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WinTWINS教程

WinTWINS教程
WinTWINS教程

WinTWINS version 2.3

Mark O. Hill

Petr ?milauer

2005

1 Preface

TWINSPAN, based partly on an earlier program called ‘Indicator Species Analysis’ (Hill et al. 1975), was written in 1979, five years before the Apple Macintosh revolutionized personal computing, and two years before MS DOS was launched. The first version of Windows did not appear till November 1985. In 1979, a personal computer was an expensive luxury possessed only by a few geeks; all serious calculations were made on mainframes. At Cornell University, newly-available computer terminals had made programming much easier than in earlier years. Programs and problems could be submitted electronically (to another room in the Cornell’s Langmuir Lab), though the output was still normally on paper. The time was therefore ripe for development of numerical methods in ecology to the point where they could become routine tools rather than interesting prospects for development.

The early proponents of numerical methods, notably Goodall (1953a, 1953b), had seen themselves as champions of objectivity. They were uncomfortable about the Zürich-Montpellier tradition of continental Europe, which had sought to construct a comprehensive system of knowledge. In the eyes of many British and American ecologists, the Z-M system was subjective and therefore intellectually dubious, because field workers sampled in a way that allowed them to prove what they wanted to find out in the first place. However, not everybody in Britain and America was convinced that objectivity and the Z-M system were in opposition. R.H. Whittaker (1962) urged ecologists to be pragmatic. He visited Tüxen in Germany, and with Tüxen’s blessing edited the monumental Ordination and classification of communities (1973) in which the various protagonists set out their points of view. The publication of a good English-language manual by the German ecologists Mueller-Dombois and Ellenberg (1974), included an exposition of ‘Tablework’, a nearly-algorithmic method of sorting two-way tables. This narrowed the gap still further.

Thus it was natural that Mark Hill, visiting Whittaker in Cornell, should seek to develop an algorithm whose purpose was to sort tables in an objective way but in the spirit of Z-M methodology. There remained a difficulty, namely that existing numerical methods almost all classified either the samples (the so-called Q methods) or the species (R methods) but did not seek to arrange both together. Underlying this difficulty was the fact that many mathematicians were committed to the metric paradigm, according to which a classification should reflect as faithfully as possible a metric compositional distances between samples (for Q methods) or between species (for R methods). By 1979, the metric paradigm for ordination had already been subjected to severe criticism (Austin 1976), and its applicability to classification was therefore also open to question.

This was the background to the writing of TWINSPAN. A practical problem that had already been solved for Indicator Species Analysis was to keep magnitude of the calculation so that it rose only linearly with the size of the dataset. (Clearly any explicit calculation of distance matrices would increase the problem to magnitude m2 if m is the number of samples, or n2 where n is the number of species.) An algorithm linear in the size of the dataset was achieved by, figuratively speaking, sending signals through the data matrix in search of resonances in which the species and samples sounded together, and then dividing the data accordingly. When the samples and subsequently the species were repeatedly divided, TWINSPAN resulted.

TWINSPAN was originally written in FORTRAN 4, a language well suited to mathematical calculations but with poor handling of alphabetical data. Some improvements

were made with FORTRAN 77, which handled alphabetical data rather better. However, when MS DOS was dropped in favour of Windows, the excellent Microsoft Fortran compiler was discontinued. TWINSPAN became difficult to run except under older operating systems such as UNIX or in a DOS window. Given that the program has retained its popularity, there is a need for it to be available in a modern form. It is with pleasure therefore that after 25 years, we present it in an updated form suitable for the 21st Century.

Mark O. Hill

Petr ?milauer

2 Copyright

The WinTWINS software consists from three parts, with different code ownership. The twindll.dll dynamic library implements the actual algorithm of the TWINSPAN method and is owned by Mark Hill’s employer, the Natural Environment Research Council of Great Britain. The executable file wintwins.exe represents a user-friendly wrapper for the method, allowing the user to easily specify analysis options and inspect analysis results. Its code is owned by Petr Smilauer, ?eské Budějovice, Czech Republic. The CanoDatC.dll dynamic library parses the input data files in format compatible with Canoco software and it is written by Cajo Ter Braak and owned by Biometris, Wageningen, The Netherlands.

All the code owners give to everyone the right to use the WinTWINS software for analysis of research data, both in non-commercial and in commercial work. This software can be further distributed in the form of installation program. Integration of any part of the WinTWINS software into any commercial or non-commercial software package is explicitly prohibited.

When using this software, please cite it as follows: Hill, M.O. & ?milauer, P. (2005): TWINSPAN for Windows version 2.3. Centre for Ecology and Hydrology & University of South Bohemia, Huntingdon & Ceske Budejovice.

This software is provided on an "AS IS" basis, without warranty of any kind, including without limitation the warranties of merchantability, fitness for a particular purpose and non-infringement. The entire risk as to the quality and performance of the software is borne by you. Should the software prove defective, you and not the authors of the software assume the entire cost of any service and repair.

The source code for the twindll.dll and wintwins.exe parts is available from its respective authors:

Dr. Mark Hill - moh@https://www.wendangku.net/doc/978118933.html,

Dr. Petr ?milauer - petrsm@https://www.wendangku.net/doc/978118933.html,

3 TWINSPAN Method

3.1 Ordered two-way tables

TWINSPAN (Tw o-way in dicator sp ecies an alysis) is a computer program designed primarily for ecologists and vegetation scientists who have collected data on the occurrence of a set of species in a set of samples. The samples may be stands, relevés, stomach contents, island faunas, or whatever is appropriate to the study. The program first constructs a classification of the samples, and then uses this classification to obtain a classification of the species according to their ecological preferences. The two classifications are then used together to obtain an ordered two-way table that expresses the species' synecological relations as succinctly as possible.

Table 1 : An ordered two-way table derived from the Dune meadow data and

ordered by TWINSPAN; the 0/1 numbering at the bottom and right specify

classifications of the samples and species

In an ordered two-way table, some of the structure of a dataset is apparent. For example in Table 1, we see that the ‘dry’ species Aira praecox, Anthoxanthum odoratum, Empetrum nigrum and Hypochaeris radicata are found especially in samples 17 and 19. Likewise the ‘wet’ species Eleocharis palustris, Potentilla palustris, Ranunculus flammula and Calliergonella cuspidata are found especially in samples 14, 15, 16 and 20. Other species such as the ‘semi-dry’ Lolium perenne and Poa pratensis avoid the wettest samples, while the ‘semi-wet’ Agrostis stolonifera avoids the driest samples.

In this case the arrangement reflects one major variable. This is often what is found. However, in some cases, more complex groupings are revealed and (often) aberrant samples or groups of samples are identified.

3.2 Differential species

The ‘wet’ and the ‘dry’ species are examples of differential species. A differential species is one with clear ecological preferences, so that its presence can be used to identify particular environmental conditions. In Table 2.1, the ‘wet’ species Agrostis stolonifera and the ‘dry’ species Lolium perenne are examples of differential species. There is some overlap between them, but on the whole they avoid each other. On the other hand Leontodon autumnalis is a poor differential species, not showing any marked affinity for a particular group of samples.

3.3 Basic structure of TWINSPAN

TWINSPAN is designed to construct ordered two-way tables, and the method of doing so is by identification of differential species. In this respect it closely resembles the graphical method of classification outlined by Mueller-Dombois & Ellenberg (1974). It differs, however, in its treatment of the species. In the method outlined by Mueller-Dombois & Ellenberg, the species are classified at the same time as the samples. In TWINSPAN, on the other hand, the samples are classified first, and the species are classified second, using the classification of the samples as a basis.

The basic structure of TWINSPAN is as follows.

1.Classify the samples in a divisive hierarchy, dividing them first into 2 subsets, then 4, 8,

16, etc.

2.Convert the sample classification into an ordering.

https://www.wendangku.net/doc/978118933.html,ing the groups of samples as a basis, construct attributes for the species. For example,

in Table 2.1, species 1, 6, 7 and 18 would be described as possessing the attribute ‘preferential to the left side of the major division.’

4.Classify the species in the same way as the samples, but with the difference that whereas

the species were treated as attributes of the samples, the species have attributes of the kind indicated above.

5.Convert the species classification also into an ordering.

6.Print out the resulting ordered two-way table.

3.4 Making a dichotomy

The basic activity in TWINSPAN is to make a dichotomy. Indeed, as indicated above, all that the program does, in effect, is to divide up the samples into groups by repeated dichotomization, and then to do the same for the species.

It can be argued that this is a bad way to organize a table because dichotomies do not arise naturally. Indeed, Mueller-Dombois & Ellenberg (1974) recommend dividing the species into three categories, those that are preferential to one side of the division, those that are preferential to the other, and those that are indifferent. In practice, the indifferent categories are usually picked out in later dichotomies. For example the species labeled 01 in Table 1 are indifferent.

The stages of making a dichotomy in TWINSPAN are as follows.

1.Identify a direction of variation in the data by ordinating the samples. This ordination is

referred to below as the ‘primary’ ordination, and is made by the method of correspondence analysis (also known as reciprocal averaging; Hill, 1973a, 1974).

2.Divide the ordination at its middle to get a crude dichotomy of the samples.

3.Identify differential species that are preferential to one side or the other of the crude

dichotomy.

4.Construct an improved ordination (referred to below as the ‘refined’ ordination), using

the differential species as a basis.

5.Divide the refined ordination at an appropriate point to derive the desired dichotomy.

If this were all, TWINSPAN would be relatively easy to describe. However, yet a third ordination is also constructed, the ‘indicator’ ordination. This is based on a small number of the most strongly differential species, and is designed to provide a simple criterion for re-identification of the groups. So a further stage must be added.

6.Construct a simplified ordination, the ‘indicator’ ordination, based on a few of the most

highly preferential species. See whether the dichotomy suggested by the refined ordination can be reproduced by a division of the indicator ordination.

To summarize, TWINSPAN makes its dichotomies by dividing ordinations in half. There are three ordinations involved:

1.The primary ordination (correspondence analysis), which is divided to obtain an initial,

crude dichotomy;

2.The refined ordination, which is derived from the primary ordination through the

identification of differential species; and

3.The indicator ordination.

With the exception of borderline cases, the refined ordination is the one that is used to determine the dichotomy. The indicator ordination is essentially an appendage, put there for the convenience of users who want a succinct characterization of the dichotomy.

3.5 Pseudospecies

The idea of a differential species is essentially qualitative, and to be effective with quantitative data must be replaced by a quantitative equivalent. This equivalent is the ‘pseudospecies’ (Hill, Bunce & Shaw, 1975; Hill, 1977). The essential idea is that much of the quantitative information can be retained by expressing it on a relatively crude scale such as the Braun-Blanquet scale of cover-abundance (Mueller-Dombois & Ellenberg, 1974). The levels of abundance that are used in TWINSPAN to define the crude scale are here termed ‘pseudospecies cut levels’.

Consider, for the sake of example, the Braun-Blanquet scale. Ignoring the distinction between 1, +, and r, the scale is as follows:

1 0 - 4% 4 51 - 75%

2 5 - 25% 5 76 - 100%

3 26 - 50%

If quantitative data with cover expressed on a percentage scale are entered into TWINSPAN, then the Braun-Blanquet scale can be used by entering the pseudospecies cut levels:

0 5 26 51 76

Consider now a species, for example Poa annua, whose cover in one sample is 18% and in another is 36%. Although these values differ by a factor of 2, the samples have an important feature in common, namely that they share a moderate abundance of Poa annua. Given the Braun-Blanquet scale defined above, this fact can be expressed in terms of pseudospecies by saying that the samples contain the following pseudospecies:

Sample with Poa annua 18% - P. annua 1, P. annua 2;

Sample with Poa annua 36% - P. annua 1, P. annua 2, P. annua 3.

Hence, using the Braun-Blanquet scale, the samples are registered as having two pseudospecies in common, and one different. This is arguably a correct way to view them; in spite of the rather large difference in cover, the samples actually have more in common than by way of difference.

The method of pseudospecies allows quantitative values to be used as differential ‘species’ and as indicators. Thus, in TWINSPAN, instead of a differential species Poa annua, it is possible to have a differential species P. annua 2, which—with the pseudospecies cut levels defined above—occurs when and only when P. annua has cover 5% or greater.

In practice, users of WinTWINS who are mainly interested in a good tabular arrangement will hardly concern themselves with the technical detail of pseudospecies. For them it suffices to know that they are using a particular scale of abundance. However, there is one important practical point, namely that information on the occurrence of each pseudospecies is stored separately in the computer. Use of very numerous pseudospecies may therefore be undesirable with larger problems, as they use up storage space.

4 Working with WinTWINS

Each analysis is represented by a project that is stored in a file with .twp file extension. This is a binary file that cannot be directly viewed or edited with other programs. To modify project settings, you must use the Setup Wizard, a series of dialog pages, where you specify input data and other analysis options (see section 4.2 for details of this procedure).

4.1 Program workspace

WinTWINS works at any time with a single project. The project is manipulated using the commands in the program menu and the main analysis results are displayed in the WinTWINS window (see Figure 1).

Figure 1

The commands in the File submenu allow you to create a new project, open an existing one and save the project, optionally under different name (the Save As command). The project log (shown in the window) can be also printed.

The commands in the Edit submenu (the Undo, Cut, Copy, and Paste commands) provide basic support for working with the analysis log displayed in the program window.

The commands in the View submenu allow you to show or hide the program toolbar (Toolbar), show or hide the status bar at the window lower edge (Status Bar), or to change type and size of font used to display analysis log (Window Font).

4.2 Setup Wizard

The project setup wizard is shown when you select the Project / Settings menu command and also when you start the program or open new TWINSPAN project file. At the first wizard page (Figure 2), you must specify the name of data file.

Figure 2

The WinTWINS program is able to read data in condensed, full or free formats, corresponding to formats supported by Canoco? for Windows, version 4.x (Ter Braak & ?milauer 2002). The maximum allowed number of samples is 25000, maximum number of variables is 10000. Note that the later number includes not only the variables (species) present in your data file, but also the pseudo-variables (pseudo-species) that are created based on the cut levels you specify in the next setup wizard page. The maximum number of presences for variables and pseudo-variables (pseudo-species) is set to 4000000, but it should not exceed 2000000 for a classification of species to be created in addition to a classification of your samples.

After you click the Next button, WinTWINS program parses the data to check their size and range of values. This information is displayed in the following page (Figure 3) and also the suggested cut levels are adjusted for the range of data values. WinTWINS uses the default cut levels (0, 2, 5, 10, 20), but removes the levels exceeding the largest value in data.

Figure 3

You must select unique, increasing cut levels. They should be chosen so as to reflect typical values of abundance, e.g. "present", "a little", "a lot", "more-or-less dominant". It is important, however, not to over-weight the effect of dominance by including many relatively high cut levels. With percentage data the default cut levels have proved very effective, and the user is recommended to adhere to them until he or she has some experience with the method.

For each cut level, you can specify its relative weight in the analysis. Note that this weight must be specified with whole positive numbers, representing the multiple of the default weight (=1) to use for a particular level. In many applications, it is not necessary to use weights at all (i.e. to use the value of 1 for all cut levels). However, with community composition data taken from very large plots, it may sometimes be advisable to give presences and absences relatively low weights, as they may be due to anomalous small patches of terrain that occupy little of the plot area.

The last column in the Cut Levels page represents the indicator potential for individual cut levels. If a particular box is checked, the (pseudo-)variables resulting from that level (or, usually, the presence of species for the first cut level) can be used as indicators for individual splits. Very often, all levels have an indicator potential. The most common variation is that all the indicators should be real species, not pseudospecies. In this case, only the first level is checked.

Note that if you increase the number of cut levels from that suggested by the setup wizard, the extra levels do not have appropriate threshold values. You must specify the correct thresholds (increasing from top to bottom) before you can proceed to the next page.

In the next property page (Figure 4), you can select samples that will be omitted in the analysis.

Figure 4

To specify the samples to be "deleted", select them in the left-hand list and click the Select>> button. Depending on the structure of the analysed data, you might prefer your samples to be listed in the increasing order of their indices or sorted alphabetically using their names (labels). You choose the appropriate method using the two radio-button controls at the bottom.

The next wizard page (Figure 5) can be used to select species to be ignored in the analysis, based on their frequency (number of occurrences) in the data.

Figure 5

You should specify the minimum number of occurrences (positive values) that a species must have to take part in the analysis. In Figure 5, the listed five species have obviously just one occurrence (or they might be absent altogether) in the data. Note that the occurrences in the samples deleted in the previous page are ignored here.

In the next page (Figure 6), you can explicitly specify species to omit from the analysis. Note that all the species in your data are shown there, even those with implied omission by the preceding page. The final list of omitted species represents a logical union of the two lists.

Figure 6

The Nondiagnostic Species wizard page (Figure 7) seems similar to the previous one, but species selected here are not completely omitted from the analysis. They are just ignored when WinTWINS looks for diagnostic species, used in the indicator ordination step (see section 3.4). This is useful, for example, if the indicator criterion is to be applied by relatively inexperienced field workers. It may be then better if difficult taxonomic groups are omitted.

Figure 7

In WinTWINS, you can also specify specific weights for some samples and/or species, that are combined with the sample and species weights implied by the reciprocal averaging (RA) algorithm, used in the TWINSPAN method.

In the Sample Weights wizard page (Figure 8), you may specify non-default user weights for samples. Samples not present in the list have the default user weight (1.0).

Figure 8

To remove weighted samples from the list, select the corresponding rows in the list and click the Delete button. Use the Add button to specify additional weighted samples.

A new dialog box is shown (see Figure 9).

Figure 9

In this dialog box, all the samples with default weight are listed. Select in the list the samples to be weighted, enter the required weight (range 0.001 to 1000.0) and click the OK button. To change weight value for an already weighted sample, you must first Delete it in the parental page and then specify new weight for it here.

A similar property page is also available for species. The species weights are applied to all corresponding pseudo-species that result from the specified pseudo-species cut levels. The weights have an effect on the species classifications as well.

The final page of the project setup wizard (Figure 10) collects the options concerning the TWINSPAN algorithm and also the output shown in the WinTWINS main window or stored in the classification file.

Figure 10

The maximum number of division levels (1 to 9) determines the maximum level of recursive splitting for samples (in the sample classification) and for species (in the species classification). Even with large data sets there is little purpose in continuing to subdivide groups beyond a certain limit. Six levels of division are apt to produce about 64 groups. If there is large number of groups, then interpretation can be difficult. Users will soon get a feel for how much division they require with any problem. Rarely will they want fewer than four levels, and almost never more than seven.

The groups of samples or species (in species classification step) smaller than the value specified in the Minimum group size for division field will not be further divided. It must be noted, however, that groups smaller than the specified size will often be formed, e.g. when the natural structure of the data is one large group and a few outliers. It is generally better to control the maximum number of division levels (preceding parameter) than to control the size of generated groups, though there certainly does come a size below which it is not worth dividing groups further.

The value specified in the Maximum number of indicators per division determines the maximum number of species that can be used in the indicator ordination (see section 3.4). If no indicator ordination is desired, then this parameter can be set to zero. If a particular dichotomy can be specified precisely by an indicator ordination based on a smaller number of indicators than the maximum, then the smaller number will be used.

The Number of species in final tabulation is used when creating the two-way table at the end of WinTWINS output (the table is created in two alternative formats, see section 5.7).

It is often inconvenient to clutter this table with rare species. Therefore only the N commonest species are shown, where N is the value specified here.

The diagrams of division display in a simple form how the indicator ordination relates to the refined ordination, and in particular whether the misclassifications are approximately borderline cases (see section 5.4 for further explanation). If the Show diagrams of division in the analysis log option is checked, a text-form scatter diagram is present in the analysis log for each dichotomy (split).

The hierarchical classification of samples and species can be stored in simply formatted text file (known as the "machine-readable copy of solution" in the previous TWINSPAN versions), typically with a .pun extension. If the Store classification in a file option is checked, the output file name should be specified in the Classification file name edit field. WinTWINS project setup wizard fills the file name field with a default value, which is the file path for the input data, with the file extension changed to .pun.

If the final option, named Continue with the project analysis, is checked, WinTWINS continues, after you click the Finish button, with the actual analysis of the project data.

Instead of pressing the Finish button, you can also use the Back button to return to previous pages, to review or modify the settings made there.

4.3 Analysis output

The analysis results are placed (except the classification of individual samples and species, placed in the classification file) in the WinTWINS window, where they can be inspected, copied to other programs and saved into a file with text format (using the Project / Save log … menu command). To make reading of the analysis log shown in the WinTWINS window easier, you can adjust the size of displayed characters using the dialog displayed by the View / Window Font. Note that the output formatting relies in many places on use of a fixed pitch (non-proportional) font, such as Courier or Courier New. If you select instead a typeface with varying width of individual characters, the layout of many tables will be broken.

The output from the TWINSPAN method is described in the next chapter.

5 WinTWINS Output

5.1 Reading the data matrix

The first part of the output concerns the input of the data matrix and the omission of samples. The cut levels are explained above. Only the beginning and end of the data matrix are printed, and all quantities are multiplied by 1000 and rounded to the nearest integer. Values of -1 indicate the end of a sample. Thus a record

1 46000 5 2500 -1 1 56000 6 4500 -1

would refer to two samples, one with species 1 having quantity 46.0 and species 5 having quantity 2.5, and the other with species 1 having quantity 56.0 and species 6 having quantity 4.5. The matrix is printed out in the form that is held in the computer in order to remind the user of two things:

1.How the length of the raw data array relates to the number of non-zero items in the data

matrix; and

2.That quantities smaller than 0.001 are lost in roundoff.

5.2 Entry of parameters

The program gives information about parameters entered when the project was set up. After the input parameters, three important statistics on the data are printed out:

1.Length of data array after defining pseudospecies;

2.Total number of species and pseudospecies; and

3.Number of species, excluding pseudospecies and ones with no occurrences.

With big problems these statistics may be relevant to determining whether it is necessary to reduce the number of pseudospecies to make room for the data in the computer.

5.3 Classification of the samples

Divisions are made successively, according to the scheme below.

1

*

┌─────────┴─────────┐

││

2 3

*0 *1

┌────┴────┐┌────┴────┐

││││

4 5 6 7

*00 *01 *10 *11

Each group is represented by two numbers, one in decimal, one in binary notation. If, in the hierarchy above, the symbol * is replaced by the number 1, then the decimal and binary numbers can be seen to be identical. Thus 10 is the representation of 2 in binary code, 110 represents 6, etc.

In general, group n is divided to obtain group 2n (the ‘negative’ group) and group 2n+1 (the ‘positive’ group). The binary representation of the nodes of the hierarchy is more directly interpretable than the decimal representation, 0 denoting a left arm and 1 denoting a right arm.

***********************************************************************************

DIVISION 1 (N= 20) I.E. GROUP *

Eigenvalue 0.531 at iteration 3

INDICATORS, together with their SIGN

Agr sto 1(+) Ran fla 1(+) Lol per 5(-)

Maximum indicator score for negative group 0 Minimum indicator score for positive group 1

Items in NEGATIVE group 2 (N= 12) i.e. group *0

1.......

2.......

3.......

4.......

5.......

6.......

7....... 10...... 11...... 17...... 1

8...... 1

9......

Items in POSITIVE group 3 (N= 8) i.e. group *1

8....... 9....... 12...... 13...... 14...... 15...... 16...... 20......

NEGATIVE PREFERENTIALS

Ach mil 1( 7, 0) Ant odo 1( 6, 0) Bel per 1( 6, 0) Bro hor 1( 5, 0) Ely rep 1( 5, 1) Hyp rad 1( 3, 0)

Lol per 1( 10, 2) Pla lan 1( 7, 0) Poa pra 1( 11, 3) Tri pra 1( 3, 0) Vic lat 1( 3, 0) Ach mil 2( 6, 0)

Ant odo 2( 6, 0) Bel per 2( 6, 0) Bro hor 2( 5, 0) Ely rep 2( 5, 1) Hyp rad 2( 3, 0) Lol per 2( 10, 2)

Pla lan 2( 7, 0) Poa pra 2( 10, 3) Tri pra 2( 3, 0) Ant odo 3( 5, 0) Bro hor 3( 3, 0) Ely rep 3( 5, 1)

Leo aut 3( 8, 1) Lol per 3( 8, 1) Pla lan 3( 6, 0) Poa pra 3( 9, 2) Rum ace 3( 3, 0) Ant odo 4( 4, 0)

Ely rep 4( 5, 1) Leo aut 4( 4, 0) Lol per 4( 8, 1) Pla lan 4( 3, 0) Poa pra 4( 7, 2) Tri rep 4( 3, 1)

Leo aut 5( 4, 0) Lol per 5( 8, 0) Pla lan 5( 3, 0) Tri rep 5( 3, 1) Lol per 6( 6, 0) Poa tri 6( 3, 1)

POSITIVE PREFERENTIALS

Agr sto 1( 2, 8) Alo gen 1( 3, 5) Ele pal 1( 0, 5) Jun art 1( 0, 5) Jun buf 1( 1, 3) Pot pal 1( 0, 2)

Ran fla 1( 0, 6) Sag pro 1( 3, 4) Cal cus 1( 0, 3) Agr sto 2( 2, 8) Alo gen 2( 3, 5) Ele pal 2( 0, 5)

Jun art 2( 0, 5) Jun buf 2( 1, 3) Pot pal 2( 0, 2) Ran fla 2( 0, 6) Sag pro 2( 3, 4) Cal cus 2( 0, 3)

Agr sto 3( 2, 8) Alo gen 3( 1, 5) Ele pal 3( 0, 5) Jun art 3( 0, 5) Jun buf 3( 0, 3) Cal cus 3( 0, 3)

Agr sto 4( 2, 7) Alo gen 4( 1, 4) Ele pal 4( 0, 5) Jun art 4( 0, 3) Jun buf 4( 0, 2) Bra rut 4( 3, 4)

Agr sto 5( 1, 3) Alo gen 5( 1, 3) Ele pal 5( 0, 2)

NON-PREFERENTIALS

Leo aut 1( 11, 7) Poa tri 1( 8, 5) Rum ace 1( 3, 2) Tri rep 1( 10, 6) Bra rut 1( 9, 6) Leo aut 2( 11, 7)

Poa tri 2( 8, 5) Rum ace 2( 3, 2) Tri rep 2( 9, 5) Bra rut 2( 9, 6) Poa tri 3( 7, 4) Tri rep 3( 4, 3)

Bra rut 3( 4, 4) Poa tri 4( 7, 4) Poa tri 5( 5, 2)

End of level 1

***********************************************************************************

Figure 11 First dichotomy resulting from application of WinTWINS to the dune meadow data. The indicators have been underlined and emboldened. It may seem surprising that the pseudospecies Sag pro 2 (3, 4) is a positive preferential. The reason for this is that it occurs in 3/12 = 25% of the samples in the negative group, and in 4/8 = 50% of the samples in the positive group. It is twice as likely to occur in the positive group as in the negative group and hence qualifies as preferential.

Consider the output for a dichotomy line by line (refer to Fig. 11).

Line 1 gives the number of the group to be divided, both in decimal and in binary notation, together with the number of elements that it contains.

Line 2 gives information on the primary ordination (correspondence analysis). Each iteration involves eight passes of the data.

Lines 3-5 specify the indicator ordination. Each sample is given an ‘indicator score’ found by adding +1 for each positive indicator and -1 for each negative indicator that it contains. The sign (+ or -) of each indicator follows immediately after its name in the list of indicators. The division derived from the indicator ordination is specified on line 5. The two values printed are the maximum indicator score for a sample to be assigned to the negative group, and the minimum score for it to be assigned to the positive group. If these values are A and B respectively, then B is always 1+A.

In the example, only those samples with an indicator score of 0 or less are included in the negative group. Referring to the two-way table (Table 1), it can be seen that two samples (numbers 3,4) have indicators for both sides, namely Lol per 5 (high abundance of Lolium perenne) indicating the drier end and Agr sto 1 (presence of Agrostis stolonifera) indicating the drier end. These samples are assigned to the negative group, but are obviously somewhat borderline – though not so much so as to count as borderline cases for this dichotomy. (In the second division *0, separating the extreme ‘dry’ groups 17,19 from the ordinarily ‘dry’ samples, the sample 18 is signified as a borderline positive.) In the first division, the extreme ‘dry’ samples 17, 19 contain no indicators for the first division but are classified correctly.

The indicators are listed in an approximate order of effectiveness. Thus in Fig. 11, Agrostis stolonifera (positive) is a better indicator than Ranunculus flammula (positive) and Lolium perenne 5 (negative).

5.4 Relation between indicator ordination and refined ordination

This section is somewhat technical, and is for readers who want to understand how borderline and misclassified cases are defined. We consider here the ordinations for the first dichotomy obtained when classifying the Danube meadow data discussed by Mueller-Dombois & Ellenberg (1974). A scatter diagram showing the position of the samples is shown below (Fig.

12).

For ease of computing the ordination is divided into segments. These have no special significance, but are merely a convenient way of calculating where to locate the zone of indifference. The critical zone (Fig. 12) is a zone near the centre of the refined ordination where it is allowable to make divisions. There are five possible positions for the zone of indifference such that it lies entirely within the critical zone. The location of the zone of indifference is selected to minimize the number of misclassified samples (see below).

Segments of the refined ordination are shown along top of the scatter diagram, which is not to scale. The critical zone (segments 5-12) is 20% of the length of the whole ordination. The length of the segments within the critical zone is one-quarter of the length of the segments outside it.

Borderline negatives are those items that are in the negative group and which also lie in the zone of indifference. In Fig. 12, sample 16 is a borderline negative, and is assigned to the negative group because it has an indicator score of -1. The refined ordination is highly polarized, so that there are normally few borderline cases. A borderline case is assigned to its class according to its indicator score, the refined ordination being held in this case to be indecisive.

Misclassified negatives are those samples lying to the left of the zone of indifference but whose indicator score would assign them to the positive arm of the dichotomy. This is regarded as a failure on the part of the indicator ordination to reproduce the dichotomy accurately, and

hence as a ‘misclassification’. Because such samples are outside the narrow zone of indifference, the refined ordination takes priority.

Items in positive group, borderline positives, and misclassified positives are defined as for negatives.

Fig. 12 Relation between indicator ordination and refined ordination for Danube meadow data (not discussed here). The segments of the refined ordination are indicated along the top of the diagram. Segments 5-12 constitute the ‘critical zone,’ and segments 8-11 constitute the ‘zone of indifference’ (abbreviated Z.I.) in the diagram. Samples are designated as ‘borderline cases’ if they lie in the zone of indifference. In this example, only sample 16 is borderline.

5.5 Preferential species and pseudospecies

Negative preferentials are those pseudospecies and species that are at least twice as likely to occur on the negative side as on the positive side. Only those that occur in at least 20% of the samples on the negative side are listed. Values given in brackets are actual numbers of occurrences, so that the entry

Lol per 2( 10, 2)

signifies that Lolium perenne occurs with abundance 2 or more in 10 samples on the negative side of the dichotomy and in 2 samples on the positive side of the dichotomy (Tab. 1). When there is a very uneven split, negative preferentials can easily occur in more samples on the positive side of the dichotomy than on the negative side. Suppose, for example, that the split is

into 2 samples on the negative side and 10 on the positive. Then a species that occurs in 2 samples on the negative side and 4 samples on the positive side is a good negative preferential. It has 100% frequency on the negative side and 40% frequency on the positive side, and is therefore 2.5 times as likely to occur on the negative side as on the positive side.

Positive preferentials are defined as for negative preferentials; non-preferentials are pseudospecies and species that are reasonably common and which are not preferentials. Here again, only those that achieve 20% frequency on one side or the other are listed.

5.6 Species classification

Species are classified by WinTWINS in much the same way as samples. However, there is an important difference in that the species classification is made in the light of the sample classification, and not using the raw data. In fact, the species classification is made on the basis of fidelity, i.e. using the degree to which species are confined to particular groups of samples. For example, in Tab. 1, Aira praecox and Achillea millefolium are both completely faithful to group *0 of the sample hierarchy—i.e. they have no occurrences outside this group. However, Aira is also completely faithful to group *00 of the sample hierarchy, whereas Achillea is not.

Species are assigned attributes according to differing degrees of fidelity to sample groups. For example, both Aira praecox and Achillea millefolium will be registered as having the attribute ‘very highly faithful to group *0’, but Aira is also very highly faithful to group *00, whereas Achillea is not. Indeed, Achillea occurs widely outside group *00, in group *01.

Because the species classification is made on the basis of fidelity to groups defined by the sample classification, altering the level of division of the classification may alter the species classification even if no other changes are made.

The species classification differs from the sample classification in that ‘indicator characters’ are of little interest. It is scarcely of much significance to know that (for example) ‘low level of fidelity to sample group X’ is a preferential attribute of a particular group of species. Consequently, the indicator ordination is omitted from the calculation and output.

If the data set is very large, there may be no room for the new matrix of species' attributes as well as the original matrix. If so, then the species classification is abandoned.

5.7 Order of species and samples

The samples are generally ordered so that the group *1 is smaller than *0, and thereafter so that *01 resembles *1 more than *00 resembles *1. Further divisions are also ordered by similarity. Species are ordered so that species in group *0 generally occur in sample group *0 and species in group *1 generally occur in sample group *1. Thus the ordering of each dichotomy is not arbitrary, but is designed to ensure that the occurrences of species are located on the positive diagonal (Tab. 1).

These orderings are printed out for two purposes. In the first place, the final table may not contain all the less common species, so that the orderings may be convenient as an indication of where the rarer species would come in the arrangement. Secondly and more important, the final tabulation refers to the samples by number, not by name as elsewhere in the program. The (historic) reason for this is that it was difficult to write the names vertically using FORTRAN 4. In WinTWINS, the sample names are available in the second tabulation, in TSV format. This can be read directly into a spreadsheet.

钢琴入门:汤普森简易钢琴教程

钢琴入门:汤普森简易钢琴教程

钢琴入门教程:小汤(汤普森简易钢琴教程》 《小汤》的学习目的是:通过对中央C附近的音符进行反复认音练习,掌握五线谱基础知识,并将线谱与键盘有机地联系起来;通过数拍子,培养正确的节奏感。为下一步的学习打下一个良好的基础 第一册涵盖的音域有意识地作了限制。只介绍中央C以上的五个音和以下的五个音,时值也从全音符到四分音符为止,不再扩展,这样就有可能包括许多以复习形式出现的曲例,不必另找补充教材。总之,本教程的每一册课本都保持各自的完整性,都有各自的书写练习、视谱练习和复习曲目,在以后的各册中还将增加技巧练习。 伴奏: 书中大部分曲例,配有供教师和家长用的伴奏谱。它们都经过精心的创作,使那些简易的小曲听起来尽可能像结构庞大的乐曲的片断。这样做有很多好处,不仅有可能用不同的调弹奏,避免总是徘徊在C大调上,令人生厌;而且可以用自己严格的速度和鲜明的节奏对学生施加影响,特别是他们在弹奏中带有充满活力的节拍重庆,能使学生一开始就“感觉”到节奏的存在。 第一册:《约翰.汤普森简易钢琴教程一》 A 音符节奏:(图 1) (图2) B 音域:中央C为中心,上下五个音(见图2) C 节拍:4/4 、2/4、 3/4 D 调性:C调 重点:主要以认识五线谱、手指编号,一拍二拍三拍四拍音符组合。 《小汤1》: 1.严格地只在白键上弹奏。 2.在附点前较早引入了切分节奏(《雷格泰姆舞》、《弗吉尼,我的故乡》、《摘棉花的老人》、《我的忧愁谁知道》) 3.三拍子的巧妙进入。《小矮人进行曲》紧接《小矮人舞曲》。 4.逐渐增加手指数量。 第一学时

内容:从钢琴键盘至练习题 本课时的知识点:1.音名、五线谱、全音符、二分音符、四分音符、中央C 2.钢琴键盘、基本弹奏姿势、基本手型 本课时的重点:1.中央C在五线谱与钢琴键盘上的位置、四个音符的不同形状及时值 2.正确手型中手指支撑与手腕放松的平衡感觉 本课时的难点:1.音符时值在弹奏中的把握、唱名与音名的本质区别 2.大指弹奏中央C的正确手型 练习把握:1.反复确认键盘上中央C在高音谱表与低音谱表上的不同位 置、 2.四个音符长短时值的练习:我采用一个比喻方法,叫数苹果法,具体做法是,在一个相同距离内(比如学生放在钢琴上的书的长短为例)学生拍一下,嘴数一拍,节拍器响一次等于手拍一下的时间,而我就告诉他们,拍一次一个苹果。这个方法对于年龄小(4-5周岁,下同)的初学学生掌握拍子、用节拍器练习节奏非常适用。 3.大指弹奏中央C时虎口的开度、手指支撑时力的均衡。 时间安排:各年龄段不同,我这里以年龄小的学生为例。开始每天以15-20分钟为基点,然后循序渐进逐步增加时间。 第二学时 学习内容:火车、玛丽有只小羔羊、海军工兵、伞兵。注:1.年龄小的学生,可把内容分为两次上课和练习。2.根据学生的心里特点,老师可把课本内容顺序做一定调整,便于学生集中学习和记忆。 知识点:1.高音谱表D、E音名的位置、低音谱表B、A音名的位置 2.键盘上D、E、B、A的位置 3.左右手2、3手指在键盘上的站立练习 4.曲子四拍子、三拍子中强拍的弹奏 重点:1.高音谱表、低音谱表中新学音名的位置 2.键盘上新学音名位置的确认

钢琴基础教程(五线谱)37747

五线谱钢琴基础教程(1) 基础 篇 1 键盘知识中央C 五线谱入门线上线间八度 2 线上音符线间音符白键7个音符 3 (一)你用的键盘乐器 无论你是拥有一个真正的钢琴,还是一个电钢琴、电子琴或风琴,这里的教程都会教你认识键盘,弹奏五线谱曲子,并学习基本的五线谱知识。 简单说来,钢琴的学习包括认识键盘,将手放到合适的位置,如何控制运用你的手指,如何用双手而不是单单右手来共同弹奏,当然还有如何看懂五线谱钢琴曲谱。 你是用哪种键盘乐器来学习的呢?一共有多少个键盘?我建议你最好使用有61个键盘的那种。如果你的键盘有重力感觉(垂重感键盘)的就更好了,就更接近真实钢琴的机械装置和触感。一般来说简易低档的电子琴的键盘没有重力感设计,键盘的按下时没有什么阻力(比较真实的钢琴键盘就会知 道)。 (二)白键盘黑键盘从哪里开始呢? 看到键盘可能一开始会迷惑:这么多的键盘---88个键我如何能记住呢?

不过你很快就可以总结出黑键的分布规律:即三个黑键和两个黑键规律性的排列,而且间隔是完 全一样的。 你还会发现上图的白键上有规律的标出绿色的字母C,这个C是出现在两个黑键左面的白键上的。至于这个为何叫C以后会详细介绍。另一个你要注意记忆的是键盘中央的C位置,既所谓的中央C。这是一个需要牢记的位置,你以后会发现这个标志性的C的很多意义。而下面的中央C位置是真实钢琴的 键盘位置。 (三)钢琴键盘的分组五线谱基本要素

上图最上面的就是你经常看到的钢琴的五线谱,中间那个空心圆在短横线的位置---线间就是中央C。这个中央C位置是你弹奏任何一个钢琴曲子都要参考的键盘。 五线谱是记录音乐的一种语言,就象英语、汉语一样,它同样有自己的规则,告诉你弹什么和如何弹奏。最明显的特征就是左端的谱号形式-----高音谱号和低音谱号一起成联合谱表,这是一个标准的钢琴五线谱形式。音符(后面还要讲)在线间或线上。 将中央C的一组白色键盘灰颜色填充,你会发现以C为一个组,七个白色琴键加上五个黑色键盘(两个黑色和三个黑色的)构成一12个键盘组,而且这个C组不断重复。随便用左手或右手弹奏这些不同的 组会发现越往右侧的声音越高,越往左声音越低。 (四)C 和八度 上面的图示显示出在中央C右面和左面的其他的C在五线谱上面的位置。从中可以看出,在键盘上有规律的C的位置排列到了五线谱上面就没有什么规律可循。换句话说,不同C组的键盘位置在五线谱位置上没有什么联系,你只能通过大量的练习和不断的记忆来逐渐掌握。 线上音符

网店美工视觉设计实战教程(全彩微课版)-48481-教学大纲

《网店美工视觉设计实战教程(全彩微课版)》 教学大纲 一、课程信息 课程名称:网店美工:店铺装修+图片美化+页面设计+运营推广(全彩微课版) 课程类别:素质选修课/专业基础课 课程性质:选修/必修 计划学时:21 计划学分:2 先修课程:无 选用教材:《网店美工视觉设计实战教程(全彩微课版)》,何晓琴编著,2018年;人民邮电出版社出版教材; 适用专业:本书可作为有志于或者正在从事淘宝美工相关职业的人员学习和参考,也可作为高等院校电子商务相关课程的教材。 课程负责人: 二、课程简介 随着网店的迅速普及和全民化,衍生了“淘宝美工”这个针对网店页面视觉设计的新兴行业。本书从淘宝美工的角度出发,为淘宝卖家提供全面、实用、快速的店铺视觉设计与装修指导。主要包括网店美工基础、图片调色、图片修饰、店铺首页核心模块设计、详情页视觉设计、页面装修、视觉营销推广图制作等,最后针对无线端进行首页、详情页视觉的设计与装修。本书内容层层深入,并通过丰富的实例为读者全方面介绍淘宝美工在日常工作中所需的知识和技能,有效地引导读者进行淘宝店铺装修的学习。 本课程主要对淘宝美工的设计基础和方法进行详细介绍,通过学习该课程,使学生了解网店美工的基本要求,以及掌握网店的设计与制作。 三、课程教学要求

体描述。“关联程度”栏中字母表示二者关联程度。关联程度按高关联、中关联、低关联三档分别表示为“H”“M”或“L”。“课程教学要求”及“关联程度”中的空白栏表示该课程与所对应的专业毕业要求条目不相关。 四、课程教学内容

五、考核要求及成绩评定 注:此表中内容为该课程的全部考核方式及其相关信息。 六、学生学习建议 (一)学习方法建议 1. 理论配合实战训练进行学习,提高学生的实战动手能力; 2. 在条件允许的情况下,可以申请一个网店,进行深入学习; 3. 提高学生的是设计感和审美能力; (二)学生课外阅读参考资料 《网店美工:店铺装修+图片美化+页面设计+运营推广(全彩微课版)》,何晓琴编著,2018年,人民邮电出版社合作出版教材

钢琴入门:汤普森简易钢琴教程

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