CN103440415B - Tree population Distribution Pattern based on Mixed modes Measurement Method - Google Patents

Abstract

The invention discloses a kind of tree population Distribution Pattern based on Mixed modes Measurement Method, judge tree population Distribution Pattern according to the distributed constant t of seeds sp in forest and statistic DM of structure: IfThen can determine whether as random distribution；IfThen: as DM<when 1, it is judged that for assembling, as DM>1, it is judged that for being uniformly distributed.Can accurately judge Population Distribution Pattern, simple, clear, effectively.

Description

Tree population Distribution Pattern based on Mixed modes Measurement Method

Technical field

The present invention relates to a kind of tree population Distribution Pattern Measurement Method, particularly relate to a kind of Forest tree seed based on Mixed modes Group Distribution Pattern Measurement Method.

Background technology

The Analysis of Spatial Distribution Pattern of population is the weight of research species characteristic, population interaction and population and environmental concerns Want means, always one of study hotspot in ecology (Pukkala and Gadow, 2012).Spatial framework reflects kind The individual mutual relation to each other on horizontal space of group is population biology characteristic, plant in interspecies relation and environment bar The result of part comprehensive function, is the importance of population space attribute, is also one of the quantum feature of population.Empty to population Between the research and illustrating of Distribution Pattern contribute to the in-depth understanding to structure of community, solve the tree arrangement in afforestation and felling Utilizing question.

Population Distribution Pattern can be by the change of forest number of individuals in analysis sample prescription, single the spacing size of wood, each Dan Mu Obtain with the angle distribution that single wood is constituted about and interspecies relation etc..In prior art, Pattern of Population's Research approach can It is divided between quadrat method, distance method, uniform angle and kind isolation.

Quadrat method is a kind of Analysis of Spatial Distribution Pattern method of classics, owing to it exists basic quadrat size and initial sample prescription position Some problems such as the determination put, so that sampling is with the biggest subjectivity, have impact on the accuracy of result of study.

Distance method is also the main method studying Spatial Distribution Patterns of Forest Trees at present in the world, such as: aggregate index R (Clark And Evans, 1954), pair-correlation function (Stoyan and Stoyan, 1992;Pommerening, 2002) and based on The L-function (Ripley, 1977) of Ripley K-function, the main cause of limiting distance method application is that field needs time-consuming expense The forest position coordinates of power measures.

Have also appeared nearly ten years uniform angle method (Gadow et al., 1998;Hui and Gadow, 2002； Aguirre et al.,2003;Li et al., 2012), its advantage (is closed with two-phase in distance method except avatars intuitively Function is the same with Ripley function) outward, can also be used with numerical expression (Pommerening, 2006).But, uniform angle counts in the wild Also need to carry out the judgement of neighboring trees angle according to investigations.

Pielou(1977) segregation index proposed carrys out the individual separation situation between analysator based on nearest-neighbor method, for many Individual kind also can only compare two-by-two, and the precondition of application is the necessary random distribution of the individuality in standing forest, for the most even group Shape distribution group easily cause irrational description (Upton and Fingleton, 1985；F ü ldner, 1995).

For overcoming the defect of Pielou segregation index, Gadow and F ü ldner etc. proposes Mixed modes (Gadow and Füldner,1992;Gadow,1993;Füldner,1995;Pommerening,2002;Aguirre et al.,2003;Hui Et al., 2011) concept, and attempt to derive seeds distributional class by the relation analyzing seeds Mixed modes and seeds strain number ratio Type (Gadow, 2003；Graz, 2004).But, domestic and foreign literature so far yet there are no relevant directly utilizing at expression tree Kind of degree of isolation aspect science understands, the report of simple and effective Mixed modes systematic analysis Population Distribution Pattern in terms of data acquisition Road.

Summary of the invention

It is an object of the invention to provide a kind of tree population Distribution Pattern based on Mixed modes simple, clear, effective to survey Degree method.

It is an object of the invention to be achieved through the following technical solutions:

Tree population Distribution Pattern based on the Mixed modes Measurement Method of the present invention, according to the distribution ginseng of seeds sp in forest Number t and statistic DM of structure judge tree population Distribution Pattern:

$t=\frac{|{\stackrel{\&OverBar;}{M}}_{\mathrm{sp}}-{\stackrel{\&OverBar;}{M}}_E|}{s_{\stackrel{\&OverBar;}{M}}},$ $\mathrm{DM}=\frac{{\stackrel{\&OverBar;}{M}}_{\mathrm{sp}}}{{\stackrel{\&OverBar;}{M}}_E};$

IfThen can determine whether as random distribution,Be 95% the degree of reliability on, degree of freedom For N_spT value when-1；

IfThen: as DM<when 1, it is judged that for assembling, as DM>1, it is judged that for being uniformly distributed；

In above formula:

$s_{\stackrel{\&OverBar;}{M}}=\frac{s}{\sqrt{N_{\mathrm{sp}}}}=\frac{\sqrt{\frac{{N-N}_{\mathrm{sp}}}{N-1}(1-\frac{{N-N}_{\mathrm{sp}}}{N-1})\left(\frac{N-4}{N-1}\right)}}{\sqrt{N_{\mathrm{sp}}}};$

Represent the standard error of the Mixed modes distribution of random distribution seeds sp, i.e. overall in each sampling with repetition result it Between difference, now the Mixed modes of seeds sp defers to hypergeometric distribution；

S is the variation situation between the standard deviation of random distribution seeds sp Mixed modes, i.e. sample each variable value interior；

N represents the effective number of individuals in mixed forest after forest elimination edge effect；

For seeds sp Mixed modes in mixed forest；

N_spEffective number of individuals after seeds sp eliminates edge effect in expression standing forest；

For the principle according to hypergeometric distribution, the mathematics phase of its Mixed modes during seeds sp random distribution Prestige value.

As seen from the above technical solution provided by the invention, the forest based on Mixed modes that the embodiment of the present invention provides Population Distribution Pattern's Measurement Method, owing to judging forest according to the distributed constant t of seeds sp in forest and statistic DM of structure Population Distribution Pattern: $t=\frac{|{\stackrel{\&OverBar;}{M}}_{\mathrm{sp}}-{\stackrel{\&OverBar;}{M}}_E|}{s_{\stackrel{\&OverBar;}{M}}},$ $\mathrm{DM}=\frac{{\stackrel{\&OverBar;}{M}}_{\mathrm{sp}}}{{\stackrel{\&OverBar;}{M}}_E};$ If $t\&le;t_{\mathrm{\&alpha;}=0.05,\mathrm{\&nu;}=N_{\mathrm{sp}}-1},$ Then can determine whether as random distribution；IfThen: as DM<when 1, it is judged that for assembling, as DM>1, it is judged that for being uniformly distributed.Can accurately judge that population is divided Cloth general layout is simple, clear, effectively.

Accompanying drawing explanation

Fig. 1 is that in the embodiment of the present invention, a hypothesis is shown by forest community and the Species structure point general layout of 3 compositions It is intended to；

Fig. 2 is the forest distributed points general layout schematic diagram surveying standing forest sample ground A in the embodiment of the present invention；

Fig. 3 is the forest distributed points general layout schematic diagram surveying standing forest sample ground B in the embodiment of the present invention.

Detailed description of the invention

The embodiment of the present invention will be described in further detail below.

Tree population Distribution Pattern based on the Mixed modes Measurement Method of the present invention, its preferably detailed description of the invention is:

Tree population Distribution Pattern is judged according to the distributed constant t of seeds sp in forest and statistic DM of structure:

$t=\frac{|{\stackrel{\&OverBar;}{M}}_{\mathrm{sp}}-{\stackrel{\&OverBar;}{M}}_E|}{s_{\stackrel{\&OverBar;}{M}}},$ $\mathrm{DM}=\frac{{\stackrel{\&OverBar;}{M}}_{\mathrm{sp}}}{{\stackrel{\&OverBar;}{M}}_E};$

IfThen can determine whether as random distribution,Be 95% the degree of reliability on, degree of freedom For N_spT value when-1；

IfThen: as DM<when 1, it is judged that for assembling, as DM>1, it is judged that for being uniformly distributed；

In above formula:

$s_{\stackrel{\&OverBar;}{M}}=\frac{s}{\sqrt{N_{\mathrm{sp}}}}=\frac{\sqrt{\frac{{N-N}_{\mathrm{sp}}}{N-1}(1-\frac{{N-N}_{\mathrm{sp}}}{N-1})\left(\frac{N-4}{N-1}\right)}}{\sqrt{N_{\mathrm{sp}}}};$

Represent the standard error of the Mixed modes distribution of random distribution seeds sp, i.e. overall in each sampling with repetition result it Between difference, now the Mixed modes of seeds sp defers to hypergeometric distribution；

S is the variation situation between the standard deviation of random distribution seeds sp Mixed modes, i.e. sample each variable value interior；

N represents the effective number of individuals in mixed forest after forest elimination edge effect；

For seeds sp Mixed modes in mixed forest；

N_spEffective number of individuals after seeds sp eliminates edge effect in expression standing forest；

For the principle according to hypergeometric distribution, the mathematics phase of its Mixed modes during seeds sp random distribution Prestige value.

The labor of tree population Distribution Pattern based on the Mixed modes Measurement Method of the present invention:

1. Mixed modes concept:

Mixed modes (M_i) definition for not belonging to shared by individuality of the same race with reference to setting with reference to the 4 strain nearest neighbor wood j of tree i Ratio, expression formula is:

M_iRepresent the Mixed modes that the i-th strain is individual.

Calculate the average Mixed modes of standing forestFormula be:

$\stackrel{\&OverBar;}{M}=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{M}_i---\left(1\right)$

In formula: N represents forest individual amount in mixed forest (eliminating the effective number of individuals after edge effect).

Seeds Mixed modes in mixed forestComputing formula be:

${\stackrel{\&OverBar;}{M}}_{\mathrm{sp}}=\frac{1}{N_{\mathrm{sp}}}\underset{i=1}{\overset{N_{\mathrm{sp}}}{\mathrm{\&Sigma;}}}{M}_i---\left(2\right)$

In formula: N_spThe strain number (after eliminating edge effect, effective number of individuals of these seeds) of sp seeds in expression standing forest.

2. Mixed modes judges the theoretical basis of Species structure and method:

According to the principle of hypergeometric distribution, during seeds random distribution, the mathematic expectaion of its Mixed modes is:

${\stackrel{\&OverBar;}{M}}_E=\frac{{N-N}_{\mathrm{sp}}}{N-1}---\left(3\right)$

Here statistic DM is built,

$\mathrm{DM}=\frac{{\stackrel{\&OverBar;}{M}}_{\mathrm{sp}}}{{\stackrel{\&OverBar;}{M}}_E}---\left(4\right)$

If it is applicant's understanding that a seeds general layout is random in mixed forest, then, the mathematic expectaion of DM is 1, as Really population is Assembled distribution, then have DM < 1；If population at individual distribution arranges evenly than random distribution and (is and uniformly divides Cloth), then there is DM > 1.This is because in the case of seeds strain array becomes (the strain number ratio of each seeds in mixed forest) certain, tree When planting bulk distribution, the chance met due to same seeds is big, say, that the nearest neighbor wood of this seeds Dan Mu is other seeds Probability diminish, calculate according to Mixed modes formula, when will show that the value of the average Mixed modes of these seeds is than this seeds random distribution The average Mixed modes value of forest is little；Equally, when being uniformly distributed, the chance met due to same seeds is little, allows for the mixed of its seeds Friendship degree is more than the Mixed modes of random distribution seeds.

Above-mentioned inference is exemplified below.Assume the forest community having the random distribution of a manual simulation, analogue window Size is 100*100m, and simulation strain number is 1000 strains.This group is respectively accounted for 1/ by 3 compositions, each seeds strain number equalization 3, and each seeds have different Distribution Pattern's types, if the some general layout of seeds a is that random distribution, the some general layout of seeds b are Be uniformly distributed, the some general layout of seeds c is Assembled distribution (as shown in Figure 1).This manual simulation is calculated with software Winkelmass The seeds Mixed modes (as shown in table 1) of forest community, setting buffers is that 5m (will distance every standing forest sideline 5m in sample ground Within annular region be set to relief area, forest therein is only cooked neighboring trees, and the region of relief area cincture is core space, therein All forests are as participating in Mixed modes calculating with reference to tree).

As expected, the result of table 1 the most clearly confirms above-mentioned inference.The population a of random distribution is in group Mixed modes is almost equal with expected value, and its ratio is close to 1；Equally distributed population b Mixed modes in group is more than expected value, And the population c of Assembled distribution has a relatively low Mixed modes in group, and the ratio of its value and expected value is less than 1.

Table 1 seeds Mixed modes, expected value and ratio

The significant difference degree of the Mixed modes expected value when seeds Mixed modes average of actual measurement and this seeds random distribution can T-distribution is utilized to test:

$t=\frac{|{\stackrel{\&OverBar;}{M}}_{\mathrm{sp}}-{\stackrel{\&OverBar;}{M}}_E|}{s_{\stackrel{\&OverBar;}{M}}}---\left(5\right)$

Wherein

$s_{\stackrel{\&OverBar;}{M}}=\frac{s}{\sqrt{N_{\mathrm{sp}}}}=\frac{\sqrt{\frac{{N-N}_{\mathrm{sp}}}{N-1}(1-\frac{{N-N}_{\mathrm{sp}}}{N-1})\left(\frac{N-4}{N-1}\right)}}{\sqrt{N_{\mathrm{sp}}}}$

In formula:When representing seeds sp random distribution, its Mixed modes defers to the standard error of hypergeometric distribution, and s is seeds sp The standard deviation (Sachs, 1992) of its Mixed modes during random distribution.

Principle according to t-distribution inspection: ifThen can determine whether as random distribution；If it is actualAs DM<when 1, it is judged that for assembling, as DM>1, it is judged that for being uniformly distributed.

3. comparative study:

The method of above-mentioned Mixed modes inspection general layout is referred to as DM method.For checking the effectiveness of the method, spy is by itself and gathering Index R contrasts.

Aggregate index R is the ratio of meansigma methods desired average distance with under random distribution of adjacent nearest forest distance, logical The most also referred to as nearest-neighbor method analytic process (Nearest neighbor analysis, NNA).The computing formula of aggregate index R is (Clark-Evans, 1954):

$R=\frac{{\stackrel{\&OverBar;}{r}}_A}{{\stackrel{\&OverBar;}{r}}_E}---\left(6\right)$

In formula:Average distance between the=adjacent individual plant observed；Average departure between=desired adjacent individual plant From.

${\stackrel{\&OverBar;}{r}}_A=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{r}_i$ ${\stackrel{\&OverBar;}{r}}_E=\frac{1}{2\sqrt{\mathrm{\&rho;}}}$

In formula: n=area is the number of individuals in the sample ground of A square metre；=the number of individuals of every square metre；r_iFor i-th Distance between individuality and its nearest-neighbor method.

If R=1, then forest is random distribution；If R ＞ 1, then forest is for being uniformly distributed, and maximum can reach 2.1491； If R ＜ 1, then forest is Assembled distribution, and R trends towards 0, shows that the distance between trees is more and more intensive.

Actual measurement can test (Kint et al., 2000) with the departure degree predicted with normal distribution:

$u=\frac{{\stackrel{\&OverBar;}{r}}_A-{\stackrel{\&OverBar;}{r}}_E}{{\mathrm{\&sigma;}}_E}---\left(7\right)$

${\mathrm{\&sigma;}}_E=\sqrt{\frac{4-\mathrm{\&pi;}}{4\mathrm{\&pi;\&rho;n}}}=\frac{0.26136}{\sqrt{\mathrm{\&rho;n}}}=\frac{0.26136}{\sqrt{n^2/A}}---\left(8\right)$

In formula: σ_EBe density be that ρ meets Poisson distributionStandard deviation.

Principle according to normal distribution-test: if | u | ＜ 1.96, then can determine whether as random distribution；If actual | u | ＞ 1.96, as R<when 1, it is judged that for assembling, as R>1, it is judged that for being uniformly distributed.

4.DM method application example in Natural Mixed Forest:

The Mixed modes method that Pattern of Population is judgedIt is applied to NW China Xiaolong mountain in Gansu wildwood.Test standing forest Being positioned at Xiaolong mountain in Gansu forestry pilot office all sorts of flowers forest farm, geographical coordinate is 33 ° of 30 '～34 ° of 49 ' N, 104 ° of 22 '～106 ° of 43 ' E, Height above sea level 1700m, belongs to warm temperate zone to north subtropical zone of transition.Stand type is pine oak theropencedrymion, and the density of crop is 888 Strain/hectare, mean DBH increment 19.5cm, mean stand height 14m, seeds quantity is up to 33 kinds, and chief species have Sharptooth Oak (Quercus Aliena var.Acuteserrata Maxim.), too white maple (Acer giraldii Pax), Acer ginnala Maxim. (Acer ginnala Maxim.), wych-elm (Ulmus glabra Huds.), Pinus armandi Franch-P. Komavovii Lavl. (Pinus armandii Franch.), Symplocoris Paniculatae (Symplocos paniculata (Thunb.) Miq.), Gansu Fructus Crataegi (Crataegus kansuensis Wils.) and hirsutism Fructus Pruni pseudocerasi (Cerasus polytricha (Koehne) Y ü et Li) etc..

Every wood location long term monitoring test plot woods that the present embodiment analyzes 2 pieces (sample ground A and B), area is 70 × 70m The Tree Distribution i.e. Population Distribution Pattern (as shown in Figure 2 and Figure 3) of chief species (strain number > 30 strains) in point.Fix for these 2 pieces The most all have recorded diameter of a cross-section of a tree trunk 1.3 meters above the ground D in sample ground > the forest tree species title of=5cm, the diameter of a cross-section of a tree trunk 1.3 meters above the ground, the height of tree, hat width etc..Soft with Winkelmass Part calculates forest stand spatial structure parameter Mixed modes, relief area 5m.And the kind of standing forest is carried out testing according to the above-mentioned general layout method of inspection Group Distribution Pattern's inspection (as shown in table 2).

The chief species Distribution Pattern assay of table 2 Natural Mixed Forest

As shown in Table 2, two kinds of general layout methods of inspection are basically identical to the assay of seeds general layout.Two kinds of methods are only to sample In ground A, the judged result of the distribution of seeds Pinus armandi Franch-P. Komavovii Lavl. occurs in that inconsistent situation.It practice, Pinus Armandi Population in sample ground A Distribution is evident as bulk (see figure 2), is judged as assembling (bulk) with DM, and aggregate index R is then judged as at random, belonging to erroneous judgement.Can Seeing, Mixed modes method DM can accurately judge Population Distribution Pattern, overcomes the theoretical defects of aggregate index R, i.e. trees arest neighbors Body the most always in trees group (group) (Cox, 1971;F ü ldner1995).Mixed modes method DM of general layout inspection and classics The coincidence rate of aggregate index R reaches 91%, and rate of accuracy reached 100%.

The above, the only present invention preferably detailed description of the invention, but protection scope of the present invention is not limited thereto, Any those familiar with the art in the technical scope of present disclosure, the change that can readily occur in or replacement, All should contain within protection scope of the present invention.Therefore, protection scope of the present invention should be with the protection model of claims Enclose and be as the criterion.

Claims (1)

1. tree population Distribution Pattern based on a Mixed modes Measurement Method, it is characterised in that according to seeds two-phase in forest Close statistic DM of the distributed constant t of function and structure and judge tree population Distribution Pattern:

$t=\frac{|{\stackrel{\&OverBar;}{M}}_{sp}-{\stackrel{\&OverBar;}{M}}_E|}{s_{\stackrel{\&OverBar;}{M}}},DM=\frac{{\stackrel{\&OverBar;}{M}}_{sp}}{{\stackrel{\&OverBar;}{M}}_E};$

IfThen can determine whether as random distribution,Be 95% the degree of reliability on, degree of freedom be N_spT value when-1；

IfThen: as DM<when 1, it is judged that for assembling, as DM>1, it is judged that for being uniformly distributed；

In above formula:

$s_{\stackrel{\&OverBar;}{M}}=\frac{s}{\sqrt{N_{sp}}}=\frac{\sqrt{\frac{N-N_{sp}}{N-1}(1-\frac{N-N_{sp}}{N-1})\left(\frac{N-4}{N-1}\right)}}{\sqrt{N_{sp}}};$

Represent the standard error of the Mixed modes distribution of random distribution seeds pair-correlation function, i.e. overall interior each sampling with repetition result Between difference, now the Mixed modes of seeds pair-correlation function defers to hypergeometric distribution；

S is the variation situation between the standard deviation of random distribution seeds pair-correlation function Mixed modes, i.e. sample each variable value interior；

N represents the effective number of individuals in mixed forest after forest elimination edge effect；

For seeds pair-correlation function Mixed modes in mixed forest；

N_spEffective number of individuals after seeds pair-correlation function eliminates edge effect in expression standing forest；

For the principle according to hypergeometric distribution, the mathematical expectation of its Mixed modes during seeds sp random distribution.