Population Density Estimation Based On Distance

The investigation of plant population density is the foundation for the detection,management,and protection of related biological resources.In order to estimate population density,how to design effective sampling methods and how to develop robust estimation methods based on sampled data are two very important issues.For the first problem,the literature usually uses sample methods and distance sampling methods to collect data; Relatively speaking,distance sampling is more resource efficient and not affected by terrain than sampling methods,so it is widely used to collect data.With distance sampling data,this paper focuses on the second issue.Early studies assumed that the distribution of populations in space was uniform,and used Poisson distribution to model the distribution of population numbers; The distribution of plant populations is characterized by aggregation,which is often not consistent with reality.Shen et al.(2020)proposed a moment estimation method for population density based on negative binomial distribution to describe the aggregation of plant populations.However,this method still has two shortcomings:(1)Moment estimation may not be effective enough;(2)Ignoring the impact of habitat on population density heterogeneity;(3)The possibility of missing data during the sampling process was not considered.In order to overcome these three shortcomings,this paper will use a more general probability model,based on the complete likelihood method,to propose an effective robust estimation of population density.Unlike negative binomial distribution,finite mixed Poisson distribution is a nonparametric method for modeling counting data.This model is commonly used in the literature to approximate the mosaic distribution of plant populations(Steen et al.,2008);However,under this model,research on population density estimation is still lacking.In order to fill the gap in this research,this paper uses finite mixed Poisson distribution to describe plant aggregation,and proposes a maximum likelihood estimation of population density based on distance sampling data.It is well known that the growth of plants strongly depends on their ecological environment.For example,alkaline soil environment is conducive to the growth of plants such as cacti; This type of plant has a higher density in habitats with higher soil ph values,but is almost extinct in habitats with lower ph values.In order to characterize the impact of habitat on population density heterogeneity,this paper uses a logarithmic linear model to establish a relationship between population density and habitat variables,and studies the maximum likelihood estimation of population density in a Poisson regression model.Unlike the maximum likelihood estimation in the classical generalized linear model,the likelihood function in this study involves a large number of integration operations,and the calculation is relatively complex.To solve this problem,this paper develops an efficient and stable numerical algorithm based on Newton iterative method,using polar coordinate transformation and MCMC algorithm.Due to the limitations of the observer’s measurement range,distance sampling data may have right censoring.That is,the tree closest to the observation point may not be observed by the observer; At this point,we can only know that the closest distance between the observer and the tree is greater than the observation range.If this part of the censored data is not considered,the estimation of population density may be biased.This paper proposes a right censored model based on Poisson’s regression model and studies the maximum likelihood estimation method of population density using the method of survival analysis for processing right censored data.Finally,this paper verifies the effectiveness of the proposed method through a large number of numerical simulations and forest land data in Tiantong Mountain Nature Reserve.