1. Community and gradient analysis: Matrix approaches in macroecology The world comes in fragments

2. Biogeography Species occurrences across a fragmented landscape 1.Islands 2.Lakes 3.River bed and irrigation systems 4.Mainlands continental distributions habitat islands mountain tops and valleys fragmented landscapes scattered distributed host plants 5.Cities and anthropogenic habitats 6.Routes of species invasion 7.Experimental plots (natural, macro-, mesocosm experiments)

3. Galapagos Islands The Darwin finches

4. The Darwin finches (Sanderson, Am. Scient. 2000) A presence – absence matrix reflects the distribution of species across sites

5. The distribution of ground beetles across Mazurian lake islands In presence – absence matrices zeros denote species absence, ones denote species presences. Absences might be caused either by real absences of species or by incomplete detection.

6. Biogeographic matrices are static descriptions of colonization patterns. Colonization and extinction are permanent processes. In reality presence – absence pattern change whole the time. It makes therefore a difference if we use temporal point data to construct our matrices or a time series. Time series data contain much more entries but might be ecologically unrealistic.

7. Dispersion Extinction Time axis Time series matrices have too many entries and do not reflect real ecological patterns. They do not give information on real species interactions For a proper assessment of ecological patterns we need point data. The comparison of point and time series matrices gives information about dispersion rates.

8. The distribution of ground beetles across Mazurian lake islands Abundance matrices contain additional information. Abundance matrices might be based on point or averaged time series data.

9. Mutual interaction matrices Food web example 1.Food webs 2.Host – parasite networks 3.Plant – herbivore networks 4.Pollination networks 5.Predator – prey networks 6.Competition networks 7.Species impact networks Translation of a food web into a matrix. Ones denote direct links. Generalist predator Specialist predator Typical terrestrial food web

10. Interaction strength is expressed by probabilities or by frquencies of interaction A quantitative food web

11. Interaction matrices Pollination networks Plants Bees From Kratochwil et al. 2009 From Ollerton et al. 2003

12. How to present a presence – absence matrix? Unsorted raw dataSorted according to marginal totals Sorted to maximize species turnover Correspondence analysis Reciprocal averaging (seriation)

13. Ecological gradients Sorting of matrix columns according to ecological gradients allows for an assessment of the the importance of environmental variables. Spatial or ecological Distance

14. Species turnover Species turnover or beta diversity is a special case of species segregation where there is an ordering change in species composition across the sites. Raw matrix Ordinated presence – absence matrix Unexpected occurrences Spatial distance between species Ecological distance between sites Basic patterns

15. Nested subset patterns Random matrix ordered according to row/colum totals A nested matrix ordered according to row/colum totals Unexpected presence Unexpected absence A pattern where the species composition of species poorer assemblages form true samples of the species composition of species richer assemblages is called a nested subset pattern. Nestedness is common among biogeographical and interaction matrices.

16. Causes of nestedness

17. The mass effect Regional abundance within the metacommunity Colonization of sites with different carrying capacities (areas) Proportional colonization of sites according to metacommunity abundance and carrying capacities Passive sampling causes a nested subset pattern. The mass effect is fundamental to all neutral models in ecology. Ecologists are mainly interested in process beyond mass effects. They are interested in ecological interactions.

18. Checkerboard matrix Checkerboards are 2x2 submatrices with perfect species exclusion. Classical competiton theory predicts high numbers of checkerboards under intense competition of species. Reciprocal averaging Any perfectly segregated matrix can be reordered by reciprocal averaging to appear highly aggregated. Aggregation and segregation are in fact two sites of the same coin. Aggregated matrix Which matrix is expected under severe competition? Negative species associations

19. Compartmented matrices The existence of well defined compartments points always to the fact that the species assemblage under study is not homogeneous (a true community) but an artificial sample of species. In these cases we should deal with the compartments as separate communities. Matrix analysis is able to identify natural ecological entities. Tools are either cluster analysis of ordination. Positive species associations Boundary clumping. Species ranges are coherent.There are no gaps (embedded absences) in the sequence of occurrence.

20. Patterns in biogeographic presence – absence matrices Jared Diamond’s 1975 assembly rules 1. „If one considers all combinations that can be formed from a group of related species, only certain ones of these combinations exist in nature.” 5. „Some pairs of species never coexist, either by themselves or as part of a larger combination.” Dan Simberloff The Tallahassee mafia and his followers (particularly Steven Hubbell and other neutralists ) argued that patterns of species co-occurrence (associations) are mainly random. The competition view of nature A neutral view of nature Jared Diamond

21. Gotelli, McCabe 2002 The frequency of segregated matrices in ecological meta-communities 34 of a total of 96 meatcommunities (35%) were significantly (two sided 95% confidence limits) segregated. Standardized effect size P(  - 1.96  < X <  + 1.96  ) = 95% The distribution of Z should have a mean of zero and a standard deviation of one. Thus under a normal approximation 95% of values should range inside -1.96 < Z < +1.96

22. Equiprobable randomProportional random, nestedUnequal abundances Species turnoverProportional segregated Compartmented Equiprobably segregated Equiprobably aggregatedNested Nine types of theoretical matrices to mimic observed patterns. What pattern do we expect under intense competition.

23. Which matrix type is expected under severe competition? 1800 matrices with different structure, fill and size. Two metrics to identify species segregation and species clumping (aggregation). Competition should result in a low degree of aggregation and a higher degree of segregation.

24. Equiprobable randomProportional segregatedEquiprobably segregated The null expectation of matrix pattern under intense competition are A random matrix or A segregated matrix with pronounced differences in species abundances. Randomness might be the outcome of strong negative species interactions.

25. A meta analysis of 471 empirical presence – absence matrices. In 273 matrices the segregation metric was higher than the aggregation metric (58%). 34 matrices (7%) had negative clumping Z-scores and significantly positive segregation Z-scores. 94 matrices (20%) had negative clumping and positive segregation Z-scores. There is no prevalence of segregation (negative species interactions). These results do not corroborate the assembly rule model.

26. Only 73 empirical matrices had significant turnover. 346 matrices were nested. Only 3 empirical matrices were more nested than expected from passive sampling. Nested Anti- Nested

27. Are interaction matrices different? FW: food webs, P: pollination webs, SD: seed dispersers. Open dots: not significant at the 5% error level From Bascompte et al. 2003 Significantly nested networks Not significantly nested networks From Bastola et al. 2009 Observed degrees of nestedness in empirical mutualistic networks increase biodiversity and minimizes the degree of competition.

28. Nestedness and specialization Part of generalist species Part of specialist species Generalist species interact mainly with other generalists. Specialists interact either with generalists or with specialists. Generalists Specialists GeneralistsSpecialists