Determining spatial heterogeneity in species richness of plant community

Introduction

Species richness in plant communities is determined by various natural and anthropogenic factors, but its precise determinants are difficult to elucidate. Although it is clear that bio- and geo-historical events over the past 10,000 years have played a major role (Rieseberg and Willis 2007; Wilkinson 2012), they do not account for all spatio-temporal variation seen in the present species richness pattern. The stage of biological succession, natural variation in vegetation (caused by climatic and edaphic conditions, saline levels, natural disturbances and so on) and anthropogenic disturbances (e.g. cultivation and modification of land) all cause changes in species richness within given bio- and geo-historical constraints (Pielou 1979; Begon et al. 1996). Furthermore, intra- and inter-specific interactions, and interactions between organisms and their environments, will cause spatio-temporal variation in species richness pattern. More recently, the complex effects of above- and underground environments on vegetation, and especially underground niche structure, have been shown to also affect species richness (Mommer et al. 2010; Hiiesalu et al. 2012). Niche hypothesis indicates that each species in a biological community occupies temporally and spatially inherent habitat which is often mutually exclusive among species (Hutchinson 1957; Begon et al. 1996).

Occurrence frequency, number of individuals (density), cover and biomass per unit area (Bonham 2013), and number of species and species composition per quadrat (Shiyomi et al. 2010) are often censused in vegetation surveys. Since 2000, we have proposed several methods for field surveys and statistical analyses of herbaceous plant populations and communities (Shiyomi et al. 2000; Chen et al. 2006, 2008a,b; Chen and Shiyomi 2014; Gao et al. 2014). However, there are still many unresolved questions, one of which is how to express the spatial characteristics of species richness. The spatial characteristics of species richness are assumed to be divided into the three categories based on the niche hypothesis: (i) Species composition and richness are similar among quadrats; (ii) Species composition varies greatly among quadrats, with many species in some and few in others; (iii) Species are randomly distributed among quadrats.

Here, we propose a method to determine the spatial patterns of species richness for any plant community, present field examples of survey, analysis and interpretation applying the proposed method, and discuss the factors underlying spatial variation in species richness.

Materials and methods

Survey method and analysis

We suppose that in a field survey the number of species in each of N quadrats (intentionally set at random sites), each of which has a given area, are counted, and n species were recorded in the total of N quadrats. The mean and variance for the number of species counted per quadrat are expressed by m and v_obs (subscript obs means observed), respectively. Next, suppose that species i occurs in s_i quadrats of the total N, and the probability (or relative frequency) of occurrence for species i is expressed as P_i (i.e. P_i = s_i/N; i = 1, 2, …, n). We further assume that all n species occur in random quadrats. Then, the mean number of species per quadrat, m, and the variance among quadrats, v_ran (ran indicates random), are expressed by the following equations given by Shiyomi et al. (2010):

(1)

(2)

For example, let the number of quadrats be 10, and seven species, A, B, C, D, E, F and G occur at 5, 2, 3, 4, 3, 10 and 9 quadrats, respectively (i.e. N = 10 and n = 7). Then, each species is assigned to random quadrats as shown in Table 1a, where 1 indicates occurrence and blank indicates absence. The relative frequencies of occurrences to the 10 quadrats (i.e. P_i), are 0.5, 0.2, 0.3, 0.4, 0.3, 1.0 and 0.9 for species A to G, respectively; the mean per-quadrat species richness, m, is 3.6 and the variance among quadrats (v_obs) is 1.156, as estimated from “Total 2” in Table 1a. The expected variance is calculated based on Equation 2: v_ran = 0.5 (1 – 0.5) + 0.2 (1 – 0.2) + … + 0.9 (1 – 0.9) = 1.16, which is very near to the variance estimated for the 10 quadrats in this example (1.156).

Table 1. Mean and variance for seven species in 10 quadrats: artificial examples (1 indicates presence of the species)

Species name/Quadrat number	1	2	3	4	5	6	7	8	9	10	Total 1
(a) A case in which species are arranged based on random numbers
A	1	1	1		1					1	5
B									1	1	2
C		1		1				1			3
D		1				1	1			1	4
E			1				1			1	3
F	1	1	1	1	1	1	1	1	1	1	10
G	1	1	1	1	1	1		1	1	1	9
Total 2	3	5	4	3	3	3	3	3	3	6	36
(b) A case in which species are arranged uniformly to obtain the minimum variance among quadrats
A	1		1		1		1		1		5
B				1	1						2
C		1	1							1	3
D	1			1				1	1		4
E		1				1	1				3
F	1	1	1	1	1	1	1	1	1	1	10
G		1	1	1	1	1		1	1	1	9
Total 2	3	4	4	4	4	3	3	4	4	3	36
(c) A case in which species are arranged aggregately to obtain the maximum variance among quadrats
A	1	1	1	1	1						5
B	1	1									2
C	1	1	1								3
D	1	1	1	1							4
E	1	1	1								3
F	1	1	1	1	1	1	1	1	1	1	10
G	1	1	1	1	1	1	1	1	1		9
Total 2	7	7	6	4	3	2	2	2	2	1	36
	n (1)	n (2)	n (3)	n (4)	n (5)	n (6)	n (7)	n (8)	n (9)	n (10)

• (a) Mean (m) = 3.6; Variance (v_obs) = 1.156; True variance (v_ran) = 1.16 (based on Equation 2).
• (b) Mean (m) = 3.6; Variance (v_min) = 0.24 (based on Equation 3).
• (c) Mean (m) = 3.6; Variance (v_max) = 4.64 (based on Equation 5).
• Total 1: the number of occurrences for each species; Total 2: the number of occurrences at each quadrat.
• n_(i): the total number of species occurred at quadrat i.

Due to intra- and inter-specific interactions (density-dependent effects, avoidance and attraction, autocorrelation among sampling units in the vegetation, etc.), species are not always arranged independently. Therefore, v_obs, which is estimated from field data, must differ from v_ran. For example, in the case that a mutual avoidance or exclusion among species levels out the number of species in the area, the variation in species richness among quadrats must be less than in the case where all species are arranged randomly; i.e. v_obs < v_ran. By contrast, where attraction or a high local death rate leads to species aggregation, variation in species richness among quadrats must be larger than where species are arranged randomly; i.e. v_obs > v_ran.

When species richness is completely identical among quadrats, the variance of species counts must take the minimum value, v_min, of 0. However, as the mean number of species per quadrat is generally a non-integer, it is not practically possible for quadrats to contain a non-integer number of species; for example, when as in Table 1b the entire occurrence is 36 for 10 quadrats, the mean richness is 36/10 = 3.6 which is not integer; that is, m is a number with a decimal point, and then v_min ≠ 0 because each quadrat cannot have 3.6 species (non-integer number of species). Let the number(s) to the left of the decimal point be x and the number(s) to the right be y. Then, m is expressed as x + y. For example, for m = 3.6, x = 3 and y = 0.6 (Table 1b). Let the numbers of species realistically possible in any given quadrat be x and x + 1, and let the relative frequency of each be 1 – y and y, respectively. Then, the mean number of species per quadrat, m, is x(1 – y) + (x + 1)y = x + y. In the example above, the relative frequency that there are three species in a given quadrat is 1−0.6 = 0.4, and the relative frequency that there are four species is 0.6; thus, m = 3 × 0.4 + 4 × 0.6 = 3.6. Then, the variance, v_min, is written as:

(3)

for the entire community. Even if the number of species follows any distribution, its minimum variance among quadrats is v_min. In the above numerical example, v_min is estimated as 0.4 × (3 − 3.6)² + 0.6 × (4 − 3.6)² = 0.24.

Next, a case in which variance among quadrats is at its maximum, v_max, is calculated as follows. Let the total number of occurrences among all quadrats for each species be s₁, s₂, …, s_n for n species, as above. Here, let all symbols indicating occurrence (i.e. 1) be written from the leftmost columns (Table 1c), and let the total number of species that occurred at each quadrat be recorded in the bottom row (Total 2) as n_(i). n₍₁₎ corresponds to the total number of species, and n_(i) decreases gradually to the right in Total 2 (i.e. n_(i) ≥ n_(j) for j > i). The mean number of species, m, and variance, v_max, are expressed as:

(4)

(5)

The variance expressed by Equation 5 takes the maximum value under the constraint of the given mean, m. In Table 1c, v_max = 4.64 for m = 3.6 (as same as in Table 1a,b).

To summarize, (i) v_obs and v_ran are located between v_min and v_max. (ii) When the scale of patch size in a community exceeds quadrat size, and/or species avoid or exclude each other, species richness based on observation may tend to be uniform among quadrats and v_ran > v_obs. (iii) By contrast, where aggregation occurs due to attraction or uneven resource distribution (Pielou 1975), both community structure and species richness will vary widely among quadrats, and v_ran < v_obs. (iv) When species are distributed randomly/independently, v_ran ≈ v_obs. (v) A χ² test may be used to statistically discriminate among (ii) to (iv).

Results and discussion

Table 2 shows seven results from the three surveys in China and one in Japan. In the 25 × 25-cm quadrats in both the A. scoparia grassland and A. ordosica shrubland, v_obs < v_ran (significant at α = 0.05 and 0.001, respectively), but in the 50 × 50-cm quadrats in both communities, H₀: v_obs = v_ran was accepted at α = 0.05. Thus, species were distributed somewhat uniformly among the 25 × 25-cm quadrats, and the actual community “unit” size may have been larger than the quadrat size, which suggests that antagonistic interactions may have operated between species or that some species excluded others and occupied a large, patchy area. Conversely, v_obs > v_ran (significant at α = 0.001) in the weedy grassland, indicating aggregation potentially due to the patchy death of some plant species in response to excessive density and resulting in large variation in species richness among quadrats. In the T. mongolicus grassland, v_obs was statistically similar to v_ran for both quadrat sizes (not significant at α = 0.05), which suggests that species were distributed randomly/independently among quadrats and that species interactions were neutral (or non-autocorrelation).

These results suggest that species richness in each quadrat may depend on the niche hypothesis because v_obs ≠ v_ran in some surveys, although we were unable to find direct evidence for this conclusion. Species distribution is strongly influenced by various natural and anthropogenic factors and depends on both physical, chemical and biological niche requirements and the available species pool (van der Maarel and Sykes 1993; van der Maarel et al. 1995; Duncan et al. 1998). The presence of more niche types means that more species with more diverse niche requirements can live in an area.

If each niche size is so large spatially that several quadrats are contained within it, the plant community would take the form of large uniform patches. Therefore, variation in species richness among quadrats would be relatively small, i.e. v_obs < v_ran. Conversely, if the niche size is spatially small relative to quadrat size, the plant community would consist of many small patches, each with different characteristics. In such cases, the actual variation in observed species richness among quadrats, v_obs, might be nearly equal to or greater than the hypothetical random variation, v_ran. These tendencies are shown in the comparison of two quadrat sizes for A. scoparia grasslands and the A. ordosica shrubland in Table 2; i.e. v_obs < v_ran when we used small quadrats of 25 × 25 cm², but v_obs ≈ v_ran for larger quadrats of 50 × 50 cm². As quadrat size is often determined arbitrarily by the investigator, ensuring that an adequate quadrat size is used is important when measuring vegetation characteristics (Auerbach and Shmida 1987; Bonham 2013). Therefore, it should be determined to meet the survey's objective based on our experiences, and there is not any common quadrat size.