Almost all small data sets used to illustrate the functioning of methods eventually passed though Excel, for either data input, simple analyses or data presentation. In spreadsheets, data are usually organized as shown in Figure 2.8 that is, in a single data matrix with releves organized in columns and species and environmental variables in rows. For import and export into other programs I used commas, semicolons or tabulators separating data fields, which are accepted by almost all databases and statistical packages. The tasks I have conducted using spreadsheets are Numerically integrating differential equations for dynamic modelling. All models presented in Section 10.1 are implemented in Excel. A column is chosen for each state variable that is, X1, X2, as well as its derivative SX1 St, SX2 St. For time step t 0 the initial values are written in a row in the following row the formula for deriving the state at t 1 is entered. Dragging these cells down by, for example, 100 rows...
The well-known spreadsheets are probably the most widely known software applications that can help build quite sophisticated models. Microsoft Excel is by far the best-known and widely used spreadsheet. However, there is also Lotus 1-2-3, which actually pioneered the spreadsheet concept and is now owned by IBM, or the open-source OpenOffice suite. The latest addition is Numbers, the Macintosh spreadsheet program. All offer very similar functionality. The other option is to use Google spreadsheets, which reside on the web and can be shared among several developers, who can then access and update the document from anywhere around the world using just an Internet browser. The basic functionality that comes with spreadsheets is that formulas can be programmed using some very simple conventions. For dynamic models, these formulas can be reiterated, using a TIME column, and using the results of previous calculations (rows) to generate the values for the next time step.
Lines of code in a common programming language such as Fortran, Visual Basic, C, C++, or Java. However, it is becoming increasingly more common to construct and link model components in a visual or 'icon-based' modeling environment. Proprietary visual modeling environments (e.g., Stella (isee systems, Inc.), Vensim (Ventana Systems, Inc.), POWERSIM (Powersim Software AS), and Model Builder (ESRI, Inc.)) are systems where models are constructed by assembling and linking icon-based model components using a sophisticated button- and menu-driven Graphical User Interface. There are three advantages in using these systems for agricultural model development (1) they typically contain a large number of built-in functions (e.g., mathematical, logical, and statistical including risk and Monte Carlo analysis) that greatly simplify model development and evaluation (2) they are easy to learn, intuitive to use, and familiar to users of Windows-based software and (3) they can readily import and...
As explained in Section 1.4, ecological data are obtained as object-observations or sampling units which are described by a set of state values corresponding to as many descriptors, or variables. Ecological data are generally recorded in a table Descriptor (spreadsheet) where each column j corresponds to a descriptor yj (species present in Object the sampling unit, physical or chemical variable, etc.) and each object i (sampling site, sampling unit, locality, observation) occupies one row. In each cell (ij) of the table is found the state taken by object i for descriptor j (Table 2.1). Objects will be denoted by a boldface, lower-case letter x, with a subscript i varying form 1 to n, referring to object xi. Similarly, descriptors will be denoted by a boldface, lower case letter y subscripted j, with j taking values from 1 to p, referring to descriptor yj. When considering two set of descriptors, members of the second set will generally have subscripts k from 1 to m.
I formalize this explanation as a simple dynamic model below, then discuss its basic behavior using values from Mikea research (which I have operationalized in a spreadsheet). Like all simple models, this one requires a certain relaxation of real world accuracy in favor of increased generality. Modelers commonly make this tradeoff when offering a new hypothetical set of interactions the number of interacting variables are kept to a minimum so that the effect of each can be easily understood (Starfield and Bleloch 1986). The important simplifying assumptions of this model are that every day must be spent either foraging or farming (no resting or engaging in other activities). A day spent doing either activity provides a constant gain, either in the present (foraging) or in the future (farming).
Although GIS software is becoming more accessible and user-friendly, it is also becoming more powerful, which can increase the length of the learning curve. As noted by Johnston (1998), ecologists should not assume that mastering GIS software will be as rapid as learning word processing or spreadsheet software. Problems that arise can be difficult to solve without access to an experienced practitioner. Such people can be difficult to find, even in academic environments, because they
Independent of selection of any other unit. This can be achieved by assigning every unit in the population a number, then selecting a sample of these according to randomly generated numbers. Alternatively, random numbers can be used to select intersection points on a sample grid. Random numbers can be obtained from statistical tables, or can be generated by some pocket calculators as well as some spreadsheets or statistical analysis software. It is important to use numbers that genuinely are randomly generated in this way, and not simply plucked from the air in some arbitrary fashion.
One cannot enumerate all the individuals in a pedon. Instead, several samples must be removed to the laboratory for extraction and enumeration. The number of samples removed must reflect the abundance, diversity and heterogeneity within the pedon. Guidelines to calculate the number of samples and pedons to use, in order to obtain adequate confidence intervals, can be found in most standard statistic text books (see quadrats), using Hendricks' method or Wiegert's method, and at http www.exetersoftaware.com The latter can be particularly useful to estimate optimal quadrat sizes and the numbers of quadrats to use, if it cannot be done quickly on a calculator or with spreadsheets. Figure 3.1 illustrates the effect of sample size and number of samples on a particular area with the same spatial pattern of a species. The variation is demonstrated further in Table 3.1. It is possible to use nested quadrats to obtain an experimental estimate of the best pedon size and sample volumes for the...
Computer simulations are being increasingly relied upon to reveal key factors and integrate them to evaluate the impacts of invasions from crop rotation and Bt-resistant insects. Initial modeling attempts involved the creation of simple spreadsheet-based models of adult insect behavior and population genetics to study the development of insect resistance to transgenic corn. Some models explicitly considered spatiotemporal dynamics in an agroecosystem consisting of transgenic Bt plants, insects susceptible to Bt toxins, and adapted Bt-resistant insects that can grow on Bt plants. Model results showed that invasion of Bt-resistant insects leads to spatially inhomogeneous distributions of plants and insects. In addition, spatially averaged plant biomass was shown to be strongly dependent on the duration of the Bt-resistant insect reproduction period. Concurrent to modeling insect resistance to transgenic corn, modeling efforts also focused on explaining how rotation resistance may have...
Values of N generated from simulations using equation 5.4 are displayed in Fig. 5.4. Starting with 10 germinating plants, Fig. 5.4a shows a flow diagram of the sequence of calculations in the simulation (such simulations can be written in widely available spreadsheet packages). This is an iterative process in which we generate a value for Nt+1 and then use it as the new Nt and so on. You should check the first few iteration values given in Fig. 5.4b.
The net weights for each waste category in each sample are usually entered into a computer spreadsheet. For each waste category in each group of samples to be analyzed (for example, residential samples and commercial samples), the following should be calculated from the data in the spreadsheet
Missing values may be represented in data matrices by numbers that do not correspond to possible data values. Codes such as -1 or -9 are often used when the real data in the table are all positive numbers, as it is the case with species abundance data otherwise, -99 or -999, or other such unambiguous codes, may be used. In spreadsheets, missing values are represented by bullets or other such symbols.
There are many reasons why matrix algebra is especially well suited for ecology. The format of computer spreadsheets, in which ecological data sets are now most often recorded, is a matrix format. The use of matrix notation thus provides an elegant and compact representation of ecological information and matrix algebra allows operations on whole data sets to be performed. Finally, multidimensional methods, discussed in following chapters, are almost impossible to conceptualise and explain without resorting to matrix algebra.
Information is produced when data are placed into context (such as being part of a data set or set of experiments, particularly when designed to answer hypotheses) or manipulated. In an experiment one collects data, then transforms or combines it for analysis or aggregation in order to test hypotheses. Both data and information may be stored and manipulated digitally in databases, though ecologists often use spreadsheets for this purpose. Knowledge is the result of interpreting or synthesizing information it is the conclusion of the hypothesis-testing process. Ecological knowledge is largely found in the scientific literature as publications however, it is also possible to store knowledge in knowledge bases, analogous to databases. Identification keys or guides used or created by ecologists fall into the knowledge category.
Compilation in a databank requires that all information obeys stringent formal and technical rules laid down in reference lists, meta-data and data models. Databanks of different formats and complexity were established, ranging from simple spreadsheets to relational and object-based data models that allow flexible definitions and comprehensive documentation of meta-data. Simple databanks are able to exchange data freely if the same standards, database formats, definitions, and reference lists are used. The success of phytosociological databanks is so far due to rather simple management software packages such as TURBOVEG, which is currently the most widespread program in Europe and beyond, distributed free of charge or at small cost along with taxonomic reference lists and tools to create, edit, and analyze phyto-sociological tables.
There are several specialized mathematical packages designed to help solve mathematical problems. As such they can be useful for modeling, since after all models are mathematical entities, which need to be solved. These packages are not very helpful in formulating models. In this regard, they are as universal as spreadsheets. But unlike spreadsheets, which are quite well known and intuitive to use, the mathematical packages have a steep learning curve, and require learning specialized programming languages. On the benefit side, the computing power and versatility of mathematical methods you get is unsurpassed.
Least squares A method of determining the best straight line to fit a series of points on a graph. This 'best line' minimizes the square of the distances of the points to the line as measured along the y-axis - the direction in which the greatest experimental error is expected. The calculation is a standard feature of scientific calculators and spreadsheets.
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