CN111831971B - Bird density estimation method - Google Patents

Bird density estimation method Download PDF

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CN111831971B
CN111831971B CN202010671298.4A CN202010671298A CN111831971B CN 111831971 B CN111831971 B CN 111831971B CN 202010671298 A CN202010671298 A CN 202010671298A CN 111831971 B CN111831971 B CN 111831971B
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CN111831971A (en
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张日权
伊剑锋
丁辉
刘威
王平平
徐海根
刘玉坤
方方
陈萌萌
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East China Normal University
Nanjing Institute of Environmental Sciences MEE
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Abstract

The invention discloses a bird density estimation method, which comprises the steps of firstly, acquiring field data in the same ecological environment; step two, obtaining beta0And beta1An estimated value of (d); step three, beta obtained by step two0And beta1Is calculated from the total number of samples
Figure DDA0002582397620000011
Step four, the total number of samples obtained through the step three
Figure DDA0002582397620000012
Calculating bird density values
Figure DDA0002582397620000013
The invention provides a novel method for estimating bird population density better by comprehensively and accurately using data information, which can ensure that the data information is more accurately and completely utilized, improve the accuracy of model parameter estimation and obtain a more accurate bird density estimation value.

Description

Bird density estimation method
Technical Field
The invention relates to the field of ecological environment monitoring, in particular to a bird density estimation method.
Background
The estimation of the number density of birds has always been an important topic of concern for operators of animal ecology and wildlife management. How to objectively, comprehensively and accurately estimate the density of birds has great significance for monitoring the ecological environment and protecting the biodiversity. The bird density estimation method can objectively reflect the change trend of bird populations and plays an important role in the aspects of biodiversity protection management and planning, ecological environment detection and the like.
In the practical application process, because the observation distance from the observed object to the sample line cannot be obtained in practice, the average value of the distance scale is commonly used in the conventional method at present to replace the actual observation distance, such as: the distance scale A is 0-25m2The scale range of (A) is 25-100 m; thus, the distance scale A is generally considered1Has an actual observation distance of 12.5 m and a distance scale A2The observation distance of (2) is 62.5 meters, and the average value of the distance scale is adopted to replace the actual observation distance, so that the information is inaccurate.
In addition, in practice, the detection rate of bird density is influenced by information such as ecological environment and temperature, and the traditional method does not consider comprehensive information of distance scale and covariates, so that the information is inaccurate, and the accuracy of finally estimated bird density is influenced.
Disclosure of Invention
Therefore, the technical problem to be solved by the invention is to overcome the defect that the estimation result is inaccurate due to inaccurate and incomplete data information utilization in bird density estimation in the prior art, and the invention provides a novel method for estimating the bird population density better by comprehensively and accurately using the data information.
A bird density estimation method comprising:
step one, acquiring field data in the same ecological environment;
dividing the sample line single-side distance of the ith sample line into A1,A2,A3,…,AHH consecutive sample distance scales; the field data comprises the number M of sample lines and the length L of the ith sample lineiDistance w between one side of the sample line, distance A between the ith sample line and one side of the sample line1Number of observations within n1iThe distance scale A of the ith sample line falling on the single side of the sample line2Number of observations within n2i…, dimension A of distance between the ith sample line and one side of the sample lineHNumber of observations within nHiAnd covariate Z of ith splinei(ii) a Wherein the total observed number of the ith sample line is ni，ni＝n1i+n2i+…+nHi；
Step two, obtaining beta0And beta1An estimated value of (d);
let the probe function g (x) represent the conditional probability of the sample observed at a distance x from the sample line;
obtaining a probe function formula:
Figure BDA0002582397600000021
lnσ2＝β0+β1z, wherein x is more than or equal to 0;
according to a Bayesian formula, obtaining the following formula I:
Figure BDA0002582397600000022
in the formula I, f (x) represents a probability density function that a sample is detected when the distance sample line is x;
substituting the detection function formula into the formula I, and converting to obtain a formula II:
Figure BDA0002582397600000023
let the number of birds observed on the ith sample line be ni1, …, M; h distance scales A1,A2,…,AHHas a probability density function of f1(x)、f2(x)、…、fH(x)；
Obtaining a likelihood function expression:
Figure BDA0002582397600000031
maximizing the likelihood function to obtain beta0And beta1An estimated value of (d);
step three, beta obtained by step two0And beta1Is calculated from the total number of samples
Figure BDA0002582397600000032
Let P (object observed | Z) denote the probability that the sample is observed under the condition that the covariate is Z, g (x | Z) denote the probability that the sample is detected when the distance to the sample line is x under the condition that the covariate is Z, and f (x | Z) denote the posterior density of the detection of the sample when the distance to the sample line is x under the condition that the covariate is Z, then:
Figure BDA0002582397600000033
Figure BDA0002582397600000034
wherein pi (x) is 1/w;
the total number of samples is calculated as:
Figure BDA0002582397600000035
formulation of probe function and beta0And beta1The total number of the samples is calculated after the estimated value is substituted into a calculation formula of the total number of the samples
Figure BDA0002582397600000036
Step four, the total number of samples obtained through the step three
Figure BDA0002582397600000037
Calculating bird density values
Figure BDA0002582397600000038
Total number of samples
Figure BDA0002582397600000039
Substitution into
Figure BDA00025823976000000310
The bird density value can be calculated
Figure BDA00025823976000000311
The partitioning of the ecological environment comprises:
a: arbor forest, B: bush and cutover, C: farmland, D: grassland, E: desert or gobi, F: residence point, G: inland water body, H: coastal area, I: and (5) swamp.
Wherein, the specific division rule of the ecological environment is shown in the following table 1:
TABLE 1
Figure BDA0002582397600000041
Further, in the second step, the distance between the bird and the sampling line can be divided into H consecutive sample distance scales by using H-1 numerical values, such as: the distance of birds from the spline can be divided into three consecutive sample distance scales using two values, and further, the distance of birds from the spline can be divided into 3 consecutive sample distance scales A using 2 values of 25 and 1001、A2And A3Wherein the sample distance scale A1Is 0-25, sample distance scale A2Is 25-100, sample distance scale A3Is 100m or more.
The covariate Z is temperature or humidity and the like.
W is 200.
Obtaining bird density values
Figure BDA0002582397600000042
Then, a bootstrap method is adopted to construct bird density value
Figure BDA0002582397600000043
The confidence interval of (c).
The confidence interval was 95%.
The technical scheme of the invention has the following advantages:
1. the invention does not use the average value of the distance scale to replace the actual observation distance x, only uses the scale information of the observation distance x, and improves the accuracy of data information utilization; meanwhile, the method of the invention also increases and utilizes the information of covariates, such as the information of ecological environment, temperature and the like, so that the calculation of the detection rate is more accurate; by the method, more accurate and complete data information utilization can be ensured, the accuracy of model parameter fixation is improved, and more accurate bird density estimation values can be obtained.
2. After the density estimation is obtained, the method processes density estimation data by adopting a bootstrap method, gives an estimated standard deviation and a 95% confidence interval thereof, and further ensures the precision of the density estimation.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings can be obtained by those skilled in the art without creative efforts.
FIG. 1 is a graph of the density distribution of white under eco-A conditions;
FIG. 2 is a graph of the density distribution of white under eco B conditions;
FIG. 3 is a graph of the density distribution of white under eco-C conditions;
FIG. 4 is a density profile of white head bulbul under eco A conditions;
FIG. 5 is a density profile of white head bulbul under eco B conditions;
FIG. 6 is a density profile of whitehead bulbul under eco-C conditions;
FIG. 7 is a density profile of the North Red Tail, 40498under eco A conditions;
FIG. 8 is a density profile of the North Red Tail, 40498under eco B conditions;
FIG. 9 is a density profile of the North Red Tail, 40498under eco C conditions;
FIG. 10 is a density profile of orange fin noise \40539under eco A conditions;
FIG. 11 is a density profile of orange fin noise \40539under eco B conditions;
fig. 12 is a graph showing a density distribution of a large-spotted woodpecker under the ecological environment a.
Detailed Description
Example 1
A bird density estimation method comprising:
the observation data of white under the ecological environment a of Chongqing city in 2015 is taken as an example, and the specific observation data is shown in table 2. The 0-25m distance is divided into distance scale A in Table 21Dividing the distance of 25-100m into a distance scale A2Dividing the distance of 100m or more into a distance scale A3。
TABLE 2
Figure BDA0002582397600000061
Let the distance of white 40545 from the sample line be x, probe function
Figure BDA0002582397600000071
lnσ2＝β0+β1z, where z is the average temperature, in practice w is 200, then
Figure BDA0002582397600000072
And is
Figure BDA0002582397600000073
Figure BDA0002582397600000074
If the total number of the M sample lines is set, the number of birds observed on the ith sample line is niOne (i ═ 1...., M), then the likelihood function formula can be expressed as:
Figure BDA0002582397600000075
the temperature data in table 2 is substituted into the likelihood function formula, and the substitution is as follows:
Figure BDA0002582397600000076
by maximizing the likelihood function, one can obtain
Figure BDA0002582397600000077
Thus, β is0And beta1The total number of the observed objects can be obtained after the estimated value is substituted into the calculation formula of the total number of the samples
Figure BDA0002582397600000078
Comprises the following steps:
Figure BDA0002582397600000081
the density of white 40545 was estimated as:
Figure BDA0002582397600000082
then constructing bird density value by using bootstrap method
Figure BDA0002582397600000083
The steps of confidence interval of (a) are as follows:
the first step is as follows: randomly extracting sample lines for estimating bird density in a certain sampling area, wherein 80% of the sample lines are extracted each time;
the second step is that: constructing point estimates in the foregoing manner based on the extracted spline;
repeating the first step and the second step for multiple times to obtain multiple point estimates; if we perform 100 repeated decimation on the sample lines of the selected region, 100 point estimation values can be obtained.
The third step: constructing a 95% confidence interval for the point estimate; namely: the interval consisting of 2.5% quantile points and 97.5% quantile points of the 100-point estimate was constructed as shown in table 3.
Table 3 white at habitat a 2015 year density estimate and 95% confidence interval
Figure BDA0002582397600000084
Using the same procedure described above, bird density of white was also estimated in 2015 under eco-C (farm) conditions of different provinces, and the estimation results are shown in table 4.
TABLE 4
Figure BDA0002582397600000091
In practice, the detection rate of bird density is affected by information of ecological environment, temperature and the like, and the traditional method uses less information of covariates (ecological environment, temperature). In order to enable the calculation of the detection rate to be more accurate, the method and the device utilize the information of all covariates to estimate the parameters, and only utilize the scale information of the observation distance to enable the estimation of the model parameters to be more accurate. And after obtaining the density estimation, a bootstrap method is adopted to give an estimated standard deviation and a 95% confidence interval thereof, so that more accurate bird density estimation is further obtained. The method is feasible in statistical theory and practical application.
According to the invention, the density estimated values of the white in different areas under different ecological environments and at different time points are obtained by calculation by adopting the formula, and the density estimated values are drawn into a density distribution diagram on a map, as shown in fig. 1-3.
Example 2
The present embodiment is different from embodiment 1 in that sample data is different in the present embodiment. In this embodiment, the sample densities of the white head bulbul in the ecological environment a, the ecological environment B and the ecological environment C, the sample densities of the northern red tail 40498in the ecological environment a, the ecological environment B and the ecological environment C, the sample densities of the orange wing noise 40539 in the ecological environment a and the ecological environment B, and the sample densities of the large-spotted woodpecker in the ecological environment a are estimated, and the estimated density values are plotted as a density distribution graph, as shown in fig. 4 to 12.
Comparative example 1
The comparative example adopts a variable distance sampling method in the prior art, and the obtained observation data is input into Distance6.0 to analyze information such as population density.
In this comparative example, the data analyzed are shown in table 5 below:
table 5 traditional method white density estimation and 95% confidence intervals in habitat a in 2015
Figure BDA0002582397600000101
By comparing with the data obtained in the prior art and according to the opinion fed back by relevant experts of Nanjing environmental protection institute, the species distribution diagram and the annual variation trend result finally obtained by the new method are accurate and reliable under the condition that the accurate distance between the observed object and the sample line cannot be obtained.
It should be understood that the above examples are only for clarity of illustration and are not intended to limit the embodiments. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. And obvious variations or modifications therefrom are within the scope of the invention.

Claims (7)

1. A bird density estimation method, comprising:
acquiring field data in the same ecological environment;
dividing the sample line single-side distance of the ith sample line into A1,A2,A3,…,AHH consecutive sample distance scales; the field data comprises the number M of sample lines and the length L of the ith sample lineiDistance w between one side of the sample line, distance A between the ith sample line and one side of the sample line1Number of observations within n1iThe distance scale A of the ith sample line falling on the single side of the sample line2Number of observations within n2i…, dimension A of distance between the ith sample line and one side of the sample lineHNumber of observations within nHiAnd covariate Z of ith splinei(ii) a Wherein the total observed number of the ith sample line is ni，ni＝n1i+n2i+…+nHi；
Step two, obtaining beta0And beta1An estimated value of (d);
let the probe function g (x) represent the conditional probability of the sample observed at a distance x from the sample line;
let the probe function formula:
Figure FDA0002582397590000011
lnσ2＝β0+β1z, wherein x is more than or equal to 0;
according to a Bayesian formula, obtaining the following formula I:
Figure FDA0002582397590000012
in the formula I, f (x) represents a probability density function that a sample is detected when the distance sample line is x;
substituting the detection function formula into the formula I, and converting to obtain a formula II:
Figure FDA0002582397590000013
let the number of birds observed on the ith sample line be ni1, …, M; h distance scales A1、A2…,、AHHas a probability density function of f1(x)、f2(x)、…、fH(x)；
Obtaining a likelihood function expression:
Figure FDA0002582397590000021
maximizing the likelihood function to obtain beta0And beta1An estimated value of (d);
step three, beta obtained by step two0And beta1Is calculated from the total number of samples
Figure FDA0002582397590000022
Let P (object observed | Z) denote the probability that the sample is observed under the condition that the covariate is Z, g (x | Z) denote the probability that the sample is detected when the distance to the sample line is x under the condition that the covariate is Z, and f (x | Z) denote the posterior density of the detection of the sample when the distance to the sample line is x under the condition that the covariate is Z, then:
Figure FDA0002582397590000023
Figure FDA0002582397590000024
wherein pi (x) is 1/w;
the total number of samples is calculated as:
Figure FDA0002582397590000025
formulation of probe function and beta0And beta1The total number of the samples is calculated after the estimated value is substituted into a calculation formula of the total number of the samples
Figure FDA0002582397590000026
Step four, the total number of samples obtained through the step three
Figure FDA0002582397590000027
Calculating bird density values
Figure FDA0002582397590000028
Total number of samples
Figure FDA0002582397590000029
Substitution into
Figure FDA00025823975900000210
The bird density value can be calculated
Figure FDA00025823975900000211
2. The bird density estimation method according to claim 1, wherein in the second step, the distance of the birds from the sampling line is divided into three consecutive sample distance scales by using two values, 25 and 100 respectively, and the distance of the birds from the sampling line is divided into A1、A2And A3These 3 consecutive sample distance scales, where,sample distance dimension A1Is 0-25m, sample distance scale A2Is 25-100m, sample distance scale A3Is 100m or more.
3. A bird density estimation method according to claim 1 or 2, wherein w is 200.
4. A bird density estimation method according to any one of claims 1 to 3, wherein bird density values are obtained
Figure FDA0002582397590000031
Then, a bootstrap method is adopted to construct bird density value
Figure FDA0002582397590000032
The confidence interval of (c).
5. A bird density estimation method according to claim 4, wherein the confidence interval is 95%.
6. A bird density estimation method according to any one of claims 1-5, wherein the covariate Z is temperature or humidity.
7. The bird density estimation method of any one of claims 1-5, wherein the partitioning of the ecological environment comprises:
a: the wood of a tree forest is treated by the method,
b: the method for cultivating the shrub forest and the cut land,
c: the agricultural field is provided with a plurality of agricultural fields,
d: the method comprises the following steps of (1) preparing a grassland,
e: in desert or gobi, the plants are in desert or gobi,
f: at the point of residence, the location of the dwelling,
g: the water body on the inland is provided with a plurality of water bodies,
h: along the sea, the water-saving device is arranged,
i: and (5) swamp.
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