which input parameters have a significant

effect on the simulated migration rates. If the most influential

parameters are those which can be measured and known exactly,

this increases confidence in the results. A full description of the

methodology is provided in Appendix S2.

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 species had migrated

through all the grid cells, the average migration rate (time to

move through each grid cell, 8 km) and the overall migration

rate (time to move the entire distance, 90 km) were calculated. A

species was considered to have entered a grid cell once a repro-

ducing adult could be found in at least one patch. The establish-

ment of saplings was not considered since other events (e.g.

competition, disturbance) might prevent that sapling from

reaching reproductive maturity. This is also comparable to how

migration is calculated in the pollen record (i.e. immature trees

don’t produce pollen). A species was considered to have crossed

a grid cell after mature trees were found in more than 80% of the

patches. Due to random patch-destroying events, individual

species almost never occupied 100% of the patches.

Migration rates for the first row of grid cells 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 cal-

culated for the next four rows (n = 40).

RESULTS

Sensitivity analysis

The sensitivity analysis demonstrated the range of migration

rates produced by LPJ-DISP by varying the parameters within

their published ranges. 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 from 37–162 m

year−1 for all subsequent rows. In general, migration rates were

the most sensitive to maturation age, as this parameter was

Table 1 Values used to parameterize the three test species (additional parameter values are listed in Appendix S1).

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

αdisp, a distance parameter used in the dispersal kernel; reprfrac, the fraction of carbon allocated to reproduction; kest_repr, a constant in the equation forseed production.

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

Simulated migration rates (m year−1)

Reconstructed migration rates (m year−1)Average (first row) Average (subsequent rows) Overall

Acer rubrum 48 ± 8 (34–64) 141 ± 9 (122–162) 111 Acer rubrum 80–90 McLachlan et al. (2005)

Acer 126 (80–172) Delcourt & Delcourt (1987)

Acer 200 Davis (1981)

Pinus rigida 30 ± 4 (24–37) 76 ± 12 (55–101) 60 Pinus (northern) 135 (104–170) Delcourt & Delcourt (1987)

Pinus (southern) 81 (22–174)

Tsuga canadensis 47 ± 5 (40–53) 85 ± 16 (25–100) 79 Tsuga 202 (113–278) Delcourt & Delcourt (1987)

Tsuga 200–250 Davis (1981)

Incorporating seed dispersal into a DVM

Global Ecology and Biogeography, ••, ••–••, © 2013 John Wiley & Sons Ltd 5

consistently ranked first under all the various sensitivity meas-

ures (Appendix S2). The second most important parameter was

usually r (equation 7). Although reproduction had only a weak

effect on migration rates (Appendix S2), it was always a negative

relationship (i.e. a higher proportion of carbon allocated to

reproduction resulted in slower migration).

Full migration

Using the traditional assumption of full migration, all five rows

were colonized at the same time (Fig. 1), 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.

Limited migration

Simulations with limited dispersal gave more moderate overall

migration rates. The simulated migration rates for Acer (110 m

year−1) were consistent with phylogenetic reconstructed migra-

tion rates (80–90 m year−1; Table 2). Simulated migration rates

for Pinus (60 m year−1) were also consistent with reconstructed

rates from the southern pine group. However, simulated migra-

tion for Tsuga (80 m year−1) was considerably slower than the

pollen-reconstructed rates (Table 2).

Using a logistic curve to describe the within-cell filling of

patches produced a consistent pattern. The initial stage, where

the test species was maintained in only a few patches for a long

period of time, is followed by a rapid spreading stage, once the

species had established in c. 30% of the patches (Fig. 1). Stochas-

tic processes, disturbances and cell-to-cell climate differences

caused considerable variability between grid cells even within

the same row (Fig. 1). For example, there were c. 300 years

between the first and last grid cell to be colonized in the same

row for the Pinus simulation (Fig. 1b).

DISCUSSION

DGVMs include many of the processes which are lacking in

some of the correlative SDMs, such as competition, demography

and disturbances (e.g. Higgins et al., 2012). However, the

assumption of full migration has limited their application for

questions of species range shifts. That fact that LPJ-DISP was

able to simulate the movement of vegetation across a theoretical

landscape at a rate that is consistent with historical vegetation

migrations (Table 2) represents a substantial step forward.

Simulated migration rates were two to three times slower in the

first row (Table 2) when plants were limited by dispersal and as

well as climate. Palaeo reconstructed migration rates also show a

range of values (Delcourt & Delcourt, 1987), and it is also

thought that slower migration rates were due to climatic or

other environmental constraints and the fastest migration rates

occurred when the only limiting factor was dispersal.

Acer had the fastest average and overall migration rates. This

in not unexpected considering it has the youngest maturation

age, highest fecundity and largest distance parameter (Table 1).

The overall migration rate was reasonably close to both the

Figure 1 Simulated migration in LPJ-DISP for the three testspecies in an idealized landscape (five rows of 10 grid cells). Eachline represents one grid cell (black in print, different coloursonline where each colour represents one column). The thin greylines represent the simulation with the traditional assumption offull migration. The vertical dotted line indicates the end of thewarming period (i.e. climate is now suitable for species in all gridcells). The first 1000 years were spin-up and are not shown. Eachgrid cell was c. 18 km (0.166°). For graphing purposes, distancewas calculated as the proportion of filled patches within a grid.For example, if 30% of the patches were occupied in year 2150then it had moved 5.4 km through that grid cell.

R. S. Snell

Global Ecology and Biogeography, ••, ••–••, © 2013 John Wiley & Sons Ltd6

pollen-reconstructed rate from Delcourt & Delcourt (1987) and

the genetic-reconstructed rate from McLachlan et al. (2005).

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 independ-

ent of the estimates of migration rates from palaeo and genetic

data.

Pinus migration was parameterized using data for Pinus

rigida, a northern pine; however, the simulated migration rates

were more similar to the southern pine group (Table 2). This is

probably an effect of the maturation age (identified as being the

most significant parameter for simulated migration rates in LPJ-

DISP; Appendix S2). The maturation age for Pinus rigida is 12

years (Table 1), which is the same as the average maturation age

for the southern pine group. Species in the northern pine group

had a younger average maturation age (9 years) which would

lead to faster migration rates.

Tsuga was the only test species where there was a large differ-

ence between the simulated and pollen reconstructed rates

(Table 2). Both Davis (1981) and Delcourt & Delcourt (1987)

estimated Tsuga trees to have migrated more than 200 m year−1,

which is more than twice as fast as the simulated rate. As the

model already includes long-distance seed dispersal, perhaps

this is a case of unidentified refugial populations. Recent

phylogeographic studies have been able to identify refugial

populations that persisted close to the edge of a retreating

glacier (Anderson et al., 2006; Hu et al., 2009). Refugial popu-

lations 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 matched the

simulated rates quite well (Table 2).

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 5; c = 0.5) with different

values for α (Table 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 palaeo-record, Clark

(1998) allocated up to 10% of the seeds to the tail. In reality, such

large amounts of long-distance dispersal are highly unlikely.

Dispersal within a grid cell

The use of a logistic curve may be a novel approach for describ-

ing seed dispersal between patches, but such curves have long

been used in epidemiology to describe the spread of diseases

(Berger, 1981). In spite of an unconventional spread pattern

within an individual grid cell (Fig. 1), a logistic curve does

produce migration rates at a landscape scale that are consistent

with historical vegetation migration rates (Table 2). The size of

the grid cell does influence the size of the ‘jump’ (Appendix S3).

In order to maintain the relationship across scales, the growth

rate (r) needs to be adjusted. For example, reducing the grid cell

resolution to 9 km2 requires a doubling of r to maintain the same

migration rate (Appendix S3).

It is not surprising that simulated migration rates were sen-

sitive to r, the parameter which describes the rate of within-cell

filling (equation 7). Although it would be ideal to choose a value

for r that reflects different dispersal vectors (i.e. wind, mammal,

bird), I suggest keeping this value constant until additional

research has been done. This ensures that the simulated migra-

tion rates are based on known life-history parameters which

reduces model uncertainty.

Wind versus animal dispersal

The three species 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). However, this study clearly shows that full

migration is not the same as long-distance dispersal, even for

wind dispersal (Fig. 1).

To date, most of the effort in developing a generic model for

seed dispersal has focused heavily on wind-dispersed seeds (e.g.

Govindarajan et al., 2007; Nathan et al., 2011) as wind dispersal

is a common strategy in boreal and temperate trees. Alterna-

tively, animal-dispersed seed shadows are complex and rely

heavily on the behaviour of the dispersers (Gomez, 2003). A

mechanistic model for animal dispersal needs to account for

many additional factors such as animal movement, seed detach-

ment, 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). Modelling 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 many of these processes would occur

within a grid cell. Using the framework outlined in this paper,

the only information that would be needed to simulated disper-

sal between grid cells is the amount of long-distance dispersal.

Perhaps studies that track animal movement and seed dispersal

between patches (Gomez, 2003; Levey et al., 2008) could be used

to describe patch-to-patch dispersal within a grid cell. Being able

to simulate range shifts in response to climate change for plants

with all modes of dispersal would be bring an enormous

improvement to our future climate change scenarios.

Life-history strategies and climate change

The sensitivity analysis identified age at maturation as the most

influential parameter for simulating migration rates in LPJ-

DISP. Maturation age is an important component in the life-

history strategies of trees (Loehle, 1988; Clark, 1991) and can

affect biodiversity, community composition and population

spread (Clark & Ji, 1995; Nathan et al., 2011). Delaying repro-

duction to invest in growth is a common strategy for trees in

Incorporating seed dispersal into a DVM

Global Ecology and Biogeography, ••, ••–••, © 2013 John Wiley & Sons Ltd 7

stable environments. However, if trees delay reproduction for

too long they may be unable to respond quickly to climate

change and migrate to new locations.

The sensitivity analysis also illustrated another potential

trade-off for trees, namely the cost of reproduction (Obeso,

2002). 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 reproduc-

tion means there is less carbon available for growth which puts

trees at a disadvantage when competing for light and resources.

In the light of future climate change and the importance of

being able to predict vegetation migration, it is interesting that

many life-history parameters can be influenced by environmen-

tal stress and elevated CO2 levels. Red mangrove trees started

reproducing at a much younger age when exposed to elevated

CO2, a full 2 years before seedlings typically start reproducing

(Farnsworth et al., 1996). Pinus taeda trees growing under

elevated CO2 levels also reached reproductive maturity at

younger ages and smaller sizes and produced more cones

(Ladeau & Clark, 2006). It is important to recognize that climate

change may cause modifications to life-history parameters

which can influence migration rates.

Competition between vegetation types

A strength of LPJ-DISP is that plants participate in intra- and

interspecific competition, a common deficiency in SDMs

(Hampe, 2004). Although the climate was suitable, the progres-

sion 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), 12 of the 50 grid cells still

contained at least one patch with the cold-tolerant PFT (results

not shown).

However, a limitation of this model is that incoming vegeta-

tion 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 con-

tinued 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 glacial retreat (Davis, 1981;

Delcourt & Delcourt, 1987). To simulate the movement of these

species, we would need to modify the landscape to include

natural open spaces, or increase the frequency and size of dis-

turbance events, creating more gaps in the forest and more

opportunities for shade-intolerant species to have a competitive

edge.

CONCLUSIONS

The lack of seed dispersal is a major criticism in all vegetation–

climate models. This paper presents the first time seed dispersal

has been included in a physiological dynamic vegetation–

climate model, at spatial and temporal scales that are suitable for

simulating vegetation migration. Although it can be difficult to

know for certain what vegetation migration rates were histori-

cally, the simulated migration rates can be considered reason-

able estimates and represent a significant improvement over

previous assumptions of full migration. The sensitivity analysis

also demonstrated the importance of a few key parameters,

including age at maturation and within-cell spread rates. As age

at maturation is a parameter which can easily be measured,

future work should focus on improving the parameterization of

within-cell spread (a methodological approach for choosing a

value for r). One suggestion would be to choose a value such that

the simulated migration rates correspond to independent

migration estimates for each species, if we have reason to believe

the independent migration estimates are correct. The source of

these independent estimates could be from pollen records,

phylogenetic data or from an independent, high-resolution dis-

persal model which operates over a smaller spatial extent. Ulti-

mately, adding migration limitations to dynamic vegetation–

climate models will help develop more realistic expectations for

how vegetation will respond to future climate change.

ACKNOWLEDGEMENTS

I thank my PhD supervisor S. A. Cowling for her continuous

support. B. Smith kindly allowed me to use LPJ-GUESS. J. Nabel,

I. C. Prentice and one anonymous referee provided valuable

feedback on the manuscript. Funding for R.S.S. was provided by

OGS and NSERC graduate scholarships.

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SUPPORTING INFORMATION

Additional supporting information may be found in the online

version of this article at the publisher’s web-site.

Appendix S1 Parameter definitions and values for each PFT.

Appendix S2 Sensitivity analysis for new dispersal parameters.

Appendix S3 Simulations with a smaller grid cell size.

BIOSKETCH

Rebecca Snell is a post-doctoral researcher in the

Forest Ecology group at ETH Zurich. This work was

part of her PhD dissertation at the University of

Toronto. She is interested in understanding

landscape-level distribution patterns and the processes

that influence species composition, structure and

dynamics.

Editor: Bill Shipley

R. S. Snell

Global Ecology and Biogeography, ••, ••–••, © 2013 John Wiley & Sons Ltd10