Spatial species diversity in temperate species-rich forest ecosystems: Revisiting and extending the concept of spatial species mingling

Ecological Indicators 105 (2019) 116–125

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Spatial species diversity in temperate species-rich forest ecosystems: Revisiting and extending the concept of spatial species mingling

T

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Arne Pommereninga, Arvid Svenssona, Zhonghua Zhaob, Hongxiang Wangc, , Mari Myllymäkid a Swedish University of Agricultural Sciences SLU, Faculty of Forest Sciences, Department of Forest Ecology and Management, Skogsmarksgränd 17, SE-901 83 Umeå, Sweden b Research Institute of Forestry, Chinese Academy of Forestry, Key Laboratory of Tree Breeding and Cultivation, State Forestry Administration, Box 1958, Beijing 100091, China c College of Forestry, Guangxi University, Nanning 530004, China d Natural Resources Institute Finland (Luke), Latokartanonkaari 9, FI-00790 Helsinki, Finland

A R T I C LE I N FO

A B S T R A C T

Keywords: Spatial species diversity Species mingling Species diversity maintenance Temperate natural forest Species-rich woodland community Point process statistics

Species rich woodland communities play an important role in ecosystem functioning at local, regional and global scale. With ongoing climate change and an ever-increasing human world population we certainly cannot take high species diversity for granted. In fact species diversity is a precious and threatened commodity that requires monitoring and conservation. China has a wealth of natural woodlands with high species diversity that stretch over several climate zones and even in the temperate zone tree diversity is considerable in this country. For monitoring species diversity it is crucial to rely on meaningful summary characteristics that offer sufficient information to make correct decisions in conservation. We analysed large, fully mapped plots from ten speciesrich temperate forest sites with the new species segregation function as a significantly more meaningful extension of the traditional spatial species mingling index. The new characteristic is a function of distance and we defined a number of auxiliary measures describing its shape for a more effective analysis of spatial species diversity. We could show that these auxiliary characteristics helped to classify species-rich forests as part of a cluster analysis, which supports the view that the species segregation function provides high quality information. We also successfully applied non-parametric modelling through spatial reconstruction for testing the contribution of the species segregation function to a synthesis of observed spatial species diversity patterns. The results demonstrated that the new characteristic described the complex diversity patterns well and has the potential of being a robust and effective characteristic in monitoring species-rich woodland communities.

1. Introduction Many natural forest ecosystems, particularly in tropical and subtropical climate zones, are very rich in tree species. At the same time species diversity has been considered one of the most important aspects of biodiversity (Kimmins, 2004). Worldwide conservation is concerned with maintaining species diversity or at least with slowing down the process of losing species (Carvalheiro et al., 2013). China’s forest ecosystems range from tropical to boreal forest ecosystems and are particularly rich in tree species even in the temperate zone (Fan et al., 2017; Wu et al., 2017). The quantitative description of species diversity in such ecosystems is a particular challenge. However, it is a pre-requisite for understanding the principles of natural maintenance of species diversity (Janzen, 1970; Connell, 1971; Wills et al., 1997) and subsequently for translating research findings into

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sustainable management practices both for conservation and timber production (Li et al., 2014). Most importantly, appropriate quantification methods are particularly crucial in times of considerable species diversity loss to ensure an effective monitoring of the dynamics involved (Turnbull et al., 2016). An important process in plant communities is interaction between individual plants. Grimm and Railsback (2005) coined the term individual-based ecology, focussing on the mechanistic understanding of plant interactions. Here spatial relationships and spatial scale play a particular role. In the same way, the concept of species mingling of plants (Gadow, 1993; Rajala and Illian, 2012) extends beyond the ideas of species richness and species abundance by taking the individual’s perception of local diversity into account. Species mingling is based on the neighbourhood concept, which plays a vital role in plant ecology (Pommerening and Uria-Diez, 2017).

Corresponding author. E-mail addresses: [email protected] (A. Pommerening), [email protected] (H. Wang).

https://doi.org/10.1016/j.ecolind.2019.05.060 Received 6 November 2018; Received in revised form 26 April 2019; Accepted 21 May 2019 1470-160X/ © 2019 Elsevier Ltd. All rights reserved.

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forest of Juglans mandshurica and Fraxinus mandshurica. The main species include Fraxinus mandshurica RUPR., Juglans mandshurica MAXIM., Carpinus cordata BL., Ulmus davidiana var. japonica (REHD.) NAKAI. and Pinus koraiensis SIEB. ET ZUCC. Historically this region belonged to the experimental forest farm of Jilin Forestry College and forest management ceased 60 years ago. The current tree dispersion patterns can be regarded as the result of natural processes. The four forest plots in this region are highly mixed and have a tightly closed canopy with around 20 tree species. Jiulongshan Forest is located in the western suburbs of Beijing. This is a warm-temperate broadleaved deciduous forest with planted pine species as the main tree species. The study area is located at approximately 39°57′°N and 116°05′°E. Mean annual rainfall is 623 mm, occurring primarily between June and September. Mean annual temperature is 11.8 °C and the soil is a typical mountain brown soil with a thin soil layer and high stone content. Two stands from this secondary mixed forest were included in our study, i.e. JSa and JSb. The first stand is dominated by planted Platycladus orientalis (L.) FRANCO and is mixed with some naturally regenerated species such as Quercus variabilis BLUME, Broussonetia papyrifera (L.) VENT., Ailanthus altissima (MILL.) Swingle, Prunus davidiana CARR. and Gleditsia sinensis LAM. The second stand represents a mixed forest stand planted with Pinus tabuliformis CARR. and Larix principis-rupprechtii MAYR. as main species. The forest was originally planted and had some light thinnings in the past. Compared with the other two forest areas, Jiulongshan Forest most closely resembled the structure of managed forests with a regular dispersion pattern. Xiaolongshan Forest is situated in the warm temperate-subtropical transitional zone of the north-facing slopes of the Qinling Mountain Range. The area is located at approximately 33°30′ ∼ 34°49′°N and 104°22′ ∼ 106°43′°E and is a mixed pine and oak forest. The study area’s mean annual rainfall is 600–900 mm, mean annual temperature is between 7 and 12 °C. The zonal soil is grey cinnamon soil in the north of Qinling Mountains, and in the south yellow cinnamon soil prevails. Four plots from the Xiaolongshan Forest were included in this study. The first stand, denoted as XSa, has to a large extent been shaped by natural processes. However, Structure-Based Forest Management (Li et al., 2014) has been carried out here to diversify stand structure. The forest labelled as XSa is a mixed pine-oak forest with more than 30 tree species, mainly composed of Quercus aliena var. acuteserrata MAXIM., Pinus armandii FRANCH., Dipteronia sinensis OLIV., Ulmus glabra HUDS. and Symplocos paniculata (THUNB.) WALL. EX D. DON. The second stand (XSb) has been left unmanaged and is completely natural. XSb is also a mixed pine-oak population with 30 tree species, mainly Quercus aliena var. acuteserrata MAXIM., Ulmus glabra HUDS., Symplocos paniculata (THUNB.) WALL. EX D. DON., Acer ginnala MAXIM., Cerasus polytricha (KOEHNE) YÜ ET LI. and Malus hupehensis (PAMP.) REHD. The third stand (XSc) is a natural deciduous broad-leaved mixed forest and Quercus aliena var. acuteserrata MAXIM., Dendrobenthamia japonica (DC.) FANG. var. chinensis and Acer davidii FRANCH. are the most abundant species. This forest stand was restored in the 1970s after commercial harvesting. The fourth stand (XSd) represents a virgin forest without management impact for over 100 years. The population has more than 45 tree species, mainly Quercus aliena var. acuteserrata MAXIM., Pinus armandii FRANCH., Acer davidii FRANCH. and Staphylea holocarpa HEMSL. Complementary to these data from temperate zones, we also included two datasets from tropical and subtropical climates for additional validation, see Appendix A.

Although plant neighbourhoods are crucial to the understanding of plant interactions, they can be quite varied in space. The nearest neighbours of individuals situated at low local densities can have neighbours that are comparatively far away from that particular individual. By contrast, at high local densities all nearest neighbours of an individual may only be few centimetres away. This is a particular challenge for spatial species diversity monitoring. The objective of this work was to study exceptionally species-rich temperate forests from China by introducing and testing an extension of the species mingling index, which is capable of taking different spatial scales into account and thus potentially describes species mingling in forest stands more accurately. We have tested the new mingling characteristic by means of the innovative spatial reconstruction technique, a non-parametric modelling method, and the mark mingling function (Pommerening et al., 2011; Hui and Pommerening, 2014). 2. Materials and methods 2.1. Data Detailed data from ten fully mapped forest stands have been used to test the performance of the new mingling characteristic (Fig. 1). The studied forest sites (Li et al., 2014) are from the temperate climate zone in China and are among the most species-rich temperate forest ecosystems in the world. As a consequence they are a particular challenge to spatially explicit species diversity monitoring. Most of the forest sites we analysed exhibited complex forest structures and are unique study sites representing woodland communities that have hardly been studied in a spatially explicit way in the past. This makes the data very suitable for testing new tree diversity characteristics related to species dispersal. In terms of plot sizes and locations we had to rely on local plot and data availability. For the purpose of this study, combinations of one, two or three letters have been assigned to the stands for easier identification. The letter combination is related to each stand’s geographical origin. In the case where there are multiple stands from the same region, each individual stand was given a further letter to allow the identification of stands within each region. For example, if there were four replications within a forest site, each one was given a letter in consecutive order, e.g. a, b, c and d. Jiaohe forest region has a typical temperate mixed forest including coniferous and broad leaved trees. The study area is situated in the Dongdapo Natural Reserve (43°51′–44°05′ N and 127°35′–127°51′ E), which is part of the Zhangguangcai mountain range extending from north of the Songhua river to south of the Changbaishan mountains. This area is approximately 45 km from Jiaohe in Jilin Province, China, and has a monsoon climate with dry, windy springs and warm, wet summers. Mean annual rainfall is 700–800 mm, occurring primarily between June and August. Mean annual temperature is 3.5 °C and mean minimum temperature is −22.2 °C in deep winter. The soil is classified as dark brown forest soil that has formed under the combined influences of heat and moisture in mixed forests. This soil type has accumulations of slightly acidic or neutral humus which is quite common in north-eastern China. Four plots from the Jiaohe forest region were included in this study. The first stand, denoted as Ja, is a mixed Tilia mandschuria-Pinus koraiensis forest. The most abundant tree species are Tilia mandschuria RUPR. ET MAXIM., Carpinus cordata BL., Acer mono MAXIM. and Pinus koraiensis SIEB. ET ZUCC. The second stand, denoted as Jb, is a mixed Fraxinus mandshurica-Juglans mandshurica forest. It mainly includes Fraxinus mandshurica RUPR., Juglans mandshurica MAXIM., Acer mandshurica MAXIM., Carpinus cordata BL., Acer mono MAXIM. and Pinus koraiensis SIEB. ET ZUCC. The third stand, denoted as Jc, can be described as a mixed Juglans mandshurica-Abies holophylla forest. The most abundant species are Juglans mandshurica MAXIM., Acer mono MAXIM., Acer mandshurica MAXIM., Abies holophylla MAXIM. and Ulmus davidiana var. japonica (REHD.) NAKAI. The fourth plot, denoted as Jd, represents a mixed

2.2. Measures of spatial mingling Point process statistics has contributed many methods to quantifying spatial diversity (Illian et al., 2008; Wiegand and Moloney, 2014). In one of them, the nearest-neighbour (NN) approach, first a local index value is calculated for each plant based on the information derived from every plant itself and its neighbourhood. This index value describes the spatial diversity in the immediate vicinity of each individual, i.e. in its 117

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Fig. 1. Map of China showing the locations of the three research sites.

particularly useful in woodlands with many species, because the only distinction made is between co- and heterospecific pairs of trees. In our ¯ , as a population characteristic, was study, mean arithmetic mingling, M estimated using the NN1 edge correction method. The estimator is explained in detail in Pommerening and Stoyan (2006). According to Lewandowski and Pommerening (1997) expected mingling (implying independent species marks), EM , is independent of the number of neighbours, k, and can be calculated as

local neighbourhood (Rajala and Illian, 2012). Such local, plant-based indices provide the opportunity to derive summary characteristics for the whole community in a second step. In the context of our study, it is possible to relate the mingling index of each individual to other local characteristics that may help to better understand the nature of mingling. Gadow (1993) and Aguirre et al. (2003) extended the species segregation index by Pielou (1977) to general multivariate species patterns involving k neighbours. The mingling index Mi (Eq. (1)) is defined as the mean heterospecific fraction of plants among the k nearest neighbours of a given plant i. In the analysis, every plant within a given research plot acts once as plant i.

Mi =

1 k

s

EM =

i=1

Ni (N − Ni ) N (N − 1)

(2)

with s, the number of species, N, the total number of trees in the observation window and Ni, the number of trees of species i. In analogy to ¯ and EM can be combined in an index Ψ Pielou’s segregation index, M expressing the relationship between observed species mingling and

k

∑ j=1 1 (speciesi ≠ speciesj)

∑

(1)

Having its origin in Pielou (1977) the mingling approach is 118

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completely random species mingling according to

Ψ=1−

¯ M . EM

(3)

Pommerening and Uria-Diez (2017) referred to the index defined in Eq. (3) as species segregation index. Since the index takes the expectation into account, it is normalised for the number of species involved in each study population, which the original mingling index is not, i.e. the values of species mingling typically increase with increasing number of species. Consequently, Ψ = 0, if the species are independently or randomly dispersed. If the nearest neighbours and a given tree always share the same species, Ψ = 1 (attraction of the same species leading to species segregation). The minimum value of Ψ = −1 is approached, when all neighbours are of a different species than the tree under consideration (attraction of different species). In principle, k can take any number that is justified by the ecological context of a given study plot and Pommerening (2006) has demonstrated, how k depends on the properties of the pattern under study and can be optimised for a given plant pattern. However, the problem remains that optimal k cannot be easily determined ad hoc for a given population or forest stand. Turning a problem into an asset, we con¯ for multiple k and thus transformed index Ψ to a sidered calculating M function Ψ (k) (Eq. (4)).

Ψ (k ) = 1 −

M (k ) , EM

k = 1, 2, 3, …

Fig. 2. Schematic diagram of the species segregation function Ψ ′ (r ) .

(4)

Ψ ′ (r ) tends towards a value of 0 denoting species mark independence. This characteristic is therefore a measure of decay of the mingling effect with distance. In addition we calculated the range r¯k − r¯1, i.e. the difference between the average distance to the first and the kth nearest neighbour, which we set to k = 20. Short ranges occur in tree patterns with high densities and in patterns that are highly clustered whilst long ranges are common in those with low densities. Finally we also fitted polynomials of degree two to the values of Ψ ′ at r¯k and calculated the sum of squares of deviation (SSDL, Liu et al., 2009) from linearity (Eq. (6)).

With increasing k, Ψ (k ) → 0 . Our hypothesis is that the exact way in which Ψ (k ) approaches 0 is a better quantitative description of the ¯ or Ψ alone. For plant mingling pattern in a given population than M patterns with completely random species dispersal (independent species marks) Ψ (k ) = 0 for all k. Since the same number of k can involve quite different spatial scales in different forest stands, we intended to relate Ψ (k) to a spatial scale. Even between different trees of the same forest stand k can involve quite different spatial scales. Therefore we considered the population N 1 mean distance r¯k = N ∑i rik between any individual i and its kth nearest neighbour, as this mean carries most of the information on scale. We can finally define a new function combining r¯k and Ψ (k ) , i.e. Ψ ′ (r ), which is now scale-dependent and allows better comparison between different populations (Eq. (5)).

for r = r¯k , k = 1, 2, 3, ⋯ ⎧Ψ (k ), ⎪ Ψ (k + 1) − Ψ (k ) ′ (r − − rk ), for r¯k < r < r¯k + 1, Ψ (r ) = Ψ (k ) + r¯k + 1 − r¯k ⎨ ⎪ k = 1, 2, 3, ⋯ ⎩

k

SSDL =

∑ (ΨiP − ΨiL )2

(6)

i=1

of ΨiP

and ΨiL

th

(Eq. (3)) were calculated for the i nearest The values neighbour from the polynomial (P) and linear (L) models, respectively. Deviation from linearity as expressed by SSDL is another but different measure of the decay effect of species mingling with distance. Nonlinear curves of Ψ ′ (r ) often indicate a fast decline of the species segregation effect with distance. We used these shape characteristics for supporting our visual impressions of the Ψ ′ (r ) curves and as variables in a cluster analysis with the intention to classify our forest stands according to species segregation in order to better understand the information provided by the species segregation function. The cluster analysis was based on the Ward method, an agglomerative clustering algorithm, and on the Canberra metric (Illian et al, 2008, p. 272ff; Legendre and Legendre, 2012).

(5)

′

Ψ (r ) constitutes the species segregation function we introduced and tested in this study. At the population mean distances r¯k the function has M (k ) the value Ψ (k ) = 1 − EM (Eq. (4)) and between the mean distances linear interpolation is performed. Linear interpolation involves that the Ψ (k ) values calculated at the corresponding r¯k are connected by straight lines. As a consequence the value of Ψ ′ (r ) for a distance r between r¯k and r¯k + 1 is taken to be a weighted average of Ψ (k ) and Ψ (k + 1) . The interpretation of the function graph is straightforward and basically follows the interpretation of Ψ (k ) (Fig. 2). Relating Ψ (k ) to r¯k provides additional information on the range of species segregation.

2.4. Spatial reconstruction 2.3. Characterisation of the species segregation functions Spatial reconstruction is a non-parametric modelling method for simulating the structure of a system under study. The method was first introduced by Torquato (Yeong and Torquato, 1998; Crawford et al., 2003; Torquato, 2002) and applied to simulating point processes by Tscheschel and Stoyan (2006). Pommerening and Stoyan (2008) reconstructed spatial forest structure and Torquato often described spatial reconstruction as an inverse problem, because analysis is reversed: From the knowledge of limited information provided by statistical summary characteristics the observed structures are re-established. This

For a quantitative description of the shapes of the species segregation functions we performed a linear regression on the values of Ψ′ at r¯k for k = 1, 2, 3,…, 20. We considered the intercept and the slope of the linear regression as shape parameters, where the intercept is comparable with Ψ (1) and an expression of species segregation between trees and their very first neighbour, i.e. maximum species segregation. The slope parameter expresses the average slope of the (in most cases nonlinear) function, i.e. how rapidly the species segregation function 119

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Pommerening (2014), which can be considered a variant of a generic type of mark correlation function (Baddeley et al., 2016, p. 644f.). The mark mingling function ν (r ) is the closest competitor of the species segregation function, however, it is not based on the nearest-neighbour principle but is a second-order characteristic. This implies that the statistical concepts of the mark mingling and the species segregation functions differ, which explains some of the deviations in the results. It is likely that the mark mingling function provides more information on long-range interactions than the species segregation function whilst deviations may particularly occur at short range. For validating the reconstruction quality we relied on the global envelope test based on the extreme rank length ordering of the functions involved (Myllymäki et al., 2017; Mrkvička et al., 2018). As part of this test we used the cumulative version of the mark mingling function, i.e. the mark weighted L function L ν (r ) (Pommerening et al., 2011; Hui and Pommerening, 2014) centred by L (r) (unmarked L function) of the observed data, i.e. function L ν (r ) − L (r ) . Mean simulation L(r) and L(r) of the observed data are in our case identical, as the tree locations were fixed in the reconstruction experiment. L(r) represents the behaviour of L ν (r ) in the case that the species marks are independent. Therefore the graphs of the validation function L ν (r ) − L (r ) should align with a horizontal line through zero for independent species marks. Considering the objectives of this paper, we were not interested in good reconstruction results per se but rather in improvements caused by exchanging the species segregation index Ψ (Eq. (3)) for the new species segregation function (Eq. (5)) in the contrast function (Eq. (7)). Any improvements achieved by the species segregation function indicate the usefulness of the characteristic due to better information quality. All calculations were carried out using our own R (version 3.5.1; R Development Core Team, 2018) and C++ code, the spatstat (Baddeley et al., 2016) and GET (Myllymäki et al., 2017, https://github.com/ myllym/GET/) packages.

reconstruction can then answer the question how much does a new structural characteristic, such as the species segregation function, contribute to the synthesis of a given forest structure. If, for example, two competing or alternative summary characteristics are separately used for the reconstruction of spatial forest structure, that one is to be preferred that leads to a better synthesis. Therefore one purpose of reconstruction is to test summary characteristics and this is precisely what we used the algorithm for in this study (Crawford et al., 2003). Given the objectives of this study, tree locations were not affected by this algorithm and tree sizes were ignored. The reconstruction technique is a general stochastic optimisation method based on simulated annealing (Kirkpatrick et al., 1983; Černý, 1985). A detailed description is given in Torquato (2002). In the context of this study the algorithm works as follows: (1) In an observed marked point configuration, the species marks are randomly reallocated (random labelling technique; Illian et al., 2008), in order to destroy the observed spatial species mingling pattern and possible spatial correlations. (2) To change and potentially improve this initial spatial species configuration, a pair of points with different species marks is randomly selected and the marks are swapped. (3) If Cnew < Cold (Eq. (7)), this arrangement is made permanent and Cnew is set as Cold . Otherwise the swap is reverted (improvementsonly algorithm), see Tscheschel and Stoyan (2006). (4) Steps 2 and 3 are repeated until the current contrast measure Cold falls below a pre-set value of 1E-50 or a maximum number of 1E +05 iterations is exceeded. The reconstruction method mainly depends on the choice of the contrast measure C (also referred to as energy function), which steers the simulation process. This contrast measure typically is a leastsquares error function and can be written as

C=

m

∑i =1 (f

3. Results

̂ (x i ) − f (x i ))2 ,

(7) 3.1. Stand characteristics

where m is the number of indices or function values considered in the reconstruction. f ̂ (x ) is a function estimated from the reconstructed data, f (x ) is the corresponding function estimated from the original data and x are argument values where the functions are compared. We compared two sets of reconstruction results for each forest plot, (1) where the species segregation index Ψ (Eq. (3)) has been used in the contrast measure (serving as f ̂ (x ) and f (x ) ) with k = 4 (as the most frequently used number of neighbours in the literature) and (2) where the new species segregation function Ψ ′ (r ) (Eq. (5)) has been used in the contrast measure instead. Since the tree locations were fixed, so were r¯k and therefore the algorithm could be simplified to work directly with Ψ (k ) (Eq. (4)). Each plot was reconstructed 1000 times. The two sets of resulting patterns were then validated by the mark mingling function as defined in Pommerening et al. (2011) and Hui and

Tree densities in the 10 plots were generally very high and ranged from 748 trees per hectare in Jiaohe, plot b to 2331 in Jiulongshan, plot a (Table 1). In terms of basal area per hectare, densities were moderate between 20.3 m2 in Jiulongshan, plot a and 31.7 m2 in Jiaohe, plot c. Basal area appears to be distributed over many small to medium-sized trees, which is also reflected by the mean stem diameter, dbh. Size diversity according to the dbh coefficient of variation was highest in Jiaohe, plot d (0.77), with 19 different tree species and lowest in Jiulongshan, plot a (0.29), where there are only nine different ¯ was tree species. Based on k = 4 nearest neighbours, mean mingling M lowest Jiulongshan, plot a (0.77), where also size diversity, basal area ¯ was highest in Jiaohe, plot c (0.83), and number of species were low. M where also basal area was highest. The values of the species segregation

Table 1 ¯ and Ψ were calculated for k = 4 Basic characteristics of the 10 research plots. J – Jiaohe forest region, JS – Jiulongshan Forest, X – Xiaolongshan Forest. M neighbours. Plot

Slope (°)

Mean altitude (m)

Plot size (m × m)

Density (trees ha−1)

Number of species

Mean dbh (cm)

dbh coeff. of variation

Basal area (m2.ha−1)

¯ M

Ψ

Ja Jb Jc Jd JSa JSb XSa XSb XSc XSd

17 9 9 9 17 15 13 13 17 37

660 620 620 600 145 990 1720 1720 1650 1880

100 × 100 100 × 100 100 × 100 100 × 100 40 × 80 100 × 50 70 × 70 70 × 70 50 × 65 60 × 60

1178 748 797 808 2331 1346 841 843 1486 1356

20 21 19 19 9 12 32 35 30 49

18.1 21.7 22.4 20.8 10.5 15.5 18.2 19.6 15.6 14.6

0.726 0.724 0.710 0.771 0.289 0.392 0.711 0.634 0.524 0.595

30.42 27.95 31.67 27.80 20.26 25.40 21.77 25.35 28.58 22.79

0.779 0.776 0.826 0.811 0.196 0.427 0.813 0.783 0.725 0.810

0.104 0.127 0.076 0.098 0.163 0.443 0.094 0.134 0.162 0.090

120

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′ (r ) for the ten Chinese forest stands. The stand abbreviations are explained in Section 2.1. B: The mark mingling Fig. 3. A: The species segregation function Ψ functions ν ̂(r ) for the same forest stands. The colours used are the same as in panel A.

index Ψ (Eq. (3)) were positive in all ten plots, i.e. there was an attraction of the same species (see Fig. 2). The strongest attraction of the same species occurred in Jiulongshan, plot b involving 12 species (0.44). The weakest attraction of the same species, bordering on complete spatial randomness, we found in Jiaohe, plot c (0.08), where mingling index and basal area are highest.

3.2. Mingling segregation and mark mingling functions As with the species segregation index Ψ (Eq. (3)) in Table 1, all mingling segregation functions indicated an attraction of the same species leading to conspecific clusters (Fig. 3A). On closer inspection it is apparent that some of the functions have quite different shapes compared to others, which can be studied in greater detail using the shape characteristics described in Section 2.3. Obviously, the functions relating to Jiulongshan, plot b (JSb), Xiaolongshan, plot c (XSc) and Jiulongshan, plot a (JSa) differ from most other function curves, either because of the large intercept (JSb), the marked deviation from linearity (XSc) or the steep slope/short range (JSa). Large intercepts emphasise strong attraction of the same species, a deviation from linearity often means that this strong attraction at first decreases rapidly with distance and then more slowly. The average slope also provides information on how quickly the initial segregation effect decreases or how long it lasts and the range is a reflection of tree density. Although zoomed in, the mark mingling functions ν^ (r ) (Fig. 3B) are much less discernible. The coresponding graphs are generally organised in a way different from those of the species segregation function, i.e. ν (r ) < 1 indicates conspecific attraction whilst ν (r ) > 1 suggests heterospecific attraction (see Hui and Pommerening, 2014, Fig. 3, left). However, the mark mingling function also indicates that JSa and JSb have a somewhat special mingling pattern with increasing species aggregation at larger distance (JSa) and exceptionally strong species segregation (JSb), respectively. The visual impression of Fig. 3A suggests that Ja, Jb, Jc, Jd, XSa, XSb, and XSd can be allocated to one big group sharing similar species segregation behaviour. This impression is reinforced by the cluster analysis (Fig. 4) and Table 2 (presenting the input parameters for the cluster analysis). We clearly recognise two major classes delineated by red rectangles (Fig. 4). The most common characteristic of the small first class including JSa, JSb, XSc, is the comparatively large intercept associated with all three species segregation functions. This is the class of stands with high spatial species segregation values for small k. The second

Fig. 4. Dendrogram of the ten Chinese forest stands from a hierarchical agglomerative cluster analysis (Ward’s method + Canberra metric) using the shape characteristics of Table 2 (without Ψ (1)).

large class is subdivided into two main clusters, where the first included Ja, Jc and XSd. In this cluster all three stands are characterised by comparatively small intercepts, strong linearity (small values of SSDL, Table 2) and small absolute slope parameters (moderate decline of species segregation effect). The stands in the second cluster are mainly characterised by their long range and comparatively large SSDL values (stronger deviation from linearity, i.e. rapid decline of species segregation effect). The results emphasise the value of the cluster analysis, since the differences between the associated curves in Fig. 3(A) are not so easy to see visually.

3.3. Reconstruction Here it is important to note that the special interest was in comparing the graphs in panels A with those in panels B in Figs. 5 and 6, 121

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Table 2 Shape characteristics of the species segregation function Ψ ′ (r ) . Intercept – From linear regression, expression of maximum species segregation; Ψ (1) – Value of Ψ (Eq. (3)) with k = 1; Slope – From linear regression, expression of how rapidly Ψ ′ (r ) tends towards a value of 0; Range – Difference between average distance to first and 20th nearest neighbour, SSDL – Sum of squares of deviation from linearity (Eq. (6)). Plot

Intercept

Ψ (1)

Slope

Range (m)

SSDL

Ja Jb Jc Jd JSa JSb XSa XSb XSc XSd

0.142 0.209 0.120 0.156 0.326 0.527 0.134 0.251 0.403 0.120

0.143 0.210 0.111 0.164 0.232 0.497 0.144 0.235 0.453 0.123

−0.011 −0.020 −0.010 −0.014 −0.068 −0.027 −0.009 −0.030 −0.063 −0.009

6.0 7.5 6.9 7.1 3.8 5.2 7.3 6.8 5.2 5.6

0.00046 0.00130 0.00029 0.00113 0.00014 0.00019 0.00247 0.00357 0.02627 0.00007

since it was the objective of our study to show that the use of the species segregation functions generally leads to better reconstruction results than the use of the species segregation index. In all plots, there were considerable differences between the L ν̂ (r ) − L ̂(r ) data curves and the corresponding curves of the reconstructed mingling patterns (grey patches in Figs. 5 and 6). This is likely to be a consequence of the fundamentally different types of information, nearest neighbour summary characteristics such as Ψ (k ) and second-order characteristics like the mark mingling function ν (r ) produce. Most observed data and simulations markedly differ from the null hypothesis of uncorrelated species marks (indicated by the horizontal line through 0), perhaps with the exception of plot JSa (Fig. 5, bottom). In almost all forest stands, the use of Ψ^ (k ) and multiple k markedly improved the reconstruction of the mingling pattern supporting the hypothesis of this study. It is interesting to note, that it is often for r > 4 m that improvements were achieved with the consequence that the simulation curves shifted towards the data curve (see for example Fig. 5, Jb, Jc, Jd; Fig. 6, JSb, XSa, XSc, XSd). At distances of r < 4 m the data curves in most cases are situated outside the range of simulated patterns, however, even in this distance range at least small improvements could be achieved by the mingling segregation function, see for example Fig. 5, Jb, Jc; Fig. 6, XSa, XSb, XSc. Somewhat different from the results of the other nine research plots were those for JSa (Fig. 5, bottom). Here the use of the simple species segregation index Ψ (Eq. (3)) led to similar reconstruction results compared to those achieved with the species segregation function (Eq. (5)). JSa has a simple stand structure based on a regular tree dispersal pattern and only nine species and the data curve is close to the horizontal line through 0, suggesting that the species are spatially almost uncorrelated. JSa also sticks out in the two graphs of Fig. 3 and Table 2 shows that Ψ^ ′ (r ) has an exceptionally large absolute slope but short range. The somewhat surprising result for JSa may suggest that for forests with a simple structure (in terms of the underlying point pattern) also a simple characteristic is sufficient. The most remarkable fit achieved by the species segregation function was that for JSb, where the new measure helped to successfully reconstruct the whole range of increasing deviation of the data curve from the null hypothesis. The Ψ^ ′ (r ) curve related to this plot was quite different from those of all other plots with very high values throughout its range indicating strong species segregation. The mark mingling function ν ̂(r ) confirmed this result. In the Jiaohe forest plots, variation in the simulated patterns is particularly low and there is more variation in Xiaolongshan. In the latter forest area, many trees developed from root suckers and resprouting, particularly the dominant species Quercus aliena var. acuteserrata MAXIM. This gave rise to localised species clusters that affected species mingling and segregation, because the reconstructions were

Fig. 5. Reconstruction results in terms of the mark-weighted L function L ν̂ (r ) corresponding to the mark mingling function ν ̂(r ) centred by L ̂(r ) (unmarked L function) of the observed data. The grey area represents the 95% global envelope of the curves of the 1000 simulations, while the black curve relates to the observed data. A: Reconstruction using the species segregation index Ψ^ for k = 4 (Eq. (3)) in the contrast function (Eq. (7)). B: Reconstruction based on the species segregation function Ψ^ (k ) with k = 1, …, 20. J – Jiaohe forest region, plots a-d, JS – Jiulongshan Forest, plot a.

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based on the species segregation function Ψ (k ) involving mean min¯ . The variation in the simulations was affected by the variation gling M in the tree-specific mingling index Mi (Eq. (1)). The largest variation in the simulations was observed for the two Jiulongshan plots, although these have a more simple forest structure due to their plantation origin. This result is related to the large number of trees in these plots, particularly in JSa, see Table 1, but also to the uneven species abundance distribution in JSa. Interestingly the data curves L ν̂ (r ) − L ̂(r ) have shapes that show some resemblance, e.g. those of XSa, XSb and XSc are similar to those of Jb, Jc and Jd. Ja and XSd are similar and also JSa and JSb form a group. To some degree these similarities echo the results of the cluster analysis in Fig. 4. Appendix A and Fig. A1 demonstrate that also in tropical and subtropical forests the species segregation function is also more informative than the simple species segregation index. 4. Discussion and conclusions The species segregation function Ψ ′ (r ) is a simple spatial summary characteristic that provides markedly more information on species mingling than the index Ψ particularly in forests with complex spatial structure and many species. The characteristic is comparatively easy to estimate even from small observation windows such as those used in forest monitoring. However, depending on the size of small observation windows and the number of available points, the number of nearest neighbours k used should be adequate and not too large. Particularly interesting are the curve characteristics described in Section 2.3 and listed in Table 2. They have the potential to break down species segregation patterns into specific aspects and thus to identify the causes for observed patterns. Intercept, slope and SSDL are the most interesting characteristics providing information on short range species segregation and its decay with distance. This information can be crucial in the context of species diversity conservation. Our research has also shown, that the new species segregation characteristic in connection with the curve characteristics of Table 2 allows a good classification of tree populations in terms of species segregation (Fig. 4). The reconstruction of observed mingling patterns used to evaluate the new characteristic clearly demonstrated that in the majority of cases the new species segregation function provided considerably more information than the simple index. Where this was not the case, the species mingling pattern was close to a situation of independent species marks, i.e. here the simple index measure sufficed. The species segregation function provided very good results particularly for long-distance species relationships. At distances < 4 m the difference between nearest neighbour and second-order characteristic accounted for the poorer reconstruction performance in this distance range. However, in not a single case did the species segregation function perform worse than the species segregation index and this was what our analysis was aiming to achieve. A natural extension of the species segregation function includes estimating species specific variants of Ψ (k ) and Ψ ′ (r ) for the most abundant species or for species groups. Used in the contrast function (Eq. (7)) together with the population variant of the species segregation function from this study would also improve the reconstruction results, although this is not the main purpose of this type of research. Functions similar to the species segregation function can easily be proposed for other nearest neighbour summary characteristics such as size differentiation (Pommerening, 2002) and the size segregation function (Pommerening and Uria-Diez, 2017). Such developments would greatly improve the understanding of structural diversity in complex forest ecosystems. Our approach involving multiple numbers of k nearest neighbour used in this study is also an important step towards generalising nearest-neighbour characteristics, since the choice of k is difficult and often made arbitrarily. In reality k depends on local tree density and

Fig. 6. Reconstruction results in terms of the mark-weighted L function L ν̂ (r ) corresponding to the mark mingling function ν ̂(r ) centred by L ̂(r ) (unmarked L function) of the observed data. The grey area represents the 95% global envelope of the curves of the 1000 simulations, while the black curve relates to the observed data. A: Reconstruction using the species segregation index Ψ^ for k = 4 (Eq. (3)) in the contrast function (Eq. (7)). B: Reconstruction based on the species segregation function Ψ^ (k ) with k = 1, …, 20. JS – Jiulongshan Forest, plot b, X – Xiaolongshan Forest, plots a-d.

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Author contributions

therefore it makes sense to calculate a compound characteristic involving multiple values as a result of varying k and r. Only then the analyst can ensure that important structural characteristics of a forest stand are not missed.

A.P. designed the new species segregation function and the experiments, analysed the data, programmed, did the simulations and interpreted the results. A.S. carried out some of the data analysis as part of his MSc thesis at SLU Umeå, Z.Z. and H.W. were involved in the data collection, performed analyses and simulations and contributed to the analysis of the results. M.M. advised on global envelope testing and mathematical notation. She also contributed conceptional ideas. All authors contributed to the text.

Acknowledgements M.M. was funded by the Academy of Finland (project numbers 295100 and 306875). Z.Z. was funded by the National Natural Science Foundation of China (project No. 31670640). The authors express their gratitude to Gangying Hui (Chinese Academy of Forestry, Beijing, China) and to the South African National Parks for providing the data used in Appendix A at short notice.

Declaration of Competing Interest None.

Appendix A Additional validation with tropical and subtropical data For additional validation with exceptionally species-rich tropical and subtropical data we included two sites from China and South Africa. Jianfengling Nature Reserve (108°52′E, 18°48′N) is located at the junction of Ledong County and Dongfang City in the southwest of Hainan Island in China and is one of the few well-preserved tropical forest areas in China. The reserve is situated between 700 and 1200 m above sea level and includes typical tropical mountain rain forests. Mean annual rainfall is 2652 mm, occurring primarily between May and October. Mean annual temperature amounts to 19.7 °C. The soil is classified as latosol-yellow forest soil and yellow soil. The experimental plot (abbreviated as JFL in Fig. A1) is located in the hinterland of Jianfengling Nature Reserve at an altitude of about 820 m above sea level. More than 80 tree species occur in the plot and mainly include Cryptocarya chinensis (Hance) Hemsl., Poacynum hendersonii (Hook. f.) Woods., Mallotus hookerianus (Seem.) Muell. Arg., Schima superba Gardn. et Champ. (Zhang et al., 1999; Fang et al., 2004). The plot measures 100 × 30 m and includes 246 trees. The Knysna plot is part of an Afromontane research forest situated in the Diepwalle State Forest (north of the coastal town of Knysna in South Africa at 23°09′E, 33°56′S) with mostly sandy soils and has been left to natural development since 1954 (see Gadow et al., 2016; Pommerening and Uria-Diez, 2017). The average annual maximum temperature for the region is 19.2 °C whilst the average minimum is approximately 11.1 °C. Rainfall occurs in all seasons and precipitation varies between 700 and 1230 mm. The Knysna plot has been measured on several occasions and the data used in this study are from 1997. The most frequent species include ironwood (Olea capensis L. subsp. macrocarpa), Kamassi (Gonioma kamassi E. MEY.) and real yellowwood (Podocarpus latifolius (THUNB.) R. BR. ex MIRB.). The plot measures 116 × 116 m and includes 870 trees and 20 tree species. For the two diverse (sub)tropical forests Fig. A1 demonstrates that the use of Ψ^ ′ (r ) led to an improved reconstruction of the spatial species pattern in a similar way as in Figs. 5 and 6. Interestingly, even for r < 4 m the observed black curves are mostly inside the simulation envelope. We also noted that the difference between using Ψ^ and Ψ^ ′ (r ) in the reconstruction was not as big as in some of the temperate plots of Figs. 5 and 6. This partly relates to the fact that particularly in the Jianfengling plot the tree species are almost spatially uncorrelated.

Fig. A1. Reconstruction results in terms of the mark-weighted L function L ν̂ (r ) corresponding to the mark mingling function ν ̂(r ) centred by L ̂(r ) (unmarked L function) of the observed data. The grey area represents the 95% global envelope of the curves of the 1000 simulations, while the black curve relates to the observed data. A: Reconstruction using the species segregation index Ψ^ for k = 4 (Eq. 3) in the contrast function (Eq. 7). B: Reconstruction based on the species segregation function Ψ^ (k ) with k = 1, …, 20. JFL – Jianfengling Nature Reserve plot, Knysna – Afromontane research forest situated in the Diepwalle State Forest 124

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