As for applying Compositional Analysis, you should take into account some drawbacks of this analysis: the test can be misleading when use or availability is "0" in many categories.

What I use to do is:

1) compute chi-sq goodness of fit --> check the independence of consumption and availability

2) compute selectivity index (Jacob's index, selection ratios...) --> rank the prey items according to preference

3) compute Bonferroni confidence intervals on the selectivity index --> assess selectivity (positive selection, opportunistic use, rejection)

4) if applicable, it's also possible to compute confidence intervals on the difference of pairs of selection ratios --> is item A significantly ranked over B?

Details on the methods in Manly et al 2002

Thank you very much, I didn't know about this index. Best, Valerie

Hi, You can find many examples and methods in book: Bryan F.J. Manly, Lyman L. McDonald, Dana L. Thomas,Trent L. McDonald and Wallace P. Erickson Resource Selection by Animals Statistical Design and Analysis for Field Studies. Best wishes, Cezary

Yes, I would also recommend the Jacob's index.

In a first step use the Chi²-test to find any "inhomogenities" in your data.

In a second step you should compute Baileys confidence interval to check whether your over- or under-use is statistically significant.

(Bailey, B. J. R. (1980): Large Sample Simultaneous Confidence Intervals for the Multinomial Probabilities Based on Transformations of the Cell Frequencies. Technometrics American Statistical Association and American Society for Quality: 22: 583-589 pp.)

Dear Valérie, I generally use the following method. First, a contingency table is built to test for diet taxa selectivity, comparing the observed number of individuals per taxon you recorded from the foragers with the expected ones, i.e. by multiplying, for each taxon, the total number of items by the proportion belonging to that taxon of the total sampled in the environment. The relative selectivity each taxon can be quantified using the standardized residual (SR = (observed-

expected) / square root (expected)). Also, to test whether forgers hunt the common

taxa at disproportionate rates compared with others, SR for the taxa can be plotted

against their frequencies in the environmental sample and a Pearson's

correlation test is performed.

You might also want to consider compositional analysis (Aebischer N, Robertson P, Kenward R (1993) Compositional Analysis of Habitat Use From Animal Radio-Tracking Data. Ecology 74: 1313-1325.) which basically compares proportions of available to used resources. It's been implemented in R in a package called adehabitat (27. Calenge C. The package “adehabitat” for the R software: A tool for the analysis of space and habitat use by animals. Ecological Modelling. 2006;197:516–519.).

Hi,

there are many useful selection indexes like the Jacob's one, but they lack any statistical significance. The easiest way to assess whether any selection happens –that's what you are asking about– with statistical significance is to carry out a Chi-square goodnes-of-fit test, testing whether diet is independent of resource availability or not. Besides, you can go further ussing the Bonferroni's confidence intervals, to assess which resource classes are selected positively, which negative, and which ones are used oportunistically. Further information is available in Manly et al. 1993, or in Neu et al. 1974.

Hi Valérie

You can also use the prey selection index (V) described by Pearre 1982 and its significance can be tested with a Chi square evaluation.

Pearre S.Jr. 1982: Estimating prey preferences by predators: uses of various indices, and a proposal of anothre index based on Chi-square. Can. J. Fish. Aquat. Sci. 39:914-923

Hope this helps

Michel

The spatial habitat overlap between species can be compare using the Jaccard’s similarity index (J) (Real & Vargas 1996, Real 1999, Jaccard 1912), expressed as:

J = C / (A + B + C)

where A is the number of sampled sites occupied only by species “number 1”, B is the number of sites occupied only by species “number 2”, and C is the number of sites occupied by both species. The Jaccard's similarity index is also defined as the size of the intersection divided by the size of the union of the sample sets. Associated probability for J is confronted with bibliography values, to determine if the value for the index differed from what would be expected at random (Real 1999).

In order to study the preference of different animal species for different land-use typologies, the frequency and composition of total land-use categories on occupied territories and on total study area must be calculate. Land-use composition differences between species are compared by means of G test.

In order to study the preference of different species for different crop types, data from total surface of the study area were estimated, and the availability of the cultivated typologies in occupied territories must be measure to calculate the Jacobs preference index D (Jacobs 1974):

D = (r – p)/(r + p – 2rp)

Where r is the proportion of a habitat in occupied territory, and p is the proportion of the same habitat in the study area. The index ranges from –1 (complete avoidance) to +1 (exclusive use). The value of 0 indicates that the habitat was used in proportion to its availability.

Furthermore the Ivelv’s electivity index, that works in a similar way, can be used to analyze the habitat preference of different animal species, considering also the availability of land-use typologies in the study area. For Ivelv’s electivity index, positive values indicate preference, negative values indicate avoidance, and 0 values indicate random use. Then values of this index range from -1.0 to +1.0. Following Ivlev’s electivity index (IV), the following formula was used:

IV= (U% - A%) /(U% + A%) (Aryal, 2009; Ivelv, 1964).

where “A” represents “availability typologies” and “U” represents “occupied typologies”.

Hope this helps!

Federico

You also can use teh Compositional Analysis described by Aebischer in 1993

The diet of a species does corresponds to the food availability in its habitat or geographic range, that's why members of the same species may differ in their feeding specializations because of the diet options available. I dont know what u mean by over-representation in diet, but the high incidence of unidgested food matter in the stomach of a tangible sample size of the species, will give u an idea . A regression line may not be ur best bet. I think some non-paramatric approach to regression like chi-square, or better still correspondence analysis should give u a head way.

See also Hansen 1980 article in ecology for ranked comparisons with tests of significance.

As for applying Compositional Analysis, you should take into account some drawbacks of this analysis: the test can be misleading when use or availability is "0" in many categories.

What I use to do is:

1) compute chi-sq goodness of fit --> check the independence of consumption and availability

2) compute selectivity index (Jacob's index, selection ratios...) --> rank the prey items according to preference

3) compute Bonferroni confidence intervals on the selectivity index --> assess selectivity (positive selection, opportunistic use, rejection)

4) if applicable, it's also possible to compute confidence intervals on the difference of pairs of selection ratios --> is item A significantly ranked over B?

Details on the methods in Manly et al 2002

Thanks, Maria, for your very helpful suggestion. Can you please upload Manly et al's paper here (or at least give the link)?

Here's Manly et al.s paper. I don't understand how one would measure availability of prey... Are we talking about intensive veg plots, small mammal trapping, or land cover work? I find the question very interesting, but I'm trying to wrap my brain around the big picture...

Hi Valerie, how are you doing, where are you know. There are many approaches to compare food supply (abundance) and use: trophic selection. The difficulty is to assess food availability (which is abundance mediated by accessibility) because a species has different abilities to access the trophic resource. There are several studies carried out in our group (that you know well, the group I mean) that have investigated this aspect, with different analytical frameworks. I hope this may help. Compositional analysis is one such approach, etc.

Hi i think u can use simple analysis such as T-test

Scott, there are many methods to measure prey availability. Most used in my field are traps (light traps, suction light traps, Malaise, pitfall...) placed in habitats of interest, or transects over these habitats with suction devices or beating vegetation.

But Scott's question, I believe, gets at a larger issue of the framework of the system of study. Simply measuring the abundance of all potential prey items may or may not be of particular value. Unless one has some idea about the relative habitat uses of the predators and putative prey, it is a crap shoot. As Raphael pointed out, there needs to be a decent idea of accessibility as well as relative abundance. For example, James Harwood and his lab have studied prey use by spiders using traps placed in the areas where the spiders capture their prey to get a much clearer idea of what the spiders use relative to what is actually available to them. Unless there is some clear idea of accessibility, it will be extremely difficult to determine whether a prey type is over- or underrepresented in the diet relative to abundance/accessibility.

Of course, John. Sorry I misinterpreted the question. Estimating availability requires some previous knowledge about the ecology of the target animal: not only in which habitats does it hunt, but also about morphology, handling and detection abilities... What is available for the researcher or for the sampling devices is not always the same as for the animal under study.

This will also determine the sampling design: e.g. for animals foraging upon volant arthropods we'l use light traps, but suction devices for gleaners.

I have experience of working on worms. These worms lay eggs (in the form of cocoons) in the dung. When the food is available in plenty numbers of eggs in one cocoon is 10 to 12. However when the situation is opposite (i.e. food is limited or in less supply) we found number of eggs as less as 2 or 3.

In good ecosystem the ration of predator to prey is 1:1000 i.e. if the weight of predator is 1 kg than the weight of prey should be 1000 kg.

You can refer a book of Eugine P Odum on Ecoogy.

Regards

Soham Pandya

Hi Valerie, I had the same issue to solve several years ago, we published our results using the Jacob's index after testing many methods, this was a simple one that just fits our question (see my PhD thesis published on this site).

All the best,

VB

Thank you for all these many answers! I am just back from holidays, I'll have a look at all your suggestions. I think the 4 points listed by Maria Napal are a very good summary of the different propositions. I'll be careful about the representativeness of "availability" regarding what I know about the ecology of my study species, thank you for raising this important point. Best wishes

I just read that Bailey's confidence intervals may be a good choice (Cherry 1996). Does anyone have an idea how it could be implemented in the R software or some example thereof?

Most literature I found deals with counts or presence/absence of some food items in the diet. For some of my analyses, I have proportion used (which I cannot change back to counts) vs proportion available (% pollen collected by bees vs % plants in the landscape). Would anyone have some example of a similar analysis?

Thank you very much.

As John pointed out, the appropriate method for measuring the prey availability depends, I believe, a great deal on your definition of "available" and the species (both predator and prey) that you're working on.

Regarding Bailey's test, I'm not sure you need this, at least if you do a weighted compositional analysis; function 'compana' in R, using log transformed values for use and available.

Thank you. The function is indeed quite straightforward and seems to be well applicable to my data. Why is log transformation necessary? Best

Manly et al. 2002 describes the rationale best, but simply I believe it weighs the land covers (or in your case, prey?) to each other, so to speak, thereby reducing the competitive exclusion. I.e., if land cover type A is present, then land cover type B, cannot also be present in the same cell.

I am quite late on this discussion, but for peaple that seeks to run tests based on the Jacob indice , as Maria proposed, you can check this Github link:

https://gist.github.com/ibartomeus/cdddca21d5dbff26a25e

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