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Positive scaling of mass-density (M-N) relationship under harsh environments
Bing-Ru Liu1, Dong-Liang Cheng2, Gen-Xuan Wang3
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(1 Key Laboratory of Arid and Grassland Agroecology at Lanzhou University, Ministry of
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Education, Lanzhou 730000, China;
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2College
of Geographical Science, Fujian Normal University, Fuzhou 350007, China;
3College
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of life science, Zhejiang University, Hangzhou 310029, China)
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Author
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Tel: +86 (0)571 8697 1083;
for correspondence:
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Fax: +86 (0)571 8697 1083
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Email: wanggx@zju.edu.cn
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*Supported by the National Natural Science Foundation of China (90102015, 30170161).
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Received: 7 Jan. 2007
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Accepted: 23 Apr. 2007-
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Handling editor: Da-Yong Zhang
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Abstract
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Relationship between body size and population density is one of the most
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fundamental aspects of population biology. Traditional studies indicate that plant
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biomass (M) is often negatively related with density (N), which is based on
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competition among plant individuals, and to some extent, is suitable to explain plant
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dynamics in benign situations. However, it fails to explain in harsh environments. We
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used the published data of Usoltsev (2001) and Bondarev (1997), as well as the data
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we collected in Minqin, northwest of China, to test the M-N relationship under hash
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environments. The results indicated that the value of the scaling exponent for the
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aboveground biomass vs. density was 1.19 for Larix gmelinii in Central Siberia, and
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1.87 for Artemisia arenaria in Minqin. The data showed that positive scaling
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exponents were yielded under harsh environment, and decreased with the
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improvement of abiotic conditions. It implied that the positive interactions among
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individuals might improve the utility efficiency of space. It also indicated that the
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energetic equivalence rule (EER) was not applicable to all species under all growth
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conditions. Furthermore, new and appropriate approaches should be developed to
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investigate M-N relationship under different limited resources or stress conditions, in
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order to properly understand M-N relationship.
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Key words Energy equivalence rule, environmental gradient, harsh environment,
mass-density relationship, positive interactions, positive scaling exponents.
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Relationship between body mass and density is one of the most fundamental
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aspects of population biology, and it has major implications for the structure of
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ecological communities (Brown 1995; Damuth 1998). In an even aged monospecific
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plant population, when M (biomass) and N (density) are assumed to represent two
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variables, respectively, this relationship is usually modeled as:
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M=KNλ or logM = logK +λlogN
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Where M and N are the average weight and real density of surviving individuals,
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respectively, K and λ are the constant and the scaling exponent (slope of M-N
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relationship), respectively (Yoda et al. 1963). If averaged body mass per plant plotted
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against density, this relationship becomes: m = kN γ, where the scaling exponent, γ =
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(λ - 1).
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Among a series of studies of M-N relationship for 30 years, one of controversial
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topics was the value of λ. Some workers proposed that λ was invariable regardless the
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changing of abiotic conditions (White and Harper 1970). Theoretical justifications of
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self-thinning have been reported that the classical exponent equals to -1/2 for plants
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was suggested in a crowded monoculture (Yoda et al. 1963; Westoby 1984; White
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1985; Lonsdale 1990; Yastrebov 1996) or mixed stand (Westoby 1984). The usual
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explanation of self-thinning law has been largely based on geometric properties of
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individual plant (Yoda et al. 1963; Westoby 1984; White 1985; Lonsdale 1990), and it
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was thought that a slope (λ) of −1/2 applied to all of the species within the plant
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kingdom (the intercept value, log K, was less clear)( Scrosati 2005). Theoretically, the
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previous prediction of a universal slope of −1/2 was based on the assumption that
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plants maintain the same shape (isometric growth) during self-thinning, which is now
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known to be unrealistic (Weller 1987b), therefore, its validity is still in doubt (Weller
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1987a; Zeide 1987). Hence, dynamic M-N relationships should be calculated (when in
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the linearized, log-log form) through a Model II regression technique (such as
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principal components analysis or reduced major axis), since the Model I regression
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technique of least squares linear regression should not be used for this purpose, which
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assumes that the X variable (N, in this case) should be fixed (Weller 1987a; Sokal and
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Rohlf 1995).The shallower (than −1/2) nature of the interspecific biomass-density
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slope is independently supported by a theoretical model based on trends in plant
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geometry across the plant kingdom (Weller 1989). More recent theoretical models
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based on morphological and physiological considerations specifically predict a slope
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of −1/3 for the IBDR (Enquist et al. 1998; Franco and Kelly 1998), which coincident
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with Weller’s (1989) empiric findings. And some authors proposed that the exponent
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(λ) was ought to be -1/3 for all plant species, expressing as M∝N-1/3 (West et al. 1999;
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Brown et al. 2004). This value is based on the fractal-like construction of internal
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resource distribution networks (Enquist et al. 1998; West et al. 1999). In contrast， a
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number of investigations reported that λ is closely depended on usually regulated by
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abiotic or biological factors (Yoda et al. 1963; Weller 1987a; White and Harper 1970;
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Ford 1975; Osawa 1995). Some abiotic factors, such as light, water, nutrition and
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temperature, can affect the λ directly (Thomas and Weiner 1989; Morris 1999;
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Callaway). Leaf area also intensively influenced λ, which varied around -1/2 (Osawa
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and Allen 1993; Osawa 1995), and increased λ is also observed when the light is
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weakened (Hiroi and Monsi 1966; Dunn and Sharitz 1990), or the provision of
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nutrition is decreased (Zeide 1987; Morris 2003). In a word, the variation of λ can be
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explained by the argument that intensity of competition changed along with the
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changing resource level (Morris 1999).
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It is generally believed that M-N relationship occurs and appears to be the
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consequence of negative interactions between individuals, i.e. competition for space,
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and λ will change with the variation of interaction among plant individuals (Morris
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and Myerscough 1991; Morris 1999). More recently, experimental studies have
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discovered that plant interaction may vary along the environmental gradient, and
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positive effects can emerge among plant individuals under stressful environments
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(Bertness and Callaway 1994; Callaway and Walker 1997). Positive interactions, or
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facilitation, occur when one individual ameliorates stressful abiotic or biotic
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conditions for another (Bruno and Bertness 2001). Field investigations from a wide
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variety of habitats not only have demonstrated the strong effect of facilitation on
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individual fitness, population distributions and growth rates, species composition and
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diversity, and even landscape-scale community dynamics (Callaway 1995; Bruno and
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Bertness 2001), but also have indicated that positive interactions are likely to be as
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ubiquitous as competitive interactions (Callaway 1995; Hector et al. 1999; Tewksbury
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and Lloyd 2001). Bertness and Callaway (1994) hypothesized that the importance of
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facilitation in plant organization increased with abiotic stress while the relative
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importance of competition decreased. Complex combination of the effects of
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competition and facilitation operating simultaneously among plant species appears to
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be the rule in nature (Pugnaire and Luque 2001). Obviously, M-N relationship based
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on competition seems to be suitable to explain plant dynamics in benign situations,
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but when it comes to plants in harsh environments, it will fail to do that.
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In physically harsh environments such as salt marsh, desert, and alpine habitats,
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where resource is inadequate, benefits provided by a tougher neighbor may be more
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likely to favor growth than competition with that tough neighbor is likely to reduce
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growth. The net effect of plant interactions is frequently measured as the ratio of some
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performance variables, usually the ratio biomass between individuals with and
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without removing their neighboring plants. The relative interaction index (RII), one
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way to describe the net effect of plant interaction, is expressed in the following
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equation (Armas et al. 2004):
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RII = (Bw-B0 ) / (Bw+B0 )
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Where Bw (high density) is the mass of plants with neighbors and Bo (low density)
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is the mass of isolated individuals. RII has defined limits [−1, +1], it is symmetrical
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around zero with identical absolute values for competition and facilitation,
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Competition prevails when 0≤Bw< B0< +∝ while facilitation prevails when 0≤B0 <
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Bw < +∝, when there is no interaction or the outcome is neutrals, Bw= B0. Evidently,
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RII > 0 indicated the positive interactions and positive relationship between body
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mass and density. Presumably then, the scaling exponent of M-N relationship will
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change with abiotic gradient, and the positive value would appear under the stressful
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situations.
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In this paper, we prediction that the λ is positive under harsh environments by
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establishment the M-N relationships of Gmelin larch (Larix gmelinii (Rupr.)) forests
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and desert shrub species (Artemisia arenaria DC.), which are all natural communities
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growing under extremely harsh environments, and the scaling exponent in plant
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communities varied along environmental gradients.
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Results
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The relationship between aboveground biomass and population density for two
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natural populations were shown in Fig. 1. For L. gmelinii (Fig. 1A), the regression
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equations shown are logM = 4.36 + 1.19 logN. The RMA regression indicated a
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scaling exponent of 1.19 with 95% confidence interval (CI，0.96-1.51) and an
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intercept 4.36 with 95% CI (4.11-4.78) in the poorest site Va-Vb(●) (R2=0.51,
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P<0.0001). While the scaling exponent was zero at site index V(×) and I-IV(△).
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For A arenaria (Fig. 1B), the regression equations shown is logM = 2.30 + 1.87
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logN. It indicated a scaling exponent of 1.87 with 95% CI (1.60 to 2.23) (P < 0.0001;
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R2=0.60).
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Discussions
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Trees provide an ideal opportunity to test the plant M-N relationship and energy
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equivalence rule for the plant communities (Niklas et al. 2003). Data for L. gmelinii
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growing in permafrost soil of Central Siberia were anomalous in having positive λ for
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the aboveground biomass and density (Fig. 1A). The data in which biomass decreased
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as density declines have been observed before, but dismissed as the results of
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catastrophic events, such as lodging of surviving plants, or pathogenic epidemics,
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both of which are examples of substantial density-independent mortality (Westoby
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1984). Neither lodging nor extensive pathogenic attack occurred in our studies. In
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addition, competition-density effect (C-D effect) (Kira et al. 1953; Hagihara 1999)
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also suggests a positive scaling. When population density was the only variable, and
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all other factors were held constant experimentally, nearly all populations followed
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the relationship M=kNλ, where λ varied between 0 and 1. Although C-D effect has the
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same mathematical expression as M-N relationship, it presents different ecological
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meaning. C-D effect describes a temporal variation of density during the growth until
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the appearance of density-dependent mortality; M-N relationship shows a spatial
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variation of density at mature populations once mortality commences. L. gmelinii
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experienced dramatically density-dependent mortality in population growth. For
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example, population density varied from more than 200 no. /m2 for juveniles to less
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than 0.4 no./m2 for mature stands. More important, scaling exponents of L. gmelinii
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was different with other studies carried out in trees-dominated communities.
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Numerous studies have shown that the basic allometric relationships, aboveground
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biomass scaled as the -1/3 power of stand density, surprisingly varied slightly with
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species diversity, total standing biomass, latitude and geographic sampling in area
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(Enquist et al. 1999; Whittaker 1999; Enquist and Niklas 2001). Therefore, it is not
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surprised that positive scaling might demonstrate positive interactions among
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individuals of L. gmelinii. It’s assumed that this positive relationship between body
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mass and density is based on resource limitations. As conceptualized by Callaway et
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al. (2002) for shifts in positive interactions on elevation gradient, we believe that
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temperature and nitrogen content in soil are less limiting to plant growth at benign
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environments, but continuous permafrost temperature and lower nitrogen limit plant
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growth. Amelioration of these severe stresses via facilitation by neighboring
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individuals indicated a positive relationship, rather than competition for shared
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resource, which resulted in a negative relationship.
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This positive pattern of M-N relationship should be common not only in permafrost
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but also under other stressful environments. A. arenaria in desert of northwest China
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indicated that λ is 1.87, which is higher than the boundary of C-D effect (Fig. 1B).
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This may be likely caused by the positive interactions in relatively high density. The
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physical stress of desert plant communities is severe and stress gradients arise with
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variation in water availability or fertility (Tewksbury and Lloyd 2001). Accordingly,
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positive interactions are thought to be of great importance in arid and semi-arid areas
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(Whitford 2002). Tirado and Pugnaire (2003) pointed out that high adult plant density
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would significantly increased plant product, such as flower and fruit, and showed a
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higher mass of seeds as a result of enrichment in patches. In addition, plants showed
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an increasing aboveground biomass through aggregation (Stoll and Prati 2001), and a
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positive feedback between body mass and soil water (Wilson and Agnew 1992). The
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more soil water the faster the plant growth, and the larger the plant the more soil
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water available to it.
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How positive interactions induce positive scaling? We hypothesized that the
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possible mechanism was yielded by the spatial utility. In a crowded population under
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benign environment, the aboveground competition for space was sufficient enough to
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maintain a constant leaf area index (LAI), which resulted in a negative relationship
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between body mass and density (Hutchings and Budd 1981; Osawa and Allen 1993).
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However, when the limited resource was not space but nutrients, moisture or
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temperature, the LAI changed as resource level varied, which led to the deviation
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from a slope of -1/2 (Hamilton et al. 1995). Under stressful environments (e.g. our
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study sites), space was not fully occupied by plants, and the surplus space did not
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contribute to the accumulation of aboveground biomass. The positive interactions
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among individuals might improve the utilization of space, which will lead to a
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positive M-N relationship.
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The scaling exponent of M-N relationship is often closely related with the energetic
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equivalence rule (EER). This rule states that the amount of energy that each
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population uses per unit of area is independent of its mean body size. This is a
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consequence of estimating an empirical slope of –3/4 for the relationship between
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density and mean mass per plant (m), and a slope of 3/4 for the relationship between
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metabolic requirement (B) and m (Enquist et al. 1998), combining the two allometric
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equations results in a zero exponent of population energy use (PEU) in relation to m.
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Since depending on the λ = -1/3, EER can be tested by the scaling exponent of M-N
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relationship. Although it has been shown to hold at local, regional and worldwide
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scales for tree-dominated communities, and has been hypothesized to emerge from the
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allometric rules that influence the behavior of individual plant species competing for
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space and limiting resources (Enquist and Niklas 2001), it is important to note that
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EER does not imply that PEU of a pure species is invariable with body mass, in part
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because the mean for MS-1/3 (MS: multi-species) does not equal SS-1/3 (SS:
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single-species). Firstly, some workers investigating in forest indicated that λ varied
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around -1/2 (Osawa and Allen 1993; Osawa 1995). In a forest stand thinning along a
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slope of -1/2, Ford (1975) observed that the dominant trees showed a slope of -0.9.
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Secondly, Carbone and Gittleman (2002) predicted that variation in local resource
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supply rate naturally limited population density and may alter expected scaling pattern.
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It was tested that the same species on the sites of different resource levels would lead
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to apparent differences in the scaling exponents (Hiroi and Monsi 1966; Dunn and
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Sharitz 1990; Morris and Myerscough 1991; Morris 1996). To explore the effects of
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fertility levels on the scaling exponent of M-N relationship, Morris (1996) had shown
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evidence that λ increased with decreasing fertility, and was positive under the lowest
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site (Fig. 2A). Zhen et al. (1997) investigated the scaling exponent between average
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aboveground biomass and density of Picea mongolica in Tengger Desert, and
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indicated that γ increased as the soil water content declined (Fig. 2B). Finally, our
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data showed that positive scaling exponents were yielded under harsh environment,
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and decreased with the improvement of abiotic conditions (Fig. 1). Considered
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together, these analysis demonstrated strong shifts from negative M-N relationship in
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benign environments (-1/2 or -1/3) to positive under extremely stressful environments,
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and different M-N relationships reflected variations in plant interaction in stands along
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environmental gradients within the one species (Morris 1999). Hence, EER was not
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applicable to all species under the all growth conditions.
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The positive scaling might be attributed to the improvement of spatial utility
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efficiency caused by the positive interactions. In that case, the size of an individual
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would increase with density because of the positive effect of the neighboring plants.
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Our study contributed to understanding the M-N relationships under harsh
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environments. However, it was far from providing a real explanation, and new and
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adequate approaches should be developed to investigate M-N relationship under
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different resource-limited or stress conditions.
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Materials and methods
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The Gmelin larch (Larix gmelinii (Rupr.)) forest ecosystems located in the northern
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half of Krasnoyarsk Region in Central Siberia (64o19′-71oN, 100o13′E) with 200 m
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elevation and about 322 mm annual mean precipitation, which is the only forest
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biome in the world where the continuous permafrost lies across most of their
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distribution ranges (Bondarev 1997). Ecosystem type was larch forest ecosystems on
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continuous permafrost, and characteristics of the forests in these regions were
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described in detail elsewhere (e.g. Bondarev 1997; Osawa et al. 2000). Combined
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effect of nitrogen limitation and low soil temperature results in an extremely stressful
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region for forest (Osawa et al. 2003).
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The second experiment site located in southeast of Minqin County (39o06′N,
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104o02′E, 1707 m elevation), on the eastern edge of oasis-desert ecotone of Minqin,
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northwestern of China, which is adjacent to the Tengger Desert with mobile,
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semi-mobile, and static dunes. The study area is characterized by the arid continental
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monsoon climate with strong northwest wind from Hexi Corridor in winter and spring
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(Xu 1995). Average annual temperature is 7.6 ℃. Mean precipitation is 110 mm, with
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most of it occurring from July to September while estimated potential
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evapotranspiration is about 2 664 mm. The annual evaporation is nearly 24 folds of
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the annual precipitation. The mineralization degree of water quality is 8-10 g· L - 1 and
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groundwater is buried at 17 m underground ((Ma et al. 2003). In recent years, Minqin
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has been threatened by desertification and became a typical location with shrinkage of
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vegetation along the desert fringes of China (Ma et al. 2003). As affected
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continuously by the evident descent of the underground water table and the rise of the
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soil saline degree for past 40 years, a great multitude of seeds of wood and shrub
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plants could not survive for renewal, especially the number of A. arenaria declined
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obviously, while a xerphilization shrub plant Nitraria tungutorun has progressively
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emerged, which will develop into their prosperity period and form climax desert plant
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species under trend of succession (Yang 1995, 1999). At present environmental
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deterioration has led to an extremely stressful region for growth and reproduction of
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desert shrub A. arenaria.
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The data of L. gmelinii from 118 grime in larch stands were analyzed using the
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published data of Bondarev (1997) (40 stands) and Usoltsev (2001) (78 stands). These
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data were divided into three categories: site indices I-IV presented relatively better
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conditions, site index V was somewhat worse than in indices of I-IV, and Va-Vb
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presented the poorest site condition, respectively (Usoltsev 2002, see Fig 1). The data
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of A. arenaria were collected in July 2004 at Minqin site. The quadrates of 4m×4m
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were randomly selected in 34 even-aged pure stands across the study area. In each
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sample quadrates, the number of individuals (density) was measured, and the
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aboveground biomass was harvested at ground level, then oven-dried at 80℃ for 48 h,
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and weighed.
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The M-N relationship was evaluated by the reduced major axis (RMA) regression
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of log-transformed data, using RMA 1.17 (Hamilton et al. 2004; http://www.bio.sdsu.
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edu/pub/andy/RMAmanual.pdf).
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Acknowledgements
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We sincerely appreciated A. Osawa for providing helpful information，and L.
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Niklas and Yan-Jiang Luo for making comments to this paper. We also thank the two
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anonymous reviewers for helpful comments on the manuscript. We acknowledge the
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support of National Natural Science Foundation of China (90102015, 30170161).
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1
Figure legends:
2
3
4
5
6
7
Figure 1 Relationship between aboveground biomass and population density for two natural
populations (data from Morris 1996).
(1A) Larix gmelinii. The regression equations shown are log M = 4.36+1.19 log N in Va-Vb (●).
The scaling exponent in I-IV(△) and V (×) were zero (P < 0.0001; R2=0.51). (1B) Artemisia
arenaria. The regression equation shown is log M = 2.30 + 1.87 log N by RMA regressions of
log-transformed data (P < 0.0001; R2=0.60).
8
9
10
11
12
13
14
15
16
Figure 2 Relationships between regression slopes for the aboveground biomass with density and
abiotic conditions (data from Zhen et al. 1997).
(2A) Ocimum basilicum. Three fertility levels significantly influenced the scaling exponents: λ
increased as the fertility levels declined. The scaling exponent of aboveground biomass and
density was -0.5, 0 and 0.94 at F2, F1 and F0 fertility level, respectively. (Morris 1996). (2B)
Picea mongolica. The scaling exponent of average aboveground biomass and density increased as
soil water content declined in Tengger Desert. γ was -0.91, -1.16 and -1.30 at 5.1%, 17.1% and
31.5% soil water content, respectively.
17
18
19
20
21
22
19
10000
2
Aboveground biomass (g/m )
1A
1000
100
Site index I-IV
Site index V
Site index Va-Vb
10
1E-3
0.01
0.1
1
2
Stand density (no./m )
1
1B
2
Aboveground biomass (g/m )
100
10
1
0.1
0.1
1
2
Stand density (no./m )
2
3
4
5
6
7
8
Figure 1 Relationship between aboveground biomass and population density for two natural
populations (data from Morris 1996).
(1A) Larix gmelinii. The regression equations shown are log M = 4.36+1.19 log N in Va-Vb (●).
The scaling exponent in I-IV(△) and V (×) were zero (P < 0.0001; R2=0.51). (1B) Artemisia
arenaria. The regression equation shown is log M = 2.30 + 1.87 log N by RMA regressions of
log-transformed data (P < 0.0001; R2=0.60).
9
10
11
20
1.2
2A
1.0
Scaling Exponent (M-N)
0.8
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
F0
F1
F2
Fertility Levels
1
-0.90
2B
-0.95
Scaling Exponent (m-N)
-1.00
-1.05
-1.10
-1.15
-1.20
-1.25
-1.30
-1.35
-1.40
0
5
10
15
20
25
30
35
Soil Water Content (%)
2
3
4
5
6
7
8
9
10
Figure 2 Relationships between regression slopes for the aboveground biomass with density and
abiotic conditions (data from Zhen et al. 1997).
(2A) Ocimum basilicum. Three fertility levels significantly influenced the scaling exponents: λ
increased as the fertility levels declined. The scaling exponent of aboveground biomass and
density was -0.5, 0 and 0.94 at F2, F1 and F0 fertility level, respectively. (Morris 1996). (2B)
Picea mongolica. The scaling exponent of average aboveground biomass and density increased as
soil water content declined in Tengger Desert. γ was -0.91, -1.16 and -1.30 at 5.1%, 17.1% and
31.5% soil water content, respectively.
11
21