The coarse-grid problem in ecological monitoring

2010 ◽  
Vol 466 (2122) ◽  
pp. 2933-2953 ◽  
Author(s):  
Natalia B. Petrovskaya ◽  
Sergei V. Petrovskii
Keyword(s):  
Population Size ◽  
Numerical Integration ◽  
Spatial Data ◽  
Mathematical Problem ◽  
Ecological Monitoring ◽  
Coarse Grid ◽  
Monitoring And Control ◽  
Pest Monitoring ◽  
Population Distributions ◽  
Important Message

Obtaining information about pest-insect population size is an important problem of pest monitoring and control. Usually, this problem has to be solved based on scarce spatial data about the population density. The problem of monitoring can thus be linked to a more general mathematical problem of numerical integration on a coarse grid. Numerical integration on coarse grids has rarely been considered in literature as it is usually assumed that the grid can be refined. However, this is not the case in ecological monitoring where fine grids are not available. In this paper, we introduce a method of numerical integration that allows one to accurately evaluate an integral on a coarse grid. The method is tested on several functions with different properties to show its effectiveness. We then use the method to obtain an estimate of the population size for different population distributions and show that an ecologically reasonable accuracy can be achieved on a very coarse grid consisting of just a few points. Finally, we summarize our mathematical findings as a protocol of ecological monitoring, thus sending a clear and practically important message to ecologists and pest-control specialists.

scholarly journals Challenges of ecological monitoring: estimating population abundance from sparse trap counts

2011 ◽  
Vol 9 (68) ◽  
pp. 420-435 ◽  
Author(s):  
Natalia Petrovskaya ◽  
Sergei Petrovskii ◽  
Archie K. Murchie
Keyword(s):  
Population Size ◽  
Numerical Integration ◽  
Spatial Data ◽  
Population Distribution ◽  
Species Abundance ◽  
Ecological Monitoring ◽  
Field Studies ◽  
Pest Species ◽  
Population Size Estimates ◽  
Size Estimates

Ecological monitoring aims to provide estimates of pest species abundance—this information being then used for making decisions about means of control. For invertebrate species, population size estimates are often based on trap counts which provide the value of the population density at the traps' location. However, the use of traps in large numbers is problematic as it is costly and may also be disruptive to agricultural procedures. Therefore, the challenge is to obtain a reliable population size estimate from sparse spatial data. The approach we develop in this paper is based on the ideas of numerical integration on a coarse grid. We investigate several methods of numerical integration in order to understand how badly the lack of spatial data can affect the accuracy of results. We first test our approach on simulation data mimicking spatial population distributions of different complexity. We show that, rather counterintuitively, a robust estimate of the population size can be obtained from just a few traps, even when the population distribution has a highly complicated spatial structure. We obtain an estimate of the minimum number of traps required to calculate the population size with good accuracy. We then apply our approach to field data to confirm that the number of trap/sampling locations can be much fewer than has been used in many monitoring programmes. We also show that the accuracy of our approach is greater that that of the statistical method commonly used in field studies. Finally, we discuss the implications of our findings for ecological monitoring practice and show that the use of trap numbers ‘smaller than minimum’ may still be possible but it would result in a paradigm shift: the population size estimates should be treated probabilistically and the arising uncertainty may introduce additional risk in decision-making.

Crushing of an Elastic-Perfectly Plastic Ring or Tube Between Two Planes

1987 ◽  
Vol 54 (1) ◽  
pp. 159-164 ◽  
Author(s):  
C. Y. Wang
Keyword(s):  
Plastic Deformation ◽  
Numerical Integration ◽  
Mathematical Problem ◽  
Plastic Ring ◽  
Perfectly Plastic ◽  
Analytical Approximations ◽  
Original Shape ◽  
Thin Ring ◽  
Elastic Perfectly Plastic

A thin ring is crushed between two rigid planes. Due to plastic deformation the ring does not recover its original shape when the compression is removed. For an elastic-perfectly plastic flexural material, the ring undergoes two to five different stages. The mathematical problem is formulated and solved by exact numerical integration and accurate analytical approximations.

Numerical integration by systematic sampling

1950 ◽  
Vol 46 (1) ◽  
pp. 111-115 ◽  
Author(s):  
P. A. P. Moran
Keyword(s):  
Numerical Integration ◽  
Bounded Variation ◽  
Mathematical Problem ◽  
Random Variable ◽  
Mean Value ◽  
Lattice Points ◽  
Systematic Sampling ◽  
Image Position ◽  
Infinite Sum

Recent investigations by F. Yates (1) in agricultural statistics suggest a mathematical problem which may be formulated as follows. A function f(x) is known to be of bounded variation and Lebesgue integrable on the range −∞ < x < ∞, and its integral over this range is to be determined. In default of any knowledge of the position of the non-negligible values of the function the best that can be done is to calculate the infinite sumfor some suitable δ and an arbitrary origin t, where s ranges over all possible positive and negative integers including zero. S is evidently of period δ in t and ranges over all its values as t varies from 0 to δ. Previous writers (Aitken (2), p. 45, and Kendall (3)) have examined the resulting errors for fixed t. (They considered only symmetrical functions, and supposed one of the lattice points to be located at the centre.) Here we do not restrict ourselves to symmetrical functions and consider the likely departure of S(t) from J (the required integral) when t is a random variable uniformly distributed in (0, δ). It will be shown that S(t) is distributed about J as mean value, with a variance which will be evaluated as a function of δ, the scale of subdivision.

scholarly journals Interpolation of spatial data – A stochastic or a deterministic problem?

2013 ◽  
Vol 24 (4) ◽  
pp. 601-629 ◽  
Author(s):  
M. SCHEUERER ◽  
R. SCHABACK ◽  
M. SCHLATHER
Keyword(s):  
Spatial Data ◽  
Convergence Rates ◽  
Mathematical Problem ◽  
Computer Experiments ◽  
Underlying Structure ◽  
Kernel Selection ◽  
Deterministic Problem ◽  
Interpolation Accuracy ◽  
Interpolation Procedure ◽  
Modelling Assumptions

Interpolation of spatial data is a very general mathematical problem with various applications. In geostatistics, it is assumed that the underlying structure of the data is a stochastic process which leads to an interpolation procedure known as kriging. This method is mathematically equivalent to kernel interpolation, a method used in numerical analysis for the same problem, but derived under completely different modelling assumptions. In this paper we present the two approaches and discuss their modelling assumptions, notions of optimality and different concepts to quantify the interpolation accuracy. Their relation is much closer than has been appreciated so far, and even results on convergence rates of kernel interpolants can be translated to the geostatistical framework. We sketch different answers obtained in the two fields concerning the issue of kernel misspecification, present some methods for kernel selection and discuss the scope of these methods with a data example from the computer experiments literature.

The limiting properties of population distributions with particular application to manpower planning

1983 ◽  
Vol 20 (1) ◽  
pp. 19-30 ◽  
Author(s):  
Mark Woodward
Keyword(s):  
Population Size ◽  
Stable Distribution ◽  
Population Distribution ◽  
Manpower Planning ◽  
Expected Value ◽  
Practical Applications ◽  
Population Distributions ◽  
Number Of Classes

A model for predicting expected-value population distributions is developed, assuming that all movements are Markovian and time-homogeneous. Each individual is classified by the amount of time he has spent in the population and by which of a number of classes, of an unspecified nature, he inhabits. The limiting properties of the population distribution are derived, and, in particular, conditions for convergence to a stable distribution are given.Some discussion of the relevance of the theory to practical applications is given, primarily to manpower planning when recruitment occurs purely to maintain a specified overall population size.

scholarly journals Performance of baited traps for integrated management of Hypothenemus hampei Ferrari (Coleoptera: Scolytinae) in a conilon coffee crop in Rondônia State, Brazil

2020 ◽  
Vol 13 ◽  
pp. e913
Author(s):  
Moisés Santos De Souza ◽  
José Nilton Medeiros Costa ◽  
Marcelo Curitiba Espindula ◽  
Alexandre de Almeida e Silva
Keyword(s):  
Population Control ◽  
Integrated Management ◽  
Control Area ◽  
Hypothenemus Hampei ◽  
Monitoring And Control ◽  
Coffee Plantations ◽  
Pest Monitoring ◽  
Baited Traps ◽  
Two Factors ◽  
Important Pest

Hypothenemus hampei (Ferrari) is an important pest worldwide. Methods of monitoring and control using baited traps are not yet established in coffee plantations in the Brazilian Amazon. The objective of this work was to record, for the first time, results of the use of baited traps in coffee plantation located in Rondônia, in favor of the control and pest monitoring. Two areas were delineated: i) with use of the traps baited with  ethanol/methanol (1:1), treatment; ii) without use of traps (control). For comparison of results, two factors were considered: damaged fruits (damage by H. hampei) and infested (H. hampei inside of fruits). It was observed higher levels of damaged fruits per plants in the control area compared to the area where traps were used. The density of the pest population per plants found on infested fruits was also higher in the control area compared to the trapping area. These results suggest that traps baited with ethanol/methanol (1:1) are an effective alternative for population control of pest also in the coffee plantations in Rondônia, where there is no such management with this tool. Use of the baited traps to monitor the insect accurately revealed that the flight stimulus of the colonizing females is influenced by values of the environmental variables. According to the results, colonizing females are more active in the afternoon. Therefore, in order to achieve more efficient control of H. hampei, the best time to apply control agents is between 2:00 pm and 6:00 pm.

scholarly journals Arthropods of the Limarí River basin (Coquimbo Region, Chile): taxonomic composition in agricultural ecosystems

2021 ◽  
Vol 53 (1) ◽  
pp. 245-253
Author(s):  
Jaime Pizarro-Araya ◽  
Fermín M. Alfaro ◽  
Rodrigo A. Muñoz-Rivera ◽  
Juan E. Barriga-Tuñon ◽  
Luis Letelier
Keyword(s):  
Taxonomic Composition ◽  
Semiarid Region ◽  
Agricultural Activity ◽  
Vegetable Crops ◽  
Monitoring And Control ◽  
Dry Land ◽  
Norte Chico ◽  
Pest Monitoring ◽  
Arthropod Species ◽  
Starting Point

The Limarí valley, located in the Coquimbo Region of Chile, is an important agricultural area that is immersed in the transverse valleys of the Norte Chico. In recent decades, the continuous expansion of agriculture towards dry land zones has favored the migration and establishment of potential pests, such as arthropods, that may affect crops or be zoonotic agents. Based on the limited knowledge we have about the arthropod group present in the Limarí basin, our objective is to describe the taxonomic composition of the assemblage of economically important arthropods inhabiting this basin of the semiarid region of Chile. After reviewing historical data, specimen collections, and the specialized literature, a total of 414 arthropod species were recorded. Of the total number of species recorded, 92.5% were insects, the most diverse taxon, with 11 orders. Arachnids, in turn, were represented only by Acari with 31 species. The most widely represented orders of insects were Coleoptera, Hemiptera, and Lepidoptera. Within Coleoptera the most species-rich families were, in decreasing order of importance, Curculionidae, Coccinellidae, Cerambycidae, Scarabaeidae, Chrysomelidae (Bruchinae), Ptinidae, and Bostrichidae; within Hemiptera these were Aphididae, Diaspididae, Coccidae, Pseudococcidae, Pentatomidae and Rhopalidae; and within Lepidoptera they were Noctuidae and Tortricidae. We hope this study serves as a starting point for identifying the most diverse arthropod groups and developing pest monitoring and control programs. Highlights: A large percentage of phytophagous species, mainly belonging to Acari, Lepidoptera, Hemiptera and Coleoptera, were registered in the Limarí basin. Some families of agricultural importance (Aleyrodidae, Aphididae, Coccidae, Diaspididae, Margarodidae, Pseudococcidae), were observed in large agricultural crops in the basin (e.g., vines, oranges, mandarins, lemon trees, avocado trees, walnuts, olive trees, vegetable crops). A smaller fraction corresponded to the group of predators and parasitoids, mainly represented by Coleoptera (Coccinellidae), Neuroptera (Chrysopidae) and Hymenoptera (Braconidae, Encyrtidae, Ichneumonidae, Platygastridae, Signiphoridae). The richness and spatial records of arthropods were mostly concentrated between the city of Ovalle and the estuary of Punitaqui - the areas with most intense agricultural activity in the Limarí basin.

scholarly journals Diffusion Model for Describing the Regional Spread of Huanglongbing from First-Reported Outbreaks and Basing an Area Wide Disease Management Strategy

Plant Disease ◽  
2017 ◽  
Vol 101 (7) ◽  
pp. 1119-1127 ◽  
Author(s):  
J. L. Flores-Sánchez ◽  
G. Mora-Aguilera ◽  
E. Loeza-Kuk ◽  
J. I. López-Arroyo ◽  
M. A. Gutiérrez-Espinosa ◽  
...  
Keyword(s):  
Diffusion Model ◽  
Spatial Data ◽  
Large Scale ◽  
Disease Incidence ◽  
Management Program ◽  
Tree Canopy ◽  
Homogeneous Distribution ◽  
Diaphorina Citri ◽  
Monitoring And Control ◽  
Quantitative Evidence

Huanglongbing (HLB), a recent worldwide spreading disease on citrus, was detected in July 2009 in Yucatan State of Mexico. The objective of this study was to evaluate the fit of diffusion and classic disease gradient models to large-scale HLB spatial data originated from initial foci to improve sampling, monitoring, and control strategies for Diaphorina citri, vector of Candidatus Liberibacter asiaticus (CLas), putative agent of HLB. Four transect routes were selected: Yuc-1, Yuc-2, QRoo-1, and QRoo-2, based on the directionality of the prevailing winds and foci location of HLB infected plants. In these routes, 35 sites, 5 to 20 km apart, were selected for monthly evaluation during a 12-month period. A 10-insect sample and disease incidence and severity of HLB, further confirmed by PCR, were assessed per site. Mexican lime was more vulnerable (67.5%) than sweet orange (14%). Also, leaf symptoms were mostly found with homogeneous distribution but rarely reaching 100% of the tree canopy during the 12-month period. The diffusion model provided the best fit among the family of time-gradient curves (r2 = 0.90 to 0.99) due to the flexibility of a three-parameter model. The gradients were well conformed to the model in a 25 to 82.6 km range, having the east-west direction the longest effect. Yuc-2 and QRoo-2 transects showed 82.6 and 43.9 km gradients with a diffusion coefficient (Do) of 0.15 and 0.09, respectively. This study constitutes the first quantitative evidence of the regional spread of CLas from a single focus and the application of a flexible model that improved the fit and allowed to better compare different gradients. These results are useful to determine the size of Regional Areas of Diaphorina citri Control (ARCO), a management program currently implemented in Mexico to combat HLB.

scholarly journals Integrating Population Heterogeneity Indices with Microfluidic Cell-Based Assays

2017 ◽  
Vol 23 (5) ◽  
pp. 459-473
Author(s):  
Thomas A. Moore ◽  
Alexander Li ◽  
Edmond W. K. Young
Keyword(s):  
Single Cell ◽  
Population Size ◽  
Cell Population ◽  
Population Data ◽  
Statistical Analyses ◽  
Population Heterogeneity ◽  
Population Demographics ◽  
Population Distributions ◽  
Technical Advances ◽  
Traditional Population

Recent advances in cell-based assays have involved the integration of single-cell analyses and microfluidics technology to facilitate both high-content and high-throughput applications. These technical advances have yielded large datasets with single-cell resolution, and have given rise to the study of cell population dynamics, but statistical analyses of these populations and their properties have received much less attention, particularly for cells cultured in microfluidic systems. The objective of this study was to perform statistical analyses using Pittsburgh Heterogeneity Indices (PHIs) to understand the heterogeneity and evolution of cell population demographics on datasets generated from a microfluidic single-cell-resolution cell-based assay. We applied PHIs to cell population data obtained from studies involving drug response and soluble factor signaling of multiple myeloma cancer cells, and investigated effects of reducing population size in the microfluidic assay on both the PHIs and traditional population-averaged readouts. Results showed that PHIs are useful for examining changing population distributions within a microfluidic setting. Furthermore, PHIs provided data in support of finding the minimum population size for a microfluidic assay without altering the heterogeneity indices of the cell population. This work will be useful for novel assay development, and for advancing the integration of microfluidics, cell-based assays, and heterogeneity analyses.

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