JP6871001B2 - Wildlife population dynamics estimation device, wildlife population dynamics estimation program and wildlife population dynamics estimation method - Google Patents

Description

The present invention relates to a wildlife population dynamics estimation device, a wildlife population dynamics estimation program, and a wildlife population dynamics estimation method.

Traditionally, crop damage caused by wild animals such as deer and wild boar has become serious, and it is desired to properly conserve and manage wild animals. At present, each administrative agency such as the Ministry of the Environment, prefectures, and municipalities makes decisions on wildlife conservation and management, such as determining the required number of catches based on estimates such as the natural increase rate of wild animals and the number of individuals. Is being done.

Further, conventionally, the inventors of the present application have proposed a method for estimating the population dynamics of wild animals (see, for example, Non-Patent Document 1).

In Non-Patent Document 1, the population dynamics of Japanese deer are estimated by deriving the posterior distribution based on the prior distribution and known data regarding the natural growth rate of Japanese deer and the number of individuals (population dynamics). A method (wildlife population dynamics estimation method) is disclosed.

Hiroshi Sakata, Yasushi Kishimoto, Kanako Seki, "Estimation and Future Prediction of Population Dynamics of Sika Deer (Honshu, Hyogo Prefecture 2011)", Hyogo Wildlife Report, Forest Animal Research Center, Hyogo Prefecture, 2012, No. 1, 1 ~ 16 pages

However, in the wildlife population dynamics estimation method disclosed in Non-Patent Document 1, it is desired to further improve the estimation accuracy in order to formulate a more appropriate individual adjustment plan and capture plan.

The present invention has been made to solve the above-mentioned problems, and one object of the present invention is a wild animal individual capable of further improving the accuracy of estimation of wild animal population dynamics. To provide a population dynamics estimation device, a wildlife population dynamics estimation program, and a wildlife population dynamics estimation method.

In estimating the population dynamics of wild animals, the sex of wild animals such as the number of adult females (ratio) capable of giving birth and the number of cubs (ratio) with a particularly high mortality rate have been used. It is known that the estimation accuracy is improved by considering the distinction between the sex and age of wild animals because the composition of wild animals and age affects the population dynamics of the wild animals, especially the natural growth rate. However, it is difficult to obtain sufficient data on the distinction between sex and age of wild animals, and there is no estimation method that matches the accuracy of the data. In many cases, it became unpredictable. Therefore, as a result of diligent studies by the inventor of the present application, in order to achieve the above object, the wildlife population dynamics estimation device according to the first aspect of the present invention uses a model that defines fluctuations in the number of wild animals. , A wildlife population dynamics estimator that estimates wildlife population variability, using an overall model that defines wildlife population variability based on the total wildlife population. Specifies the first estimation means for estimating the total number of wild animals in the future, and the partial variation in the number of wild animals divided into multiple categories according to a specific sex, age, or a combination thereof. It is equipped with a second estimation means for estimating the partial population of wild animals using a partial model , and the overall model includes the natural growth rate of wild animals, the total population of wild animals, and the wild animals. Based on the total number of catches, the total number of future wildlife is defined, and the first estimation means influences the composition ratio of the wildlife category for a particular sex, age, or combination thereof. It is configured to determine the natural growth rate of the overall model based on the term not used and the rate of change of the natural growth rate that fluctuates depending on the composition ratio of the wildlife category .

In the wildlife population dynamics estimation device according to the first aspect of the present invention, as described above, based on the total number of wild animals, an overall model that defines the variation of the total number of wild animals is used. Specifies the first estimation means for estimating the total number of wild animals in the future, and the partial variation in the number of wild animals divided into multiple categories according to a specific sex, age, or a combination thereof. A second estimation means for estimating the partial population of wild animals using a partial model is provided. This allows the partial model to estimate the partial population of wildlife that is classified into a specific sex, age, or combination thereof, so that the number of adult females (ratio) and the number of cubs It is possible to derive the number of individuals (ratio) of sex and age, which are important factors that influence population dynamics such as (ratio). As a result, the number of individuals in categories (parts) that have a particular effect on the natural growth rate of animal species, such as the number of individuals capable of giving birth (ratio) and the number of individuals with different mortality rates (ratio). Since the dynamics of the ratio) are acquired more accurately, the accuracy of estimating the population dynamics of wild animals can be improved. In addition, the natural growth rate of the overall model can be determined by considering the variation from the term that is not affected by the composition ratio of the wildlife division for a specific sex, age, or combination thereof. The estimation means can more effectively reflect the influence of the composition ratio of the wildlife division on the natural growth rate. Therefore, the natural increase rate can be estimated more accurately. As a result, the accuracy of estimating the population dynamics of wild animals can be further improved. In addition, it will be possible to predict the future with high accuracy based on the capture plan for each gender and age category.

In this case, preferably, the volatility of the natural growth rate is based on at least one of the volatility of the wildlife segment composition to the birth rate and the volatility of the wildlife segment composition to survival. It is a rate that is defined and fluctuates depending on the difference in the composition ratio of wildlife categories. With this configuration, the composition ratio of the wildlife category can more accurately evaluate the effect on the natural growth rate and reflect it in the estimation results (the effect on the rate of change on the birth rate and the survival rate). Since it is defined based on at least one of the variability rates and more detailed estimates are made, the accuracy of wildlife population dynamics estimates can be further improved.

In the configuration in which the natural increase rate is determined based on the term that is not affected by the composition ratio of the wild animal category and the fluctuation rate of the natural increase rate that fluctuates depending on the composition ratio of the wild animal category, the wild is preferable. The term that is not affected by the composition ratio of the animal division is the standard natural growth rate that does not fluctuate and is preset as the natural growth rate of the wildlife population whose composition ratio of the wild animal division is the standard composition ratio. including. With this configuration, the natural growth rate of the entire model can be determined in consideration of the fluctuation from the standard natural growth rate (reference value) that does not fluctuate. The terms that are not affected by can be estimated more accurately. As a result, the accuracy of estimating the population dynamics of wild animals can be further improved.

In the configuration in which the term not affected by the composition ratio of the wild animal category includes the standard natural increase rate, preferably, the term not affected by the composition ratio of the wild animal category leads to the natural increase rate of the environment in which the wild animal inhabits. Includes environmentally-induced volatility that indicates the impact of. With this configuration, environmental factors that affect the natural growth rate (wildlife population) of the wildlife habitat are further taken into account in determining the natural growth rate. , The accuracy of wildlife population dynamics estimation can be further improved.

In a configuration in which the term not affected by the composition ratio of the above wildlife classification includes the fluctuation rate due to the environment, preferably, the fluctuation rate due to the environment is the natural increase rate due to the increase in the population density of wild animals in the habitat. Includes at least variability due to reduced population density. With this configuration, the density effect (wildlife in the habitat area) is relatively easy to model (formulate) among the fluctuation rates caused by the environment that show the effect of the wildlife habitat on the wildlife population. Since the increase in habitat density of wild animals reduces the natural growth rate of wild animals (variation rate due to habitat density), the accuracy of estimation of wildlife population dynamics can be further improved.

In the wild animal population dynamics estimation device according to the first aspect, preferably, the partial model defines the variation in the population of the cub, the adult, or both for the estimation of the population of the cub or the adult. To specify the population variation of males or females, or males or females or combinations of these categories, for the purpose of estimating the population of males, females, females or males, with the first part model Includes a second part model. When configured in this way, the partial model is divided into a first part model that defines the variation in the composition ratio of the wildlife division for age and a second part that defines the variation in the composition ratio of the wildlife division for sex. By subdividing into a model and considering it in detail, the accuracy of estimating the population dynamics of wild animals can be further improved.

The wildlife population dynamics estimation program according to the second aspect of the present invention is performed by a computer using a model that defines the fluctuation of the wildlife population, in estimating the fluctuation of the wildlife population. A first estimation method for estimating the total number of wild animals in the future, and a specific sex and age, using an overall model that defines fluctuations in the total number of wild animals based on the total number of wild animals. or, by using a partial model that defines a partial variation in the population of wild animals to be divided into a plurality by a combination thereof, and a second estimation means for performing a partial population estimates of wild animals, In the overall model, a means of defining the total population of wild animals in the future based on the natural growth rate of wild animals, the total population of wild animals, and the total number of wild animals captured, and the first Estimates include terms that are not affected by the composition of wildlife categories for a particular gender, age, or combination thereof, and fluctuations in the rate of natural increase that fluctuate depending on the composition of wildlife categories. To serve as a means of determining the natural growth rate of the overall model.

In the wildlife population dynamics estimation program according to the second aspect of the present invention, as described above, the computer is performed using a model that defines the fluctuation of the wildlife population, and the fluctuation of the wildlife population is performed. In the estimation, the first estimation means for estimating the total number of wild animals in the future, and the first estimation means for estimating the total number of wild animals in the future, using the whole model that defines the variation of the total number of wild animals based on the total number of wild animals. Estimates of future partial wildlife populations using partial models that define partial wildlife population variability divided into multiple categories according to specific gender, age, or combination thereof. It functions as a second estimation means to be performed. This allows the partial model to estimate the partial population of wild animals that are classified into a specific sex, age, or combination thereof, so that the number of adult females (ratio) and the number of cubs It is possible to derive the number of individuals (ratio), which is an important factor that influences population dynamics such as (ratio). As a result, the number of individuals in categories (parts) that have a particular effect on the natural growth rate of animal species, such as the number of individuals capable of giving birth (ratio) and the number of individuals with different mortality rates (ratio). Since the dynamics of the ratio) are acquired more accurately, the accuracy of estimating the population dynamics of wild animals can be improved. In addition, the natural growth rate of the overall model can be determined by considering the variation from the term that is not affected by the composition ratio of the wildlife division for a specific sex, age, or combination thereof. The estimation means can more effectively reflect the influence of the composition ratio of the wildlife division on the natural growth rate. Therefore, the natural increase rate can be estimated more accurately. As a result, the accuracy of estimating the population dynamics of wild animals can be further improved. In addition, it will be possible to predict the future with high accuracy based on the capture plan for each gender and age category.

The wildlife population dynamics estimation method according to the third aspect of the present invention is a wildlife population dynamics estimation that estimates wildlife population fluctuations using a model that regulates wildlife population fluctuations. A method of estimating and identifying future wildlife populations using a global model that defines wildlife population variability based on wildlife populations. Steps to estimate future wildlife partial populations using a partial model that defines partial wildlife population variability divided into multiple categories according to sex, age, or combination thereof. And , in the overall model, the steps to determine the future total wildlife population based on the natural growth rate of wildlife, the total wildlife population, and the total wildlife catch. Based on terms that are not affected by the composition of wildlife categories for a particular gender, age, or combination thereof, and the rate of change in natural growth that is influenced by the composition of wildlife categories. It includes a step to determine the natural growth rate of the overall model .

In the wildlife population dynamics estimation method according to the third aspect of the present invention, as described above, a wild animal that estimates the fluctuation of the wildlife population by using a model that defines the fluctuation of the wildlife population. This is a method for estimating the total population dynamics of wild animals, and estimates the total number of wild animals in the future using an overall model that defines fluctuations in the total number of wild animals based on the total number of wild animals. Partial wildlife populations of the future, using a partial model that defines the steps to be taken and the variation in partial wildlife populations that are divided into multiple categories according to specific gender, age, or combination thereof. There is a step to estimate. This allows the partial model to estimate the partial population of wild animals that are classified into a specific sex, age, or combination thereof, so that the number of adult females (ratio) and the number of cubs It is possible to derive the number of individuals (ratio), which is an important factor that influences population dynamics such as (ratio). As a result, the number of individuals in categories (parts) that have a particular effect on the natural growth rate of animal species, such as the number of individuals capable of giving birth (ratio) and the number of individuals with different mortality rates (ratio). Since the dynamics of the ratio) are acquired more accurately, the accuracy of estimating the population dynamics of wild animals can be improved. Also, the natural growth rate of the overall model can be determined by taking into account variations from terms that are not affected by the composition of wildlife categories for a particular gender, age, or combination thereof, and thus wildlife. The influence of the composition ratio of the above categories can be more effectively reflected in the natural increase rate. Therefore, the natural increase rate can be estimated more accurately. As a result, the accuracy of estimating the population dynamics of wild animals can be further improved. In addition, it will be possible to predict the future with high accuracy based on the capture plan for each gender and age category.

According to the present invention, as described above, the accuracy of estimating the population dynamics of wild animals can be further improved.

It is a block diagram which showed the structure of the population dynamics estimation apparatus by 1st Embodiment of this invention. It is a figure for demonstrating the outline of Bayesian estimation performed by the population dynamics estimation apparatus according to 1st Embodiment of this invention. It is a flowchart for demonstrating the population dynamics estimation process performed by the population dynamics estimation apparatus by 1st Embodiment of this invention. It is a block diagram which showed the structure of the population dynamics estimation apparatus by 2nd Embodiment of this invention.

Hereinafter, embodiments embodying the present invention will be described with reference to the drawings.

[First Embodiment]
(Structure of population dynamics estimation device)
First, the configuration of the population dynamics estimation device 100 according to the first embodiment of the present invention will be described with reference to FIGS. 1 and 2.

The population dynamics estimation device 100 according to the first embodiment of the present invention is a device that estimates the fluctuation of the wildlife population by using a model that defines the fluctuation of the wildlife population.

As shown in FIG. 1, the population dynamics estimation device 100 is mainly composed of a CPU 1, a hard disk 2, a reading device 3, a communication unit 4, and an output unit 5. The CPU 1, the hard disk 2, the reading device 3, the communication unit 4, and the output unit 5 are connected to each other by a bus 6. The population dynamics estimation device 100 is an example of a "computer" within the scope of claims.

The CPU 1 is configured to be able to control each part of the population dynamics estimation device 100. Further, the CPU 1 is configured to perform a wild animal population dynamics estimation process by executing the population dynamics estimation program 10a installed on the hard disk 2.

The CPU 1 includes an estimation means 1a, an estimation means 1b, and an estimation means 1c that execute the equations (models) [1], [2], and [3], which will be described later, respectively. The estimation means 1a is an example of the "first estimation means" in the claims. Further, the estimation means 1b and the estimation means 1c are examples of the "second estimation means" in the claims.

Various computer programs for the CPU 1 to execute, such as an operating system (not shown) and a population dynamics estimation program 10a, are installed on the hard disk 2. Further, on the hard disk 2, the number of captured fecal pellets, the fecal pellet density (value obtained by dividing the number of fecal pellets counted in the predetermined survey range by the area of the predetermined survey range), and the witness efficiency (observer per person (hunting)). It also stores known data (observed data) on the population dynamics of wild animals, such as the average value of individuals witnessed in one day. Known data may be stored in the hard disk 2 by inputting using a keyboard (not shown), or may be imported from another device via a communication unit 4 including an Ethernet (registered trademark) interface or the like.

The reading device 3 is composed of a disk drive, and can read information recorded on a portable recording medium 10 such as a CD-ROM. The population dynamics estimation device 100 can read the population dynamics estimation program 10a recorded on the portable recording medium 10 by the reading device 3 and install it on the hard disk 2. Further, the population dynamics estimation program 10a may be received via the communication unit 4 including an Ethernet (registered trademark) interface or the like. The communication unit 4 is configured to be capable of data communication with an external terminal.

The output unit 5 is connected to the display device 20, and is configured to be able to output graph information of the prior distribution and the posterior distribution, information on the estimation result, and the like to the display device 20 in the population dynamics estimation process described later. ing.

The population dynamics estimation device 100 estimates by the Bayesian estimation method that derives the posterior distribution using the prior distribution. As an example, the population dynamics estimation device 100 estimates the total future population using a process model for the total population of wild animals, including males and females. In this case, at least the total population _{(i) for} each year is an unknown value (parameter). With respect to such an unknown parameter of population dynamics (total number of individuals _(i) ), the population dynamics estimation device 100 sets the prior distribution of population dynamics and the set prior distribution as shown in FIG. It is configured to derive posterior distributions and estimate population dynamics by Markov Chain Monte Carlo (MCMC) using and known data. In the first embodiment, an example in which the posterior distribution is derived and the population dynamics is estimated by the Markov chain Monte Carlo method (MCMC) is shown, but the posterior distribution is derived by another method and the population dynamics is derived. Estimates may be made. Known data are wildlife population dynamics obtained from wildlife catches, manure density, sighting efficiency (witness information obtained from hunters), and light census surveys. Means valid data that may affect dynamics.

Total number of individuals _{(i + 1)} = Natural increase rate _{(i + 1)} x Total number of individuals _(i) -Total number of catches _{(i + 1)} ... [1]
The formula [1] is an example of the "overall model" of the claims.

Here, i represents a year. For example, if the fiscal year 2016 is i, the fiscal year 2015 is i-1, and the fiscal year 2017 is i + 1. The total population _{(i + 1)} represents the total population of wild animals, including males and females, at the end of i + 1. The natural growth rate _{(i + 1)} represents the growth rate of the population due to birth and natural death in the i + 1 year. The total population _(i) represents the total population of wild animals, including males and females, at the end of i. The total number of catches _{(i + 1)} represents the total number of wild animals caught in the i + 1 year, including males and females.

The above formula [1] defines the variation in the total number of wild animals including males and females based on the total number of wild animals including males and females at the end of i. The population dynamics estimation device 100 (estimation means 1a) estimates the total number of wild animals including males and females at the end of i + 1 (future) using the formula [1]. The total number of individuals _{(i + 1)} does not necessarily have to be derived by the above formula [1], and the formula “total number of individuals _{(i + 1)} = natural increase rate _{(i + 1)} × (total number of individuals _(i) − total number of captured animals) _{(I + 1)} ) ”may be derived.

Further, as an example, the population dynamics estimation device 100 defines _{the process model for the cub population (i)} as shown in the following equation [2], and derives the cub population. The cub is an individual before the breeding age is reached, for example, a sika deer or a wild boar is an individual under 1 year old, and other individuals are considered to be adults, although it depends on the animal species.

Number of cubs _(i) = (survival rate of cubs _(i) -(effect of density _(i) + effect of other factors _(i) )) x number of initial cubs _(i) -number of cubs captured _(i)・ ・ ・ [2]
The equation [2] is an example of the "partial model" and the "first partial model" of the claims.

Here, the cub population _(i) represents the cub population at the end of i. The larval survival rate _(i) represents the proportion of larvae that survive throughout the year in the estimated target population at the end of i. The density effect is an example of the scope of claims, "the increase in the population density of wild animals in the habitat reduces the natural increase rate and the fluctuation rate due to the population density".

The density effect _(i) represents the effect that the increase in the density of the population in the i-year reduces the natural increase rate. Specifically, the density effect represents the effect of a phenomenon such as food shortage caused by the effect of congestion on the natural increase rate. The effect of congestion means the effect of increasing the population density of wild animals in the habitat due to an increase in the number of individuals in a limited habitat and a decrease in the habitat per individual. The density effect is set to zero (0) in a state where the habitat is sufficiently wide for the number of individuals and there are no competing individuals competing for food (ideal state).

The effect _(i) of other factors represents the effect on the natural increase rate due to the environment other than the _{density effect (i)} in the i-year. Specifically, the effects of other factors represent the effects (effects) of environmental factors such as snowfall and the decrease in food (grass, etc.) due to the intense heat on the natural increase rate. The density effect and the effects of other factors take positive values. In short, the density effect and the effects of other factors always act as negative factors on the cub survival rate in the above equation [2] (model). In the first embodiment, the density effect and the effect of other factors are always taken as negative values, but depending on how the density effect and the effect of other factors are grasped, the density effect and others The effect of the factor may be a factor that takes both positive and negative (plus and minus) values. In addition, the effects of other factors are expressed in the above equation [2] (model) as unpredictable error fluctuations when there is no data to observe and evaluation is difficult, or when valid data are not obtained. It may be processed without incorporating.

The initial cub ratio _(i) represents the ratio of cubs to the total population at the start of year i. In short, the initial larvae ratio _(i) represents the ratio of the number of larvae born to the total number of individuals after giving birth at the beginning of year i and before deducting natural death or capture. The initial cub population _(i) represents the number of cubs in the early stage of year i. The number of cubs captured _(i) represents the number of cubs captured in year i.

The above equation [2] defines the variation in the number of cubs. The population dynamics estimation device 100 (estimation means 1b) estimates the number of cubs at the end of i using the formula [2].

Further, as an example, the population dynamics estimation device 100 defines _{the process model for the adult female population (i)} as shown in the following equation [3], and derives the adult female population.

Adult female population _(i) = (adult survival rate _(i) − (density effect _(i) + effect of other factors _(i) )) × initial adult female population _(i) − adult female capture number _(i)・.・ ・ [3]
The formula [3] is an example of the "partial model" and the "second partial model" of the claims.

Here, the number of adult females _(i) represents the number of adult females at the end of i. Adult survival rate _(i) represents the percentage of adult animals that survive throughout the year in the estimated target population in early year i. The initial adult female population _(i) represents the number of adult females at the beginning of year i. The number of adult females captured _(i) represents the number of adult females captured in year i.

The above equation [3] defines the variation in the number of adult females. The population dynamics estimation device 100 (estimation means 1c) estimates the number of adult females at the end of i using the formula [3].

By defining the above formulas [1] to [3], the following formula [4] that defines the number of adult males can be obtained.

Adult male population _(i) = total population _(i) -adult female population _(i) -juvenile population _(i) ... [4]

As described above, in the population dynamics estimation device 100 of the first embodiment, when estimating the population dynamics, a model created from known data such as the number of catches and a prior distribution (formulas [5] to [9] described below are used. ]) And the above-mentioned process models (the above equations [1] to [4]) are used to perform hierarchical Bayesian estimation by the Markov chain Monte Carlo method.

(Natural increase rate)
The population dynamics estimation device 100 (estimation means 1a) is configured to determine the natural increase rate of the above formula [1] by the following formula [5].

Natural increase rate _(i) = Standard natural increase rate + Gender (gender composition, that is, the ratio of male to female) and age composition effect _(i) -(Density effect _(i) + effect of other factors _(i) ) ・ ・ ・ [5]
The effect of sex and age composition is an example of the "volatility of the natural increase rate that fluctuates depending on the composition ratio of the wildlife category" in the claims. Also, the standard natural growth rate- (density effect _(i) + effect of other factors _(i) ) is the composition of the wildlife classification for a particular sex, age, or combination thereof within the claims. This is an example of "a term that is not affected by the ratio".

Here, the standard natural growth rate is preset as the natural growth rate of a wildlife population in which the composition ratio of the wildlife classification for a specific sex, age, or a combination thereof is in the standard composition ratio. It is a value that does not fluctuate. Specifically, the standard biotic potential is the case where the proportion of cubs and adult females is a preset standard proportion, and is not affected by the density effect and the effects of other factors (environmental effects). It means the natural increase rate when assumed.

As a specific example, the standard natural increase rate has a standard gender composition (sex ratio) such that the ratio of male to female is 1: 1 and the ratio of adult to cub is 2: 1. It is a value preset as a natural increase rate in the case of such a standard age structure. Therefore, if the gender composition (gender) and age composition are standard and under standard conditions that are not affected by density effects, environmental factors, or other factors, "natural increase rate = standard natural". It becomes "increasing rate". The effects of sex and age composition, the density effect, and the effects of other factors are fluctuating values, unlike the standard natural increase rate. In short, the effects of sex and age composition, the effects of density and the effects of other factors are terms for modifying the standard unvariable rate of natural increase.

The effects of sex and age composition include that the natural increase rate increases when there are many adult females, and the natural increase rate decreases when there are many young animals (young individuals with a higher mortality rate than adults). Represents the effect on the natural increase rate.

As described above, the density effect and the effects of other factors always take positive values. Therefore, in the above equation [5] (model), the negative factor (survival rate) is always relative to the standard natural increase rate. It acts as a lowering effect).

It is considered that the effect of density effect and other factors and the effect of sex and age composition influence each other. However, in the above equation [5], in order to estimate population dynamics more effectively, the effects of density effect and other factors and the effects of sex and age composition are separated as independent elements that do not affect each other. So, each can be evaluated.

The effects of sex and age composition depend on the age-specific birth rate of females and the sex and age-specific survival rates. Therefore, the population dynamics estimation device 100 (estimation means 1a) is a part that varies depending on the age composition (sex ratio), the age composition, the estimated values of the birth rate and the survival rate, and the sex composition (sex) and the age composition. The relational expression with is determined by the following equations [6] to [8]. Further, the population dynamics estimation device 100 (estimation means 1a) is configured to determine the effect of the sex and age composition of the above formula [5] by the following formula [6].

Effect of sex and age composition _(i) = Effect on fertility rate _(i) + Effect on survival rate _(i) ... [6]
The effect on the fertility rate is an example of the "volatility of the composition ratio of the wildlife category on the fertility rate" in the claims. In addition, the effect on the survival rate is an example of "the volatility of the composition ratio of the wildlife category on the birth rate" in the claims.

The population dynamics estimation device 100 (estimating means 1a) determines the effect of the above formula [6] on the birth rate by the following formula [7], and determines the effect of the above formula [6] on the survival rate as follows. It is configured to be determined by the equation [8].

Effect of the ratio of adult females on the birth rate _(i) = (Ratio of adult females _(i) -Standard ratio of adult females) x Birth rate per adult female ... [7]

Effect of cub ratio on survival rate _(i) = (early cub ratio _(i) -standard cub ratio) x (juvenile survival rate-adult survival rate) ... [8]

Here, the birth rate per adult female means the average number of offspring per adult female in one year. For example, in general, adult female deer give birth to about one offspring per year, and adult female wild boar give birth to an average of about four to five offspring per year. _{The effect (i)} on the fertility rate represents the effect of the gender composition and age composition on the fertility rate in the i-year. _{The effect (i)} on the survival rate represents the effect of the gender composition and the age composition on the survival rate in the year i. The sum of the survival rate and the mortality rate is 1 (100%).

The adult female ratio _(i) represents the ratio of the number of adult females to the total number of individuals in the year i. The standard adult female ratio represents the ratio of adult females to the total number of individuals set as a standard in advance. The standard cub ratio represents the ratio of cubs (for example, individuals under 1 year old) to the total number of individuals set as a standard in advance.

In the above equations [6] to [8], the effects of gender and age composition are mathematically expressed (modeled) independently by defining the difference between the standard gender composition and age composition and the estimated value. doing. Further, in the above formulas [6] to [8], the birth rate and the survival rate are assumed to be standard values when it is assumed that there is no influence due to the density effect and the effect of other factors (environmental effect). As a result, when assuming values such as birth rate and survival rate, which are values that are easy to define accurately based on known data to some extent and do not fluctuate, and estimation of adult female ratio and early cub ratio, etc. It becomes easier to set the prior distribution. In addition, it is possible to estimate (derive) a value (factor) that fluctuates from year to year by separating it from a value (factor) that does not fluctuate from year to year.

(What to do if estimation is not possible due to restrictions on the data that can be obtained)
Next, the measures to be taken when the estimation cannot be performed appropriately due to the limitation of the obtained data will be described. The effectiveness (accuracy) of the model (formula) depends on the amount and accuracy of the observed data obtained. Therefore, we will deal with it based on the assumptions illustrated below.

For example, the age composition is divided into 3 types, less than 1 year old, 1 year old, 2 years old and over, and lesser age groups (2 types) such as under 1 year old (juveniles) and 1 year old and over (adults). In summary, it is assumed that the birth rate or survival rate is the same in the same age group. In addition, the ratio of childbirth rate and survival rate between age groups is set and fixed. In addition, a prior distribution that limits the range is set for the ratio of birth rate and survival rate between age groups to enable effective estimation. In addition, when the age composition data is insufficient, a model that distinguishes only gender (considers only gender composition) is used. We also assume that the survival rate does not change between males and females (or a specific ratio is assumed) when gender composition data are inadequate.

Then, it is estimated by changing the rules in the model, adding new assumptions, and limiting (narrowing) the prior distribution based on the existing ecological information according to the data obtained by each of the above assumptions. It reduces power variables and enables effective population dynamics estimation by the population dynamics estimation device 100.

(Estimation processing flow of population dynamics)
Next, the population dynamics estimation processing flow executed by the CPU 1 of the population dynamics estimation device 100 will be described with reference to FIGS. 1 and 3.

First, in step S1, the CPU 1 (estimating means 1a to 1c) sets a prior distribution of unknown estimated variables. Specifically, the prior distribution of the number of individuals by sex and age, the birth rate by age, the mortality rate by sex and age, the sex ratio, the age composition, and other parameters for constructing the above equations [1] to [9]. Is created.

Then, in step S2, known data is read from the hard disk 2 by the CPU 1 (estimating means 1a to 1c), and the unknown estimated variables are prioritized in the above equations [1] to [9] (model). The distribution and known data (observed data) are input (substituted). The known data include the number of catches each year, the density of fecal pellets every year, the number of sightings each year, and the number of catches per labor unit every year.

Then, in step S3, the CPU1 (estimating means 1a to 1c) creates a posterior distribution of the target population dynamics by the Markov chain Monte Carlo method.

In step S4, the CPU 1 outputs the estimation result of population dynamics (graph data and numerical data related to future prediction simulation) to the display device 20. Based on this estimation result, a future capture plan for each gender and age will be made.

(Effect of the first embodiment)
In the first embodiment, the following effects can be obtained.

In the first embodiment, as described above, based on the total number of wild animals, the whole model (Equation [1]) that defines the variation of the total number of wild animals is used to determine the future wild animals. Estimating means 1a for estimating the total number of individuals and a partial model (Equation [2]) that defines partial fluctuations in the number of wild animals classified into a plurality of wild animals according to a specific sex, age, or a combination thereof. , Estimating means 1b and 1c for estimating the partial population of wild animals using the formula [3]). This allows the partial model (Equation [2], Equation [3]) to estimate the partial population of wildlife classified into a particular sex, age, or combination thereof, and thus of adult females. It is possible to derive the number of individuals (ratio), which is an important factor that influences population dynamics, such as the number of individuals (ratio) and the number of cubs (ratio). As a result, the number of individuals in categories (parts) that have a particular effect on the natural growth rate of animal species, such as the number of individuals capable of giving birth (ratio) and the number of individuals with different mortality rates (ratio). Since the dynamics of the ratio) are acquired more accurately, the accuracy of estimating the population dynamics of wild animals can be improved.

Further, in the first embodiment, as described above, in the overall model (Equation [1]), the natural increase rate of wild animals, the total number of wild animals, and the total number of wild animals captured are used. Therefore, the total number of wild animals in the future is defined, and the estimation means 1a is defined as a term that is not affected by the composition ratio of the wild animal category for a specific sex, age, or a combination thereof, and the wild animal category. The natural increase rate of the whole model (Equation [1]) is determined based on the fluctuation rate of the natural increase rate that fluctuates depending on the composition ratio of. This determines the natural growth rate of the overall model (Equation [1]), taking into account variations from terms that are not affected by the composition of wildlife categories for a particular sex, age, or combination thereof. Therefore, the estimation means 1a can more effectively reflect the influence of the composition ratio of the wildlife division on the natural increase rate. Therefore, the natural increase rate can be estimated more accurately. As a result, the accuracy of estimating the population dynamics of wild animals can be further improved. In addition, it will be possible to predict the future with high accuracy based on the capture plan for each gender and age category.

Further, in the first embodiment, as described above, the fluctuation rate of the natural increase rate is the fluctuation rate of the composition ratio of the wild animal classification on the birth rate, and the fluctuation of the composition ratio of the wild animal classification on the survival rate. It is defined based on at least one of the rates, and is a rate that varies depending on the composition ratio of the wildlife category. As a result, the effect of the composition ratio of the wildlife category on the natural growth rate can be evaluated more precisely and reflected in the estimation results (at least the fluctuation rate on the birth rate and the fluctuation rate on the survival rate). On the other hand, since it is defined based on) and more detailed estimation is made, the accuracy of estimation of wildlife population dynamics can be further improved.

Further, in the first embodiment, as described above, in the item that is not affected by the composition ratio of the wild animal category, the natural increase rate of the wild animal population in which the composition ratio of the wild animal category is the standard composition ratio is set. Includes a preset, stable, standard rate of natural growth. As a result, the natural growth rate of the overall model (Equation [1]) can be determined in consideration of the fluctuation from the standard natural growth rate (reference value) that does not fluctuate. The terms that are not affected by the composition ratio can be estimated more accurately. As a result, the accuracy of estimating the population dynamics of wild animals can be further improved.

Further, in the first embodiment, as described above, the term that is not affected by the composition ratio of the wild animal category includes the volatility due to the environment that shows the effect on the natural growth rate of the environment in which the wild animals live. This further takes into account the environmental variability that affects the natural growth rate (wildlife population) of the wildlife habitat in determining the natural growth rate of the wildlife. The accuracy of population dynamics estimation can be further improved.

Further, in the first embodiment, as described above, the volatility caused by the environment includes at least the volatility caused by the population density in which the increase in the population density of wild animals in the habitat reduces the natural increase rate. This is a density effect that is relatively easy to model (formulate) among the fluctuation rates caused by the environment, which indicates the effect of the wildlife habitat on the wildlife population (the wildlife population density in the habitat area). The accuracy of the wildlife population dynamics estimation can be further improved because the habitat density-induced variability) that the rise reduces the natural growth rate of wildlife is taken into account.

Further, in the first embodiment, as described above, in the partial model (Equation [2], Equation [3]), the cub, the adult, or both individuals are used to estimate the number of the cub or the adult. A first-part model (Equation [2]) that defines variability in numbers and males or females, or males or females, or these, for estimating the population of males, females, females or adult males. Includes a second partial model (Equation [3]) that defines variations in the number of individuals in a combination of categories. As a result, the partial model (Equation [2], Equation [3]) is the first partial model (Equation [2]) that defines the variation in the composition ratio of the wildlife classification with respect to age, and the wildlife with respect to sex. The accuracy of estimation of wildlife population dynamics can be further improved by subdividing into the second partial model (Equation [3]) that defines the fluctuation of the composition ratio of the above categories and considering in detail.

[Second Embodiment]
With reference to FIG. 4, the configuration of the population dynamics estimation device 200 according to the second embodiment of the present invention will be described.

In the population dynamics estimation device 200 of the second embodiment, the population dynamics estimation device of the first embodiment is set separately (as separate items) for the density effect, which is an environmental effect, and the effect of other factors. An example in which, unlike 100, the density effect and the effect of other factors are set as one term (environmental effect) without being separated will be described. The same reference numerals are used for the same configurations as those in the first embodiment, and the description thereof will be omitted.

As shown in FIG. 4, the CPU 1 of the population dynamics estimation device 200 in the second embodiment includes estimation means 201a, 201b and 201c for executing the equations (models) [1], [2] and [3], respectively. I'm out. The estimation means 201a, 201b and 201c estimate the population dynamics by substituting the effects of the density effect and other factors with the environmental effect in the above formulas [5], [2] and [3]. The estimation means 201a is an example of the "first estimation means" in the claims. Further, the estimation means 201b and 201c are examples of the "second estimation means" in the claims.

Specifically, the variation in the density effect and the effect of other factors described in the first embodiment may be strongly related to each other. Therefore, in the second embodiment, the two effects (items) of the density effect and the effect of other factors are combined into one effect (item) as an environmental effect. In this case, the environmental effect is derived by the following equation [10].

Environmental effect _(i) = (standard natural growth rate-1) x total population _(i) ÷ (marginal density _(i) x forest area _(i) ) ... [10]

Here, the limit density is a density at which the natural increase rate turns negative due to the density effect or the like when this value is exceeded. The critical density is equal to the product of the carrying capacity of the habitat and the environmental change _(i). In addition, log (environmental change) is defined as a random change factor according to the probability distribution of the normal distribution (0, β). β is a predetermined set value. As a result, the carrying capacity × environmental change _(i) is defined by the limit density, and the yearly environmental change is mathematically formulated (modeled) as the yearly change in the limit density. As a result, it becomes possible to specify a model that estimates one variable every year as the limit density. For example, a log (marginal density _(i) ) can be modeled to follow a normal distribution (standard value of marginal density, variance of annual variation).

The other configurations of the second embodiment are the same as those of the first embodiment.

(Effect of the second embodiment)
In the second embodiment, the following effects can be obtained.

In the second embodiment, as described above, the environmental effects (the effect of the wildlife habitat on the wildlife population are affected by the formulas [2], [3], [5] and [10], respectively. The number of cubs and the number of adult females are defined based on the rate of change due to the environment shown. This further takes into account environmental effects (environmentally-based variability that indicates the impact of wildlife habitat on wildlife populations) in defining cub and adult female populations. Therefore, the accuracy of estimating the population dynamics of wild animals can be further improved.

The other effects of the second embodiment are the same as those of the first embodiment.

(Modification example)
It should be noted that the embodiments disclosed this time are exemplary in all respects and are not considered to be restrictive. The scope of the present invention is shown by the scope of claims rather than the description of the above-described embodiment, and further includes all modifications (modifications) within the meaning and scope equivalent to the scope of claims.

For example, in the first and second embodiments, the number of cubs is defined by the formula [2], but the present invention is not limited to this. In the present invention, for example, the number of cubs may be defined by the following formula [11].
Cub population _(i) = cub survival _(i) ÷ (1+ (Density Effect _(i) + Other factors effects _(i))) × Initial cub population _(i) - cub captured number _{(i )} ... [11]

Further, in the first and second embodiments, an example in which the number of adult females is defined by the formula [3] is shown, but the present invention is not limited to this. In the present invention, for example, the number of adult females may be defined by the following formula [12].
Adult female population _(i) = adult survival rate _(i) ÷ (1 + (density effect _(i) + effect of other factors _(i) )) × initial adult female population _(i) − adult female capture number _(i) ... [12]

Further, in the first and second embodiments, an example in which the natural increase rate is defined by the formula [4] is shown, but the present invention is not limited to this. In the present invention, for example, the natural increase rate may be defined by the following formula [13].
Natural increase rate _(i) = (standard natural increase rate + effect of sex and age composition _(i) ) ÷ (1 + density effect _(i) + effect of other factors _(i) ) ... [13]

Further, in the first and second embodiments, the example in which the random effect of the formula [9] is defined to follow a normal distribution is shown, but the present invention is not limited to this. In the present invention, for example, the random effect may follow a non-normal distribution such as a beta distribution.

Further, in the first and second embodiments, an example in which both the formula [2] for defining the number of cubs and the formula [3] for defining the number of adult females are set has been shown. Is not limited to this. In the present invention, only one of the formula [2] that defines the number of cubs and the formula [3] that defines the number of adult females may be set.

Further, in the first and second embodiments, an example of creating (deriving) a posterior distribution by a Markov chain Monte Carlo method using a prior distribution and known data has been shown, but the present invention is not limited to this. .. In the present invention, the posterior distribution may be created (derived) by a method other than the Markov chain Monte Carlo method using the prior distribution and known data.

1a, 201a Estimating means (first estimating means)
1b, 1c, 201b, 201c estimation means (second estimation means)
10a Population dynamics estimation program 100, 200 Population dynamics estimation device (computer)

Claims (8)

A wildlife population dynamics estimator that estimates wildlife population fluctuations using a model that defines wildlife population fluctuations.
A first estimation means for estimating the total population of the wild animal in the future by using an overall model that defines the variation of the total population of the wild animal based on the total population of the wild animal.
The first estimation of the partial population of the wild animal is performed using a partial model that defines the variation of the partial population of the wild animal that is divided into a plurality of parts according to a specific sex, age, or a combination thereof. and a second estimation means,
The overall model defines future overall populations of the wildlife based on the natural growth rate of the wildlife, the total population of the wildlife, and the total number of wildlife catches.
The first estimation means is a term that is not affected by the composition ratio of the wildlife division for a specific sex, age, or a combination thereof, and the natural increase that is influenced by the composition ratio of the wildlife division. A wildlife population dynamics estimator configured to determine the natural growth rate of the overall model based on the rate of variability. The volatility of the natural growth rate is defined based on at least one of the volatility of the wildlife category composition ratio on the birth rate and the volatility of the wildlife category composition ratio on the survival rate. wherein a ratio which varies by the difference in composition ratio of the wildlife division, population dynamics estimation apparatus wildlife according to claim 1. Unaffected by the composition ratio of the wildlife division The term is a non-variable standard preset as the natural growth rate of the wildlife population in which the composition ratio of the wildlife division is in the standard composition ratio. The wildlife population dynamics estimator according to claim 1 or 2 , which comprises a natural growth rate. The wildlife population dynamics according to claim 3 , wherein the item, which is not affected by the composition ratio of the wildlife category, includes a fluctuation rate due to the environment in which the wildlife habitat affects the natural growth rate. Estimator. The population dynamics of wild animals according to claim 4 , wherein the fluctuation rate due to the environment includes at least the fluctuation rate due to the population density in which the increase in the population density of wild animals in the habitat reduces the natural increase rate. Estimator. The partial model is a first partial model that defines variability in cub, adult or both populations for cub or adult population estimation, and male, female, female adult or male adult individuals. Any one of claims 1-5 , including a second part model that defines population variations of males or females, or adult males or females or combinations of these categories for number estimation. A wild animal population dynamics estimator according to. Computer,
In estimating the variation in the number of wild animals using a model that regulates the variation in the number of wild animals, the variation in the total number of wild animals is specified based on the total number of wild animals. A first estimation means for estimating the total number of the wild animals in the future using the whole model, and
Estimates of future partial populations of wildlife using a partial model that defines partial population variability of wildlife that is divided into multiple categories according to specific gender, age, or combination thereof. second estimation means for performing,
In the overall model, as a means of defining the future total population of the wildlife based on the natural growth rate of the wildlife, the total population of the wildlife, and the total number of wildlife captured. ,
The first estimation means is a term that is not affected by the composition ratio of the wildlife division for a specific sex, age, or a combination thereof, and the natural increase that is influenced by the composition ratio of the wildlife division. based on the rate of change ratio, wildlife population dynamics estimation program for operating as a means for determining the rate of natural increase of the overall model. A wildlife population dynamics estimation method that estimates wildlife population fluctuations using a model that defines wildlife population fluctuations.
Based on the total number of individual wild animals, and performing the using the entire model that defines the variation in the total populations of wild animals, before Symbol entire population of putative wildlife,
Estimates of future partial populations of wildlife using a partial model that defines partial population variability of wildlife that is divided into multiple categories according to specific gender, age, or combination thereof. a step of performing,
In the overall model, a step of defining the future overall population of the wildlife based on the natural growth rate of the wildlife, the total population of the wildlife, and the total number of wildlife catches. ,
Based on terms that are not affected by the composition of wildlife categories for a particular sex, age, or combination thereof, and the rate of change of the biotic potential that fluctuates depending on the composition of the wildlife category. A wildlife population dynamics estimation method comprising the step of determining the natural growth rate of the overall model.

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