CN101251906A - Method for determining forest collection minimum survey area using mathematical model - Google Patents

Abstract

The invention discloses a method using a mathematical model to determine minimum survey areas of forest communities. A quadrat is selected in a forest community, the area of the quadrat is gradually enlarged, the quantity of tree species that different areas of the quadrat correspond to is statisticized, the species-area relation of the quadrat is characterized by adopting a Monod model (S is equal to aA/(1+bA)), and then the Monod model is evaluated a second order reciprocal S''. When the S'' is equal to zero or approaches to zero, the corresponding area is the minimum survey area of the forest community. The method has higher accuracy, convenience and easy operation.

Description

Determine the method for forest collection minimum survey area with mathematical model

Technical field

The present invention relates to a kind of method of statistical survey, relate in particular to a kind of method of determining forest collection minimum survey area with mathematical model.

Background technology

A forest ecosystem must occupy certain area, and all vegetation are not rambling accumulation on this area, but by certain structure of forming, and with the unified integral body of its environment structure.The sample area size is an important content in the forest survey, the size of investigation area is significant for the certain Forest Types of appropriate performance, and it directly has influence on investigation precision and cost, accurate investigation must be carried out on suitable area, therefore is subjected to numerous scholars' attention.Determine that ancient way that the kind of a plant community is formed carries out kind with exactlying and add up on this stand, but because the shared area of stand is usually very big, it also seldom is uniform that kind distributes in group, we both can not carry out all-round statistics to whole stand, also can not only investigate on a very little area in order to the kind of representing whole group and form, this adds up the suitably problem of size of area with regard to having produced when a research group kind is formed.

In the prior art, definite method of forest collection minimum survey area has: the species-area curve method.

The common central authorities that adopt at stand of this method progressively enlarge the sample prescription area at double, and the kind number that statistics increases along with enlarged areas with the relation that number of planting and sample prescription area increase, is drawn out species-area curve (species-areacurve).The feature of curve is, originally precipitous rising then slowly tends towards stability, and this is because occur many kinds in several sample prescriptions of beginning, and the kind number that increases in the sample prescription that enlarged afterwards is just less and less, and curve begins the minimum area of pairing area group when mild.

Curve flattens, and slow standard is difficult for determining, accuracy is lower, and in addition, this method workload is big, and the time and the expense of investigation cost are higher.

Summary of the invention

The purpose of this invention is to provide a kind of accuracy higher, simple and easy to do determine the method for forest collection minimum survey area with mathematical model.

The objective of the invention is to be achieved through the following technical solutions:

Of the present inventionly determine to comprise the method for forest collection minimum survey area with mathematical model

In described forest community, choose sample prescription, and progressively enlarge the sample prescription area, add up the seeds kind number of the different area correspondence of described sample prescription, and adopt the Monod model to characterize the speciesarea relationship of described sample prescription:

$S=\frac{\mathrm{aA}}{1+\mathrm{bA}}$ In the formula, a, b-parameter; S-kind number; The A-area;

Described Monod model is asked the second order inverse:

$S^{\′\′}=\frac{2\mathrm{ab}}{{(1+\mathrm{bA})}^3};$

" during smaller or equal to preset threshold, pairing area A min is the least investigation area of described forest community as S.

As seen from the above technical solution provided by the invention, the method of determining forest collection minimum survey area with mathematical model of the present invention, owing to adopt the Monod model to characterize the speciesarea relationship of sample prescription, then the Monod model is asked the second order inverse, as the second order of kind of number S reciprocal " during smaller or equal to preset threshold; pairing area A min is the least investigation area of described forest community, and accuracy is higher, simple and easy to do.

Description of drawings

The synoptic diagram that Fig. 1 progressively enlarges for sample prescription area among the present invention.

Embodiment

The method of determining forest collection minimum survey area with mathematical model of the present invention, its preferable embodiment is, in described forest community, choose sample prescription, and progressively enlarge the sample prescription area, add up the seeds kind number of the different area correspondence of described sample prescription, then, characterize species-area curve with mathematical model.

Can adopt the model of Monod.The Monod model form is:

$S=\frac{\mathrm{aA}}{1+\mathrm{bA}}---\left(1\right)$

In the formula, a, b-parameter; S-kind number; A-area (m ²).

This model has following characteristic: A=0, S=0; S increases with area A, and being tending towards maximal value promptly has asymptotic line trend; A → ∞, S=a/b.This means that the macrospecies number of plant community can be determined by a/b.

According to the definition of kind-minimum area, area increased the plant species number again and does not also have substantial increase when promptly area was increased to a certain degree.Mathematical expression is, when the second derivative (S ") of model (1) is zero (S "=0) or be approximately zero (as smaller or equal to 1*10 ^-6) time, pairing area A min is the least investigation area of described forest community.

$S^{\′\′}=\frac{2\mathrm{ab}}{{(1+\mathrm{bA})}^3}---\left(2\right)$

The value of parameter a, b can be determined with the method that returns with the value of a plurality of kinds-area correspondence by choosing described sample prescription.

Specific embodiment:

Adopt 5 full-page proof ground to analyze, these 5 full-page proof ground derive from China, Mongolia, Burma, South Africa and Germany respectively.Wherein sample ground in South Africa belongs to the subtropics natural broad-leaved forests, and area is 11850m ², Chinese sample ground belongs to the temperate zone mixed deciduous forest, sample area 10000m ², German sample ground is the temperate zone mixed deciduous forest, sample area is 5740m ², Mongolian sample ground is Taiga, sample area is 2500m ², Burma sample ground is Tropical forests, sample area is 10000m ²These data comprise locus coordinate and the composition of all forests.

As shown in Figure 1, reference area begins to choose the sample ground, center of 10m * 10m from center, full-page proof ground, the size on sample ground, center also can less than or greater than 10m * 10m, press 20m * 20m, 30m * 30m, 40m * 40m, 45m * 45m, 50m * 50m, 55m * 55m, 60m * 60m, 70m * 70m, 80m * 80m, 90m * 90m then, enlarge gradually, and carry out the seeds counting successively.Wherein, the step-length when at every turn enlarging can be 5-15 rice, as 10 meters etc.

As shown in table 1, be that number and area relationship are planted in 5 full-page proof ground.

Table 1. speciesarea relationship

Sample area/m2	Plant number
						Burma/Sinthwat	South Africa/Knysna	China/Jiaohe	Germany/Bovenden	Mongolia/Sangstai
	100 400 900 1600 2500 3600 4900 6400 8100	2 3 10 14 19 26 27 28 30	2 6 9 16 18 20 22 22 22	3 8 11 13 15 17 19 19 20	3 3 4 5 6 6 7						2 3 4 4 4

As shown in table 2, the kind in the application table 1-area respective value is determined the value of described parameter a, b with the method that returns.Then, can ask macrospecies to count Smax and minimum area Amin by method of the present invention.

The model parameter that table 2. is estimated, macrospecies number and minimum area

Experimental field

a

b

R 2

Smax

Amin

Burma/Sinthwat	0.016059	0.000428	0.976	38	3261 (60×60m)
						South Africa/Knysna	0.01974	0.000748	0.977	26	2795 (55×55m)
China/Jiaohe	0.025969	0.001202	0.98	22	2468 (50×50m)
						Germany/Bovenden	0.012793	0.001671	0.752	8	1494 (40×40m)
Mongolia/Sangstai	0.051352	0.012529	0.894	4	788 (30×30m)

Studies show that from above-mentioned data speciesarea relationship can be expressed with the Monod model, the coefficient R on each full-page proof ground ²All very high; Now for the torrid zone is maximum, subtropics and take second place in the temperate zone, the cool temperature zone minimum, this climate characteristic with Species Diversity is consistent for the macrospecies numerical table that model is estimated; Parameter b is big more, and the value that macrospecies is counted Smax is more little.

Performance model of the present invention and mathematical measure have proposed kind-minimum area and can determine by the approach of model.Promptly by to make the model second derivative be zero or be approximately zero (1 * 10 ^-6) come to determine, be difficult for the defective determined thereby efficiently solve the slow standard that flattens of species-area curve in the prior art.

The above; only for the preferable embodiment of the present invention, but protection scope of the present invention is not limited thereto, and anyly is familiar with those skilled in the art in the technical scope that the present invention discloses; the variation that can expect easily or replacement all should be encompassed within protection scope of the present invention.

Claims (7)

1, a kind ofly determines to it is characterized in that the method for forest collection minimum survey area, comprise with mathematical model

In described forest community, choose sample prescription, and progressively enlarge the sample prescription area, add up the seeds kind number of the different area correspondence of described sample prescription, and adopt the Monod model to characterize the speciesarea relationship of described sample prescription:

$S=\frac{\mathrm{aA}}{1+\mathrm{bA}}$ In the formula, a, b-parameter; S-kind number; The A-area;

Described Monod model is asked the second order inverse:

$S^{\′\′}=\frac{2\mathrm{ab}}{{(1+\mathrm{bA})}^3};$

" during smaller or equal to preset threshold, pairing area A min is the least investigation area of described forest community as S.

2, according to claim 1ly determine to it is characterized in that the method for forest collection minimum survey area that in the described Monod model, the value of parameter a, b is determined with following method with mathematical model:

Choose the value of a plurality of kinds-area correspondence of described sample prescription, determine the value of described parameter a, b with the method that returns.

3, according to claim 1ly determine the method for forest collection minimum survey area to it is characterized in that described threshold value is: 1 * 10 with mathematical model ^-6

4, according to claim 1ly determine the method for forest collection minimum survey area to it is characterized in that described threshold value is: 0 with mathematical model.

5, according to claim 1ly determine the method for forest collection minimum survey area to it is characterized in that when choosing sample prescription in described forest community, the size of selected center sample prescription is smaller or equal to 10 meters * 10 meters with mathematical model.

6, according to claim 6ly determine to it is characterized in that the method for forest collection minimum survey area that when described sample prescription progressively enlarged, each step-length that enlarges was a 5-15 rice with mathematical model.

7, according to claim 7ly determine to it is characterized in that the method for forest collection minimum survey area that when described sample prescription progressively enlarged, each step-length that enlarges was 10 meters with mathematical model.

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