Nicolaus Copernicus UniversityFaculty of Biology and Earth Sciences
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Monographs
(as pdf files)
 
 
Programs for ecological data analysis
(written in FORTRAN together with manuals in pdf format)
  • PatchOccupancy - a FORTRAN program for the study of species spatial distributions
  • RAD - a FORTRAN program for computing and fitting relative abundance distributions
  • NeutralCom - a FORTRAN program for generating neutral macroecological models
  • Sample - a FORTAN program for taking series of random samples from populations
  • Structure - a FORTRAN program for ecological ratio analysis
  • ComStruc - a FORTRAN program for ecological matrix analysis
  • Random - a FORTRAN program for generating random matrices
  • Matrix - a FORTRAN program for generating randomized ecological matrices
  • Nestedness - a FORTRAN program for calculating ecological matrix temperatures
  • CoOccurrence - a FORTRAN program for species Co-occurrence analysis
  • Pairs - a FORTRAN program for studying pair-wise species associations in ecological matrices



Hymenopteren in einem Kalkbuchenwald
A monograph

Parasitic Hymenoptera are one of the most species-rich taxa of our temperate habitats. Mean annual species numbers of European forests range between 400 to 600 species. The total number of Hymenopteran species in Europe exceeds probably 20000 species. Unfortunately, any detailed study of communities of parasitic Hymenoptera is confronted with the enormous difficulties connected with the taxonomy of the group. Detailed ecological work that deals with the whole guild at ecosystem level is therefore largely missing. The parasitic Hymenoptera in a beech forest on limestone is an attempt to fill this gab in our knowledge. It contains the summary of a long-term study of the ecology of parasitic Hymenoptera in a German beech forest (the G÷ttingen forest).

The Figure below shows the width of the study program.



The parasitic Hymenoptera in a beech forest on limestone is a monograph that first appeared in a printed version (Forschber. Zentr. Waldschadensf. Bd. 149, 2001: 1-249).

You can download the complete text as a pdf-file. The file has about 2.56 MB.



Die Hymenopteren einer Wiese auf Kalkgestein
A monograph

This is the second monograph dealing with the community ecology of the Hymenoptera. This time the community of 475 mainly parasitic Hymenoptera of a meadow on a hill on chalk in Northern Germany is described. Major attention receive ecological patterns that depend on species body sizes. Metabolic theory, temporal and spatial species turnover, and abundance distributions are discussed in detail. The Hymenoptera of a meadow  on limestone is an attempt to infer whether major recent ecological theories are applicable at the local scale. It is also a data source about the diversity of Hymemoptera in open temperate habitats. 

Approaches to community ecology



The Hymenoptera of a meadow on limestone is a monograph that first appeared in a printed version (Forschber. Zentr. Waldschadensf. Bd. 195, 2005: 1-203).

You can download the complete text as a pdf-file. The file has about 2.56 MB.



Assume the world is simple -
Basic applications of mathematics and statistics in the biological sciences

This text describes basic applications of mathematics and statistics in the biological sciences. It serves as a script based on the mathematics and statistics lecture held by me at our Faculty.

The script of the whole lecture is available as a pdf file ((Acrobat Reader
6 or higher, about 2 MB).



Modelling Biology Part I
Mathematics
Introductory course for students of biology biotechnology and environmental protection

This text describes basic modelling techniques and applications of mathematics in the biological sciences. It serves as a script based on the mathematics lecture held by me at our Faculty.

Both scipts (script I and script II)  of the whole lecture are available as pdf files (Acrobat Reader 6 or higher, about 2 MB).



Modelling Biology Part II
Data analysis and statistics
Introductory course for students of biology biotechnology and environmental protection

This text describes basic modelling techniques and applications of statistics in the biological sciences. It serves as a script based on the mathematics lecture held by me at our Faculty.

The
scipts( script I and script II) of the whole lecture is available as a pdf file ((Acrobat Reader 6 or higher, about 2 MB).



Statistical advices for biologists
Data analysis and statistics
 

The text describes advanced techniques of data handling and deals with matrix algebra, Monte Carlo and 'basic' multivariate techniques: the general linear model, analysis of variance, regression and path analysis, factor analysis, cluster analysis, discriminant analysis, multidimensional scaling and certain non-standard techniques of data analysis. Emphasis is laid on the discriminate power of these tests and on error types occurring during analyses. A major part of the course will also deal with the application of matrix algebra in statistics.

The script of this lecture is available as a pdf file ((Acrobat Reader
6 or higher, about 1 MB).


PatchOccupancy
a FORTRAN program for the study
of species spatial distributions

        Patch occupancy models are today one of the major tools for the study of spatial (and temporal) distributions of animal or plant species. The main idea behind this approach is simple. Take a community of S items (say species) with N replicates each (say individuals) and place them either randomly or according to a predefined model into the cells of a large grid. These cells may have different properties. You can now take samples out of this grid, study the resulting community structure based not on the whole community but on these samples and compare these structure with the one found in reality. By this way patch occupancy models are able to generate realistic null models in ecological research and with their aid a variety of ecological patterns might be studied

  Species-area relationships and related patterns (SAR)
  Endemics-area relations (EAR)
  Individuals-area relationships (IAR)
  Relative abundance distributions (RADs)
  Various estimators of community structure based on samples like estimators of species numbers, diversity
  and evenness, species overlap, detection probabilities, aggregation, and spatial patterns
  Patch occupancy dynamics and interpatch migrations
  Extinction and colonization rates
  Macroecological patterns, for instance biomass distributions
  Patterns related to habitat structure
  Patterns related to species body weights.

        These examples demonstrate the wide range of potential applications patch occupancy models have. It also shows that such models to be realistic have to incorporate a manifold of parameters that determine community and habitat properties. The program Patch Occupancy is an attempt for a general solution that allows computing a wide variety of different types of models with realistic initial settings. The program either uses data sets of real communities, theoretical communities generated by certain RAD models (Ulrich 2000d, 2002), or it generates model communities using a few basic community properties. Cell properties may be varied in such a way that habitat heterogeneity and carrying capacities can be modelled realistically. Additionally, the program computes a set of basic community statistics.

Download:

PatchOccupancy - the Manual
PatchOccupancy - the program

The manual is a pdf-file with about 440 kB, Patch Occupancy is a single program file
of 580 kB.



RAD
A FORTRAN program for computing and fitting
relative abundance distributions

        All ecological communities are characterized by a set of basic distributions that depend either on species body weights or on species abundances. Among them are the so-called relative abundance distributions (RADs, often also termed frequency distributions or dominance rank order distributions) are of major importance. RADs tell something about the distributions of densities in a community of animals or plants. There are several ways to visualize RADs.
        Because RADs often seem to follow simple geometric shapes ecologists have long sought to understand what causes certain RAD shapes and how to model them. This let to a large number of different theoretical models, a manifold of (often contradicting) attempts to explain observed patterns and to a more or less confusing discussion about the applicability of some models. Overviews about models, theoretical foundations and applications can be found in Preston (1962), May (1975), Sugihara (1980), Magurran (1988), Tokeshi (1990, 1993, 1996), and Ulrich (2001a, b, c, 2002)
        One of the causes for the poor state of art is surely, that it proved to be extremely difficult to fit most of the models (especially the more important ones) to given data sets. Older work often contains fits by eye and only a few papers deal explicitly with the problem of data fitting (Wilson 1991, Tokeshi 1993, Bersier and Sugihara, 1997, Ulrich 2001b). However, the problem of fitting especially the newer and more realistic stochastic models remains largely unsolved.
        RAD is an attempt to solve the problems around data fitting. The program computes and fits nearly all models proposed up to now. Additionally it returns a number of additional statistics for instance diversity and evenness indices, goodness of fit measures, and estimates of variances and confidence limits. The program also allows computing truncated distributions and takes automatically predefined samples out of the computed model distributions.

Download:

RAD - the Manual
RAD - the program

The manual is a pdf-file with about 470 kB, RAD is a single program file
of about 620 kB.



NeutralCom
A FORTRAN program for generating neutral macroecological models

        Recently, neutral macroecological models have come into the focus of ecological interest. Although the application of neutral models has already a long tradition in genetics and evolutionary theory (Kimura 1985, Kimura et al. 1994) and were proposed by Caswell in 1976 for explaining basic patterns of community structure in ecology they received only few attention of the ecologists of that days. This little interest is surely explained by the fact that the dominating paradigm of that days was that biotic interactions especially competition (even as a ghost of competition past) or predation (in the widest sense) shape local communities. Additionally, the focus of interest was the ecosystem with its local communities or guilds. This view changed with the rise of Macroecology, the ecological branch that deals with patterns above local scales, but also with the rising number of studies that denied the importance of competition and trophic relations.
        This paradigm change resulted at last in a renewed interest in neutral models. Especially the models proposed by Stephen Hubbell (1997, 2001) and Graham Bell (2000, 2001) inspired ecologists and caused intensive work in the field (Whitfield 2002).
        What are neutral ecological models? Shortly speaking these are models that treat species not as biological entities that interact but treat them as lottery balls without biotic interactions. Ecological, especially macroecological, patterns are then generated from pure chance processes. Appealing are these models for ecologists because Hubbell and Bell were able to show that many ecological patterns that were earlier explained by biotic interactions can be generated from neutral models with a very limited number of parameters. The most parsimonious versions require only birth and death rates and assume local saturation of individuals irrespective of species. Mathematically speaking, the neutral models of Bell and Hubbell treat local communities as zero sum multinomials driven by birth and death processes and allow for local immigration and emigration to held the local individual number constant.
        The models of Hubbell and Bell have a series of shortcomings. They do not deal with body weight and community biomass related ecological patterns. These include especially density-body weight distributions (Gaston 1993, Currie and Fritz 1993, Cyr et al. 1997), biomass-species diversity relations (Ulrich 2003), range size�body weight relations (Ziv 2000), and species diversity-productivity relations (Gaston 2000), and the study of succession.
        Additionally, they are static models insofar as they assume total individual numbers (at the local and the metacommunity scale) being fixed. At last, they do not include heterogeneity of habitat structures or resource distribution.
        The present program extends the models of Hubbell and Bell to include species body weights and habitat heterogeneity. In doing so it uses the patch occupancy module of PatchOccupancy, a program designed by me do model classes of patch occupancy models (Ulrich 2002). This program places individuals of species into the cells of a grid by a three step process. In a first step a species-body weight distribution is generated, the second step assigns species densities, and the third step places the individuals into the cells, where the cell properties can be varied to simulate a wide variety of heterogeneity patterns.
        Then the presents program models death, birth, immigration, emigration, and speciation patterns according to the models of Bell and Hubbell. At last, NeutralCom returns again to the PatchOccupancy kernel and samples the resulting grid according to the wide possibilities this program offers.

Download:

NeutralCom - the Manual
NeutralCom - the program

The manual is a pdf-file with about 440 kB, NeutralCom is a single program file
of about 650 kB.



Sample
a FORTRAN program for taking series of random samples from populations

        Sample is a small program that takes series of random samples from a given population. In ecological research this is sometimes necessary for constructing null models or for jackknifing and bootstrapping.

        The idea behind Sample is simple. You have a data set or a whole matrix with several data sets. The elements of this data sets (the items) occur at different proportions (probabilities, numbers, frequencies). The problem is to take random samples from these data sets that match the different occurrences of elements. For instance, if you have a community of 5 species with 100, 50, 30, 20, and 10 individuals and take 20 individuals at random you expect that your sample will have a similar frequency distribution than the population. Sample takes such random samples by picking single individuals from the populations until a predefined sample size is reached. Sample is able to process whole data matrix during one program run and computes a series of useful statistics.

Download:

Sample- the Manual
Sample - the program

The manual is a pdf-file with about 140 kB, Sample is a single program file
of about 420 kB.



Structure
a FORTRAN program for ecological ratio analysis

        Structure is a small program that computes basic statistics of data distributions like body size ratios, abundance ratios, internal variances or kernel densities. The program was especially designed for analyzing body size distributions. The present version contains six modules
  Basic statistics
  Variance test (log and linear scale)
  Ratio test (log and linear scale)
  Frequencies
  Pairwise regression
  Kernel density estimate

Download:

Structure- the Manual
Structure - the program

The manual is a pdf-file with about 290 kB, Structure is a single program file
of about 470 kB.


ComStruc
a FORTRAN program for ecological pattern analysis

        ComStruc is a small program that computes basic patterns of community structure in ecological matrices like species x site or site x variable matrices. In ecological research this is sometimes necessary for analysing species co-occurrences, or for the computation of rarefied species numbers.

        The recent standard program for analysing community structure and species co-occurrence patterns is EcoSim (Gotelli and Entsminger 2002). However, EcoSim lacks some important features and ComStruc is intended as a supplementary program. The actual version of ComStruc contains four modules: rarefaction, species overlap, community similarity, and a fitting module for relative abundance distributions.

Download:

Comstruc- the Manual
Comstruc - the program

The manual is a pdf-file with about 150 kB, ComStruc is a single program file
of about 430 kB.



Random
a FORTRAN program for generating random matrices

Random is a small program that generates ecological randomized presence-absence or abundance matrices to be used in EcoSim (Gotelli and Entsminger 2006) and in the Nestedness calculator (Atmar and Patterson 1995).

The idea of Random is simple. You have an input matrix. This matrix might be a presence absence or an abundance matrix. This matrix is randomized in such a way that the output is a file that conforms to the EcoSim or to the Nestedness Calculator standards

Download:

Random- the Manual
Random - the program

The manual is a pdf-file with about 220 kB , Random is a single program file
of about 650 kB.


Matrix
a FORTRAN program for generating randomized ecological matrices

Matrix is a program that generates ecological randomized abundance matrices to be used in EcoSim (Gotelli and Entsminger 2006) and Nestedness.

Matrix generates these matrices either according to a predefined sampling scheme or according to build in species abundance and randomization algorithms.
The basic sampling unit of Matrix is the individuals. The program samples individuals from a species pool until a predefined number of species or individuals per site is reached. The output matrices conform to the EcoSim and to the Nestedness standards. A summary output file contains basic information about the matrices.

Download:

Matrix- the Manual
Matrix - the program

The manual is a pdf-file with about 150 kB, matrix is a single program file
of about 440 kB.


Nestedness
a FORTRAN progr
am for
calculating ecological matrix temperatures

A nested structure is a basic feature of many communities spread over a series of islands or mainland sites. Nestedness measures whether the faunal composition of different study sites form perfect subsamples from a larger common species pool (a nested pattern) or whether local peculiarities occur. These peculiarities might affect several ecological processes like extinction probabilities, species turnover, competition, or reintroduction success in bioconservation. The recent standard program for computing the degree of nestedness is the Nestedness temperature calculator of Atmar and Patterson. However, this program has some well known deficiencies. It particularly uses the Random) null model that poorly accounts for effects of passive sampling.

The program Nestedness tries to overcome some of these deficiencies. It contains six different null model algorithm and allows for a full batch run. Apart from the temperature mesure it contains seven other measures of nestedness. It further allows for a choice which cells to include into the calculation. Significance of nestedness is assessed from null model standard deviations and 95% confidence limits of the null model. Three output files contain the packed matrices, the degree of unexpectedness for each matrix cell and the idiosyncratic site and species temperatures.

 Download:

Nestedness- the Manual
Nestedness - the program

The manual is a pdf-file with about 150 kB, Nestedness is a single program file
of about 460 kB.


CoOccurrence
a FORTRAN progr
am for species co-occurrence analysis

The study of species co-occurrences has a long tradition in ecology (Weiher and Keddy 1999). Particularly the long lasting and still ongoing discussion around community assembly rules (Diamond 1975, Diamond and Gilpin 1982, Gilpin and Diamond 1982, Connor and Simberloff 1979, 1983, 1984, Gotelli and McCabe, 2002, Ulrich 2004) has inspired the development of statistical tools to infer non random patterns in community assembly (Gotelli and Graves 1996, Gotelli 2000, 2001). Community assembly is often studied in terms of nestedness (Atmar and Patterson 1986, Wright et al. 1998, Ulrich and Gotelli 2007) and non-random patterns of species co-occurrences (Diamond 1975, Gotelli 2000, 2001) and the respective standard software is widely used: The Nestedness Temperature Calculator (Atmar and Patterson 1995), EcoSim (Gotelli and Entsminger 2002, and Nestedness (Ulrich 2006).

The present program CoOccurrence implements two nestedness and three common co-occurrence metrics :The discrepancy metric of Brualdi and Sanderson (1999), NODF (Almeida-Neto et al. (2008), the species combinations score (Pielou and Pielou 1968), the C-score (Stone and Roberts 1990), and the checkerboard score (Gotelli 2000). While most of these metrics are also implemented in Nestedness and EcoSim, the present program is particularly designed for the study of multiple matrices for instance in null model analysis, for the analysis of the statistical behaviour of certain metrics, and in studies of neutral models.

 Download:

CoOccurrence- the Manual
CoOccurrence - the program

The manual is a pdf-file with about 150 kB,
Cooc is a single program file of about 460 kB.

 


Pairs
a FORTRAN progr
am for studying pair-ise species associations in ecological matrices

Community assembly is often studied in terms of nestedness (Patterson and Atmar 1986, Wright et al. 1998, Ulrich and Gotelli 2007a) and non-random patterns of species co-occurrences (Diamond 1975, Gotelli 2000, 2001 Ulrich and Gotelli 2007b) and the respective standard software is widely used: The Nestedness Temperature Calculator (Atmar and Patterson 1995), EcoSim (Gotelli and Entsminger 2002, and Nestedness (Ulrich 2006).The present program Pairs extends these approaches and implements beside standard nestedness and co-occurrence metrics a new metric to study pairwise species associations: The software implements: 
The discrepancy metric of Brualdi and Sanderson (1999), 

the species combinations score (Pielou and Pielou 1968), 

the C-score (Stone and Roberts 1990),

the checkerboard score (Gotelli 2000),

the Soerensen metric, 

the togetherness score (Stone and Roberts 1992),

the species absences score (Stone and Roberts 1992),

the variance test (Schluter 1984),

a pairwise correlation test.

Pairs not only studies matrix wide patterns. It uses a Bayesian approach to detect non-random associations of pairs of species. The number of species pairs of a matrix is S(S-1/2. Hence even for medium sized matrices many ‘significantly non-random’ species pairs are expected at the 1% or 5% error level. Pairs chooses only those scores for further analysis where the number of observed instances is either larger than the mean expectation (Bayes M criterion) or larger than the upper 5% or 1% confidence limit (Bayes CL criterion). 

 Download:

Pairs- the Manual
Pairs - the program

The manual is a pdf-file with about 150 kB,
Cooc is a single program file of about 460 kB.

 

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Department of Animal Ecology, Nicolaus Copernicus University of Toru˝ Address: Gagarina 9, 87-100 Toru˝
Phone: 0048-56-6114-469, Fax: 0048-56-6114-443, E-mail: ulrichw@uni.torun.pl