Crown Architecture and Species Coexistence in Plant Communities

Annals of Botany 78 : 437–447, 1996

Crown Architecture and Species Coexistence in Plant Communities M A S A Y U K I Y O K O Z A WA*, Y A S U H I R O K U B O TA† and T O S H I H I K O H A R A‡ * DiŠision of Changing Earth and Agro-EnŠironment, National Institute of Agro-EnŠironmental Sciences, Tsukuba 305, † Center for Ecological Research, Kyoto UniŠersity, Kyoto 606-01, and ‡ The Institute of Low Temperature Science, Hokkaido UniŠersity, Sapporo 060, Japan Received : 26 September 1995

Accepted : 15 April 1996

The relationships between crown architecture and species coexistence were studied using the diffusion model and the canopy photosynthesis model for multi-species plant communities. The present paper deals with two species having different crown shapes [conic-canopy plant (CCP) and spheroidal-canopy plant (SCP)], for various initial mean sizes at the establishment stage and physiological parameter values (photosynthetic rate, etc.). Recruitment processes were not incorporated into the model, and thus simulations were made for the effects on the pattern of species coexistence of either sapling competition starting from different sapling banks or competition in single-cohort stands with little continual establishment of species until a stand-replacement disturbance. The following predictions were derived : (1) SCPs can establish later}slowly in the lower canopy layer even if they are overtopped by a CCP which established first}rapidly ; (2) if SCPs established first}rapidly and occupy the upper canopy layer, a CCP can rarely establish later}slowly in the lower canopy layer ; (3) smallest-sized CCPs can persist well in the lowermost canopy layer overtopped by a SCP, suggesting a waiting strategy of CCP’s saplings in the understorey of a crowded stand ; (4) even if CCPs established first}rapidly and occupy the upper canopy layer, an SCP can establish later}slowly in the lower canopy layer. Therefore, the species diversity of SCPs which established first}rapidly and occupy the upper canopy layer limits the number of CCP species which can establish later}slowly. In contrast, the species diversity of CCPs which established first}rapidly and occupy the upper canopy layer does not affect the number of SCP species which can establish later}slowly. The combination of initial sizes of a CCP and an SCP at the establishment stage (i.e. establishment timing) affects the segregation of vertical positions in the canopy between the two species with different crown shape, and not only species-specific physiological traits but also crown architecture greatly affects the coexistence pattern between species with different crown architectures. The theoretical predictions obtained here can explain coexistence patterns found in single-cohort conifer-hardwood boreal and sub-boreal forests, pointing to the significance of crown architecture for species coexistence. # 1996 Annals of Botany Company Key words : Diffusion equation model, canopy photosynthesis model, conifer-hardwood boreal}sub-boreal forest, sapling establishment, vertical foliage profile.

INTRODUCTION Many researchers have investigated the relationships between species-specific crown architecture, successional status and responses to gaps in trees (Pickett and Kempf, 1980 ; Kempf and Pickett, 1981 ; Veres and Pickett, 1982 ; Shukla and Ramakrishnan, 1986). Horn (1971) suggested adaptive growth dynamics at the shoot level in relation to crown architecture and light regimes in the foliage. Ku$ ppers (1989) discussed the adaptive significance of crown architecture based on cost–benefit relationships of carbon gain. However, most of these studies have simply discussed adaptive significances of species-specific tree crown architecture as simple allometries between crown dimensions (crown depth, crown width, crown area) and individual sizes [mass, stem diameter at breast height (DBH), stem height], and have not investigated the effects of individual crown architecture as vertical foliage profile on the interactions between individuals and multi-species community dynamics. Crown architecture is an important factor for photosynthetic production (Horn, 1971 ; Kikuzawa et al., 1986 ; Ku$ ppers, 1989). Tree communities are usually composed of * For correspondence.

0305-7364}96}100437­11 $18.00}0

species of various crown shapes (Kohyama, 1987 ; King, 1990 ; Kohyama and Hotta, 1990 ; note that these studies used simple allometries between crown dimensions and individual sizes for crown shape), and crown architecture may play an important role in species coexistence. In the boreal and sub-boreal zones, forests are composed of two tree groups having distinct crown shapes (e.g. Youngblood, 1995), conifers having conic crowns and deciduous broadleaved trees (hardwoods) having spheroidal crowns (e.g. Umeki, 1993). Conifers and hardwoods coexist at a large scale (Tatewaki, 1958 ; Ishikawa, 1990 ; Youngblood, 1995) and the difference in the crown architecture may contribute to species coexistence in the conifer–hardwood forests. Several researchers have investigated the effects of crown shapes on stand dynamics and species diversity of subboreal forests. Ishizuka (1984) pointed out that the spatial pattern of individual crowns affected the stand dynamics of sub-boreal forests. Fujimoto, Hasegawa and Shinoda (1991) and Fujimoto (1993) suggested that the difference in crown shape between species affected the successional status of each species. However, few have investigated quantitatively the effects of crown shapes as vertical foliage profile on community dynamics or species coexistence patterns. # 1996 Annals of Botany Company

438

Yokozawa et al.—Crown Architecture and Species Coexistence

Two distinct types of conifer–hardwood forests have been recognized (Youngblood, 1995) : multi-cohort stands where species establishment occurs continually (Stijlen and Zackrisson, 1987 ; Hofgaard, 1993) and single-cohort stands where species establishment occurs once after a standreplacement disturbance such as fire but rarely occurs during stand development until a next disturbance (Cogbill, 1985 ; Youngblood, 1995). The outcome of sapling competition is important in a sub-boreal conifer–hardwood forest (Kubota and Hara, 1995, 1996) because it gives a boundary condition for the dynamics of canopy tree competition. Kubota and Hara (1995, 1996) showed that, in the sub-boreal forest, interspecific competition between saplings was more significant for the pattern of species coexistence than that between canopy trees. The aim of the present paper is to investigate the effects of individual crown architecture as vertical foliage profile on the coexistence between plants with different canopy architectures. We simulated the growth dynamics and patterns of species coexistence of two species with different crown architectures by changing initial mean size at the establishment stage and values of several physiological parameters. The simulations made in the present paper correspond to either interspecific competition between saplings starting from different sapling banks as initial conditions (Kubota and Hara, 1996) or interspecific competition in single-cohort stands with little continual establishment of species until a stand-replacement disturbance (Youngblood, 1995). In the present paper, therefore, we did not incorporate recruitment processes. The simulation for multi-cohort mixed-species stands with continual species establishment (Stijlen and Zackrisson, 1987 ; Hofgaard, 1993) will be reported in a following paper.

the mean absolute growth rate and the mortality rate of individuals of mass w of species i at time t, respectively. For even-aged monocultures (n ¯ 1), Yokozawa and Hara (1992) derived the general Gi(t, w) function based on a canopy photosynthesis model, which was derived from the canopy photosynthetic processes of competing individuals. The model can easily be extended to the case for multispecies communities, Gi(t, w) (n & 2). Let Φi(t, z) be an averaged vertical foliage density profile within the stand at height z above ground of species i at time t: Φi(t, z) ¯

&! f ¢

LA,i

(t, z, w) fi(t, w) dw,

where fLA,i(t, z, w) is the vertical distribution density of leaf area of an individual of mass w at height z above ground for species i. From the Beer–Lambert law, light intensity at height z above ground at time of day td on day t is given by

0 1 9 &

b k I(t, t , z) dt ®r , &! 1­a k I(t, t , z) Td

i i

d

d

i i

Diffusion model and canopy photosynthesis model for a plant community We consider a multi-species plant community where each individual is growing under homogeneous environmental and competitive conditions. Let fi(t, w) denote the distribution density of the i-th species’ individuals (i ¯ 1, 2, … , n) of plant mass w at time t in a community with n species. With the inter- and}or intra-specific interactions, its distribution density varies with time. Hara (1984 a, b) developed the diffusion model for the time development of size (mass, plant height or stem diameter) distribution density for a single-species plant population. Kohyama (1992) and Hara (1993) used the model for a n-species plant community [but, they used stem diameter (DBH) as size of the model] :

®Mi(t, w) fi(t, w), (i ¯ 1, 2, … , n).

9 &!

fLA,i(t, z, w) pn,i(t, z) dz®rm wnon

9 &!

fLA,i(t, z, w)

Gi(t, w) ¯

1 u 1­rg

¯

1 u 1­rg

H(w)

Subscript i denotes each species i. The Di(t, w), Gi(t, w) and Mi(t, w) functions are the variance of absolute growth rate,

:

H(w)

b k I(t, t , z) dt ®r 1 dz®r w : , 0&! 1­a k I(t, t , z) Td

i i

d

d

i i

(1)

(4)

f

d

where ai and bi are parameters of the light-photosynthetic rate curve of species i and rf is the respiration rate per unit leaf area (the same for every species in the simulations). Here, we approximate the light-photosynthetic rate curve by a rectangular hyperbola, where bi and bi}ai represent the slope at the origin and the asymptotic value of the curve, respectively. Then, the averaged daily net photosynthetic rate of an individual of mass w of species i at time t, which is equivalent to the Gi(t, w) function, is given by

¬

¦ fi(t, w) 1 ¦# ¦ ¯ [Di(t, w) fi(t, w)]® [Gi(t, w) fi(t, w)] # ¦t 2 ¦w ¦w

:

n ¢ πtd exp ® 3 ki Φi(t, y) dy , (3) I(t, td, z) ¯ I sin ! Td i=" z where I is the irradiance incident on the canopy at midday ; ! Td is the day length ; ki is the light extinction coefficient in the canopy of species i. In eqn (3), changes in time of the irradiance intensity on the canopy can be approximated by a sinusoidal curve on cloudless days. We assume that the plant foliage reduces the intensity of radiation homogeneously without reflectance or transmittance by leaves. Then, the averaged daily net photosynthetic rate per unit leaf area of species i at height z above ground in the stand on day t, pn,i(t, z), is given by

pn,i(t, z) ¯ MODEL

(2)

f

m

non

(5)

d

where u is the conversion coefficient, rm is the respiration rate of non-photosynthetic organs, rg is the growth respiration rate (these parameter values were the same for every species in the simulations), wnon is the mass of nonphotosynthetic organs. H(w) represents the relationship

Yokozawa et al.—Crown Architecture and Species Coexistence

different among species. However, Yokozawa and Hara (1995) showed theoretically that the difference in the allocation patterns (constant, size-dependent or competition-dependent) affects the size-structure dynamics of a population only a little. Therefore, we use here only the following h-dependent relationship between the increment of stem diameter per unit time, ∆d, and the increment of plant height, ∆h,

6 A

B

Height above ground, z (m)

5

4

3

∆h ¯ β exp [®γh], ∆d

2

1

0

439

1 2 3 4 5 Diameter, d (z) (cm)

6 0 1 2 3 4 5 6 Leaf area density (m2 m–1)

F. 1. A, Vertical stem diameter profile and B, the corresponding vertical foliage profile for several values of the crown shape parameter, η, in the case of plant height h ¯ 5±0 m. The crown shape is conic for η ¯ 1 and becomes more spheroidal with an increase in η. (——) η ¯ 1 ; (----) η ¯ 3 ; (—[—) η ¯ 5 ; (±±±±±) η ¯ 10.

between the plant height and the mass of an individual. This relationship will be derived in the succeeding subsection. In this model, only light competition is considered for intraand inter-specific interactions between individuals. As in our previous papers (Yokozawa and Hara, 1992, 1995), we assume for simplicity that the mortality rate of an individual of mass w of species i at time t, Mi(t, w), is set at unity only when the daily net photosynthetic rate of an individual of species i, Gi(t, w), is negative. The functional form of Mi(t, w) is then given by Mi(t, w) ¯ 1, Gi(t, w) ! 0 ; ¯ 0, Gi(t, w) & 0.

(6)

Then, from eqn (1), the distribution density of individuals of species i decays exponentially.

(8)

where β and γ are positive constants. Equation (8) allows an individual plant to give more allocation to height growth than to stem diameter growth if the individual has a small plant height under suppressed conditions. Integrating eqn (8), we obtain the relationship between plant height, h, and stem diameter, d, d¯

1 [exp (γh)®1]. βγ

(9)

Equation (9) describes how the stem diameter, d, depends on plant height, h, in each individual plant. It should be noted that the growth rates of plant height and stem diameter in the derivative form [eqn (8)] adopted in our previous paper (Yokozawa and Hara, 1995) depends on time, while the integral form [eqn (9)] is independent of time. Therefore, the allometry of each individual is unchanged throughout the time course of its growth. We take plant height, h, as an independent variable using the relationship between d and h as eqn (9). The mass of nonphotosynthetic organs, wnon in eqn (5), is thus given as wnon ¯ αd #h ¯

α [exp (γh)®1]# h, β#γ#

(10)

where α is a positive constant. The vertical distribution of leaf area density, fLA(z, h), of an isolated individual having a stem diameter profile given by eqn (7) is derived from the pipe model theory, that the cross-section of a stem at any height above ground is proportional to the accumulated mass of leaves existing above that height of a plant (Shinozaki et al., 1964 a, b) :

Allometry and crown shape of an isolated plant θ²D(z)´# ¯

&

H

fLA(z«, h) dz«,

(11 a)

In this paper, we assume that the stem diameter profile at height z above the ground, D(z), of an individual of plant height h (m) and stem diameter at ground level d (cm) as follows : z η , (7) D(z) ¯ d 1® h

and thus

where η is a positive constant specific to each species. This functional form was used by Armstrong (1990, 1993) for representing the canopy shape of an isolated tree. We use it for the vertical profile of stem diameter. The profiles for several values of η are shown in Fig. 1 A. Moreover, we assume that plants allocate net photosynthetic gain per unit time to the growth of both stem diameter and plant height. The mechanisms of allocation patterns may be quite

where θ is a positive constant (Yokozawa and Hara, 1995). The vertical distribution of leaf area density for several values of η (hereafter we call η the ‘ crown shape parameter ’) are shown in Fig. 1 B. For η ¯ 1, the vertical distribution of leaf area density presents a conic crown shape (e.g. coniferous trees) : larger values of η give spheroidal crown shapes having larger leaf mass in the upper layer than in the lower layer [e.g. broad-leaved trees (hardwoods)], and

9 0 1:

fLA(z, h) ¯ 2θη

z

(βγ1 [exp (γh)®1]*# 91®0hz1 : zh " , η

η−

η

(11 b)

440

Yokozawa et al.—Crown Architecture and Species Coexistence

T     1. Standard Šalues of parameters used for simulations. When changing parameter Šalues of one species, those of the other species are fixed at the Šalues listed below Parameter

Value and unit

α β γ θ

5±0 g cm−# m−" 0±6 m cm−" 0±1 m" 0±04 m# cm−#

u k

0±65 g g−CO" # 0±6

a

0±075 W−" m#

b I

0±15 gCO W−" h−" 250±0 W m#−#

Td rf

14±0 h 0±6 gCO m−# d−"

rm

0±001 g g−" d−"

rg s

0±3 g g−" 0±03 cm# g−"

!

#

Definition allometric parameter : eqn (10) allocation parameters : eqns (8), (9), (10), (11), (12) parameter for leaf area distribution : eqn (11) conversion factor : eqn (5) light extinction coefficient in the canopy : eqns (3), (4), (5) parameters for lightphotosynthetic rate curve : eqns (4), (5) irradiance incident on the canopy at midday : eqn (3) daylength : eqn (3) respiration rate of leaves : eqns (4), (5) maintenance respiration rate : eqn (5) growth respiration rate : eqn (5) specific leaf area : eqn (12)

η U­¢ gives a flat-topped crown. We further assume that the foliage layer at any height above ground dies if the average daily net photosynthetic rate per unit leaf area at that height, eqn (4), is negative because of shading within the stand. Then, the vertical distribution of leaf area density can vary with development of the stand. Therefore, we represent the vertical distribution of leaf area explicitly as fLA(t, z, h). The total mass of an individual, w, is given by w ¯ wnon­wleaf ¯

α 1 [exp (γh)®1]# h­ β#γ# s

&! f (t, z, h) dz, h

LA

(12)

where the second term represents the total mass of leaves of an individual and s denotes the specific leaf area.

for two-species plant communities [n ¯ 2 in eqn (1) with Di(t, x) ¯ 0] together with the canopy photosynthesis model, eqns (2)–(5). For investigating the vertical size-structure dynamics, we focus on the time development of plant height distribution density, fi(H)(t, h). ¦ fi(H)(t, h) ¦ ¯® [G(H) (t, h) fi(H)(t, h)] ¦t ¦h i ®Mi(H)(t, h) fi(H)(t, h) ; (i ¯ 1, 2).

(13)

(t, h) denotes the mean plant height increment per where G(H) i unit time of plant height h of species i at time t, Mi(H)(t, h) is the mortality rate, which is identical to eqn (6). The lack of the diffusion terms means that once a size class is eliminated (t, h) is determined from it cannot be restored. Function G(H) i the net photosynthetic production, Gi(t, w), derived by the canopy photosynthesis model, eqns (2)–(5) : (t, h) ¯ G(H) i

∆h ¬Gi(t, h), ∆w

(14)

and, from eqn (12), the factor ∆h}∆w is given by

0

1

−" ∆h α ¯ [exp (®γh)]¬[(1®2γh) exp (®γh)®1] . ∆w β#γ# (15)

The population density of species i at time t (the number of individuals of species i per unit ground area in the stand) is given by ρi(t) ¯

&

hmax

fi(t, h) dh ; (i ¯ 1, 2),

(16)

hmin

where hmin and hmax are the minimal and maximal plant height in the stand, respectively. As an initial condition, we used the following Gaussian function : fi(0, h) ¯

9

:

Ni, (h®hi, )# ! exp ® ! ; (i ¯ 1, 2), o2πσi,h 2σi,h

(17)

and a boundary condition : Simulation method In this paper, we neglect the diffusion term [the first term in the right-hand side of eqn (1)], which represents the effects of spatial heterogeneity and genetic variations on the growth and size-structure dynamics of a population, because we consider the population which grows in homogeneous conditions, where effects of the diffusion terms are assumed to be small, and we investigate only biological meanings of the relationship between competition processes and community dynamics. The presence of the diffusion terms makes the domain of species coexistence larger than the case of no diffusion terms (Hara, 1993 ; Yokozawa and Hara, 1995). Therefore, we use a continuity equation for time development of a plant population of each species. Hereafter, we deal with the system of a continuity equation model

fi(t, 0) ¯ 0 ; (i ¯ 1, 2),

(18)

where Ni, , hi, and σi,h represent the initial population ! ! density, the initial mean plant height and the standard deviation of plant height of species i, respectively. We do not incorporate recruitment processes, and investigate the effects of the growth dynamics of either saplings starting from different sapling banks (initial conditions) or trees in single-cohort stands with little continual establishment on the pattern of species coexistence. We solved the system of non-linear partial differential equations numerically by using the Lax–Wendroff scheme (e.g. Smith, 1985). Integrations involved in eqns (2)–(4) were performed by the spline integration method (e.g. Davis and Rabinowitz, 1984). Intervals for discretization were 0±2 m for plant height h and one time unit (day) for time t.

Yokozawa et al.—Crown Architecture and Species Coexistence Simulations were carried out by changing the following parameter values for two fixed values of the crown shape parameter, η ¯ 1±0 (conic-canopy plant, CCP) and η ¯ 5±0 (spheroidal-canopy plant, SCP) : extinction coefficient (ki), slope of light-photosynthetic rate curve at the origin (bi) with the fixed value of the ratio bi}ai ¯ 2, initial mean plant height (hi, ), initial standard deviation (σi,h). When changing ! parameter values for one species, those values of the other species were set at the ‘ standard values ’ given in Table 1. Simulations were conducted over the time interval from 0 to 500 time units (days).

RESULTS For investigating the coexistence between the two species, we defined the ‘ state ’ of species i as follows : species i survives if ρi(t ¯ 500) & 0±1¬Ni, ; otherwise, species i is ! excluded by interspecific competition, where ρi(t ¯ 500) is 1.4 1.2

1.2

1

1

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2 0.05 0.1 0.15 0.2 0.25 0.3 0.35

0 Extinction coefficient of SCPs

the population density of species i at t ¯ 500 time units (days) and Ni, is the initial population density of species i ! at t ¯ 0. In the present paper, we did not incorporate recruitment processes. Thus the two species will die out eventually as time tends to infinity (t ¯ approx. 1000 time units in our simulations). To assess the outcome of interspecific competition (survive or excluded), we give the results of the state of species at t ¯ 500 time units (almost the same results were obtained also at t ¯ approx. 800 time units). Figures 2 and 3 show phase diagrams for species coexistence between conic-canopy plants (CCPs) and spheroidal-canopy plants (SCPs) at t ¯ 500 time units. In Fig. 2, the parameter values of SCPs were changed with those of a CCP kept at the standard values (Table 1). There was a domain of coexistence for the lower values of the extinction coefficient (ki) and the slope of lightphotosynthetic rate curve at the origin (bi), and the domain area of coexistence decreased with an increasing initial mean

1.4 A

1.4 1.2

1.2

1

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0.8

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0.2 0.05 0.1 0.15 0.2 0.25 0.3 0.35

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0.05 0.1 0.15 0.2 0.25 0.3 0.35 E

0.05 0.1 0.15 0.2 0.25 0.3 0.35

0 1.4

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0.05 0.1 0.15 0.2 0.25 0.3 0.35

0

0.05 0.1 0.15 0.2 0.25 0.3 0.35

Slope of light-photosynthetic rate curve at the origin of SCPs (gCO2 W

–1

h–1)

F. 2. Phase diagram of coexistence between species with a spheroidal crown (spheroidal-canopy plants, SCPs) and those with a conic crown (conic-canopy plants, CCPs). The parameter values of SCPs were changed, while those of a CCP were fixed at the standard values given in Table 1. D, only SCPs survived ; +, SCPs coexisted with a CCP. Initial mean height of SCPs ¯ 1 (A), 3 (B), 5 (C), 7 (D), 9 (E) and 11 (F) m.

442

Yokozawa et al.—Crown Architecture and Species Coexistence 1.4

1.4 A 1.2

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0.8

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0.2 0.05 0.1 0.15 0.2 0.25 0.3 0.35

0 Extinction coefficient of CCPs

D

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0

0.05 0.1 0.15 0.2 0.25 0.3 0.35

0

0.05 0.1 0.15 0.2 0.25 0.3 0.35

0

0.05 0.1 0.15 0.2 0.25 0.3 0.35

Slope of light-photosynthetic rate curve at the origin of CCPs (gCO2 W

–1

h–1)

F. 3. As in Fig. 2. The parameter values of CCPs were changed, while those of a SCP were fixed at the standard values given in Table 1. D, only a SCP survived ; +, CCPs coexisted with a SCP. Initial mean height of CCPs ¯ 1 (A), 3 (B), 5 (C), 7 (D), 9 (E) and 11 (F) m.

plant height of SCPs. For the other parameter sets, only the SCPs survived and the CCP was excluded. In Fig. 3, the parameter values of CCPs were changed with those of a SCP kept at the standard values (Table 1). There is a domain of coexistence for the higher values of the extinction coefficient and the slope of light-photosynthetic rate curve at the origin for CCPs. For lower initial mean plant heights (i.e. SCPs in the upper canopy layer and a CCP in the lower canopy layer) and higher initial mean plant heights (i.e. a CCP in the upper canopy layer and SCPs in the lower canopy layer), the domain area of coexistence became large. Figure 4 shows the time courses of population density for each species. The results for the initial mean height of 5±0 m for both the SCPs and CCPs are given. In cases A and B, the two species coexisted at t ¯ 500 time units. In cases C and D, the two species did not coexist and the CCPs were excluded earlier than the SCPs. For all the cases, the population density of CCPs began to decrease earlier than that of SCPs.

For the case of coexistence, size structures for each species and vertical light profiles are shown in Figs 5 and 6. In Fig. 5, plant height distribution of SCPs became positively skewed, and the vertical layers of CCPs and SCPs were separated with an increasing difference in the initial mean size. In this case, the vertical light profile also changed with an increasing difference in the initial mean size. Light intensity reduced rapidly in the upper canopy layer when SCPs occupy the upper canopy layer. On the other hand, in Fig. 6, the plant height distribution of CCPs was positively skewed, and the vertical layer was not separated in all the cases. The light profile did not change with a difference in the initial mean size. In Fig. 5, a bimodal size distribution of a CCP appeared only in the case where the initial mean plant height of the CCP was 5±0 m and that of the SCP was 7±0 m (Fig. 5 D). On the other hand, in Fig. 6, bimodal size distributions of SCPs appeared in the case where the initial mean plant heights of SCPs were 1±0 m and 3±0 m and that of the CCP was 5±0 m (Fig. 6 A, B).

Yokozawa et al.—Crown Architecture and Species Coexistence 1.2

1.2

Population density (m–2)

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0.2

0

443

100

200

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400

500

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F. 4. Simulated time courses of the population density of each species. (——) SCPs ; (– – – – –) CCPs. A, bi ¯ 0±15 (slope of light-photosynthetic rate curve at the origin) and ki ¯ 0±4 (light extinction coefficient in the canopy) for a SCP in Fig. 2 C with the parameter values of a CCP fixed at the standard values given in Table 1 ; B, bi ¯ 0±2 and ki ¯ 0±8 for a CCP in Fig. 3 C with the parameter values of a SCP fixed at the standard values ; C, bi ¯ 0±25 and ki ¯ 1±0 for a SCP in Fig. 2 C with the parameter values of a CCP fixed at the standard values ; D, bi ¯ 0±1 and ki ¯ 0±4 for a CCP in Fig. 3 C with the parameter values of a SCP fixed at the standard values.

DISCUSSION If the initial mean size differs between the two species, it is assumed that a species of larger initial mean size established first}rapidly after a stand-replacement disturbance (e.g. fire ; Youngblood, 1995) and occupies the upper canopy layer of the stand (SCPs of initial mean height ¯ 7, 9, 11 m in Fig. 2 D, E, F and CCPs of initial mean height ¯ 7, 9, 11 m in Fig. 3 D, E, F), while the other species of smaller initial mean size established later}slowly and occupies the lower canopy layer (SCPs of initial mean height ¯ 1, 3 m in Fig. 2 A, B and CCPs of initial mean height ¯ 1, 3 m in Fig. 3 A, B). If the initial mean size is identical, the two species established concurrently and occupy the same canopy layer (Fig. 2 C and Fig. 3 C). In the simulations of Fig. 2, CCP’s parameter values were fixed, while those of SCPs were changed, in order to investigate how many SCPs having distinct physiological parameter values can coexist with the CCP in the upper (case 1 in Fig. 7 ; Fig. 2 A, B where SCP’s initial size ! CCP’s initial size) or lower (case 2 in Fig. 7 ; Fig. 2 D, E, F where CCP’s initial size ! SCP’s initial size) canopy layer. The domain of coexistence between the two species in case 1 was larger than that in case 2, indicating that various SCPs can establish later}slowly even if they are overtopped by a CCP which established first}rapidly. This suggests that the species diversity of SCPs can be high even in the lower canopy layer overtopped by a CCP. The result that the coexistence domain in case 2 was smaller than that in case

1 indicates that the species diversity of SCPs in the upper canopy layer, which can coexist with a CCP in the lower canopy layer, is limited. As the contrapositive proposition, if various SCPs established first}rapidly and occupy the upper canopy layer, a CCP can rarely establish later}slowly in the lower canopy layer, namely, if the species diversity of SCPs is high in the upper canopy layer, that of CCPs is low in the lower canopy layer. In the simulations of Fig. 3, SCP’s parameter values were fixed, while those of CCPs were changed, to investigate how many CCPs having distinct physiological parameter values can coexist with the SCP in the upper (case 3 in Fig. 7 ; Fig. 3 A, B where CCP’s initial size ! SCP’s initial size) or lower (case 4 in Fig. 7 ; Fig. 3 D, E, F where SCP’s initial size ! CCP’s initial size) canopy layers. In case 3, the coexistence domain became larger with a decreased initial mean size of the CCP. This indicates that the smallest-sized CCPs can persist well in the lowermost canopy layer when overtopped by a SCP. This suggests a waiting strategy of conifers in the understorey of a crowded stand, which was found by Kubota, Konno and Hiura (1994) in a sub-boreal conifer– hardwood forest in Hokkaido, northern Japan. In case 4, a larger coexistence domain was realized with an increase in the CCP’s initial size. This suggests that even if various CCPs established first}rapidly and occupy the upper canopy layer, a SCP can establish later}slowly in the lower canopy layer. Case 2 predicts that the species diversity of SCPs which established first}rapidly and occupy the upper canopy layer limits the number of CCP species which can establish

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F. 5. Simulated plant height distribution densities for the coexisting species at t ¯ 500 time units (d) where the initial mean plant height of SCPs was changed (——) with that of CCPs (– – – – –) kept at 5±0 m. Light intensity profiles in the stand at t ¯ 500 time units (d) (— – —). For the SCPs, bi ¯ 0±15 and ki ¯ 0±4 ; the parameter values of the CCPs were fixed at the standard values given in Table 1. The initial mean plant height of SCPs was set at : A, 1±0 m ; B, 3±0 m ; C, 5±0 m ; D, 7±0 m ; E, 9±0 m ; F, 11±0 m.

later}slowly. In contrast, case 4 predicts that the species diversity of CCPs which established first}rapidly and occupy the upper canopy layer does not affect the number of SCP species which can establish later}slowly. We showed that the size-structure dynamics of individuals of CCPs and SCPs changed with both initial mean size (height) and physiological parameters (Figs 5, 6). The initial size distribution assumed in the model corresponds to the structural attributes of seedling or sapling banks after natural disturbances such as fire and wind, and the differences in physiological parameter values represent the functional diversity of species. Investigating the effects of initial mean size and physiological traits of the two species on community dynamics, we derived the four predictions for the coexistence pattern between CCPs and SCPs either at the sapling stage or in single-cohort stands without continual establishment of the species (Fig. 7). The combination of initial sizes at the establishment stage of the two species with different crown architecture affected the segregation of vertical positions in the canopy between the two species. The species coexistence pattern of the CCPSCP system is governed by functional relationships between

species-specific crown architecture, physiological traits and establishment timing (in terms of initial size in the model). Youngblood (1995) found two types of community dynamics after stand-replacement disturbance in singlecohort conifer–hardwood forests at the intermediatesuccessional stage in interior Alaska, although no discernible difference in associated vegetation or site characteristics was detected between the stands of these two types : in stands of type 1, hardwoods and conifers establish concurrently or conifers establish first}rapidly followed by hardwoods ; in stands of type 2, hardwoods establish first}rapidly followed by conifers. In stands of type 1, little suppression in height growth was found for both the conifer (Picea glauca) and hardwoods (Betula papyrifera and Populus tremuloides). On the contrary, in stands of type 2, height growth of the conifer was suppressed by the hardwoods. Youngblood (1995) thus predicted that the stands of type 1 would be eventually dominated by P. glauca as described for latesuccessional P. glauca stands in boreal forest (Van Cleve and Viereck, 1981) and that in the stands of type 2 P. glauca would never be dominant without reaching up to the top canopy. A conifer and a hardwood in a boreal or sub-boreal

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F. 6. As in Fig. 5. In this case, the initial mean plant height of CCPs (– – – – –) was changed with that of SCPs (——) kept at 5±0 m. Light intensity profiles in the stand at t ¯ 500 time units (d) (— – —). For the CCPs, bi ¯ 0±2 and ki ¯ 0±8 ; the parameter values of SCPs were fixed at the standard values given in Table 1. The initial mean plant height of CCPs was set at : A, 1±0 m ; B, 3±0 m ; C, 5±0 m ; D, 7±0 m ; E, 9±0 m ; F, 11±0 m.

mixed-species forest can be assumed to have conic and spheroidal crowns of the present model, respectively. However, precisely speaking, the conifers and hardwoods cannot always be assumed to be the CCPs and SCPs in the present model, respectively, because the boreal}sub-boreal hardwoods are deciduous while most conifers are evergreen [but photosynthetic production of conifers during the winter is almost zero (Tranquilini, 1979), suggesting little difference between deciduous and evergreen plants in the length of photosynthetically active period]. The community dynamics of type 2 stands in Youngblood (1995) are similar to our theoretical predictions, case 2 or case 3, and those of type 1 to case 1 or case 4. There may be differences in nutrient conservation and foliage replacement costs between conifers and hardwoods. It is, however, possible that these effects on species coexistence are small as compared with the effect of crown architecture. This is a problem to be investigated. Kubota and Hara (1996) found that saplings of Picea glehnii, P. jezoensis and Abies sachalinensis (all conifers) had deep conic and shallow flat crowns, respectively, in a subboreal forest. They also found that A. sachalinensis saplings

suppressed the growth of P. jezonensis saplings one-sidedly but that the growth of A. sachalinensis saplings was not affected by P. jezonensis saplings. These results also correspond to our theoretical predictions. Whether a P. jezonensis-dominated or A. sachalinensis-dominated sapling stand (Kubota and Hara, 1996) emerges depends on the initial conditions at sapling establishment. Many studies have investigated mainly species-specific physiological traits (shade tolerance, maximum size, photosynthetic rate, etc.) for species coexistence focusing on the trade-offs of these traits between species. The present paper shows that not only the species-specific physiological traits but also the crown architecture is important for the pattern of species coexistence. Even for the same combination of physiological parameter values, the pattern of species coexistence differs depending on the crown architecture. We should therefore include also the crown architecture for the study of species coexistence, especially in plant communities composed of species with different crown architectures, for example, conifer–hardwood sub-boreal and boreal forests.

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F. 7. Schematic diagrams for the coexistence between conic canopyplants (CCPs) and spheroidal-canopy plants (SCPs). Case 1, SCPs with various physiological parameter values can establish later}slowly in the lower canopy layer even if a CCP with the fixed parameter values established first}rapidly and overtops the SCPs ; case 2, a CCP with the fixed physiological parameter values can rarely establish later}slowly in the lower canopy layer if SCPs with various physiological parameter values established first}rapidly and overtop the CCP ; case 3, smallestsized CCPs with various physiological parameter values can persist well in the lowermost layer even if a SCP with the fixed physiological parameter values established first}rapidly and overtops the CCPs ; case 4, a SCP with the fixed physiological parameter values can establish later}slowly in the lower canopy layer even if CCPs with various physiological parameter values established first}rapidly and overtop the SCP.

ACKNOWLEDGEMENT This study was partly supported by grants from the Ministry of Agriculture, Forestry and Fisheries, and the Ministry of Education, Science and Culture, Japan. We thank Dr D. King for valuable comments. Numerical calculations were performed on the CONVEX-C3820 of the Computing Centre for Research in Agriculture, Forestry and Fishery. LITERATURE CITED Armstrong RA. 1990. A flexible model of incomplete dominance in neighborhood competition for space. Journal of Theoretical Biology 144 : 287–302. Armstrong RA. 1993. A comparison of index-based and pixel-based neighborhood simulations of forest growth. Ecology 74 : 1707–1712. Cogbill CV. 1985. Dynamics of the boreal forests of the Laurentian Highlands, Canada. Canadian Journal of Forest Research 15 : 252–261. Davis PJ, Rabinowitz P. 1984. Methods of numerical integration. Second edition. London : Academic Press. Fujimoto S, Hasegawa S, Shinoda S. 1991. Difference between tree species in stem survival potential to volcanic ash and pumice

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