Perhaps you can use the Von-Foester equation and its modifications in your case.

Depending on your research design it would great if you could compare forest edge v.s. forest nterior; different succesional chronosequences; or natural v.s. anthropogenic habitats. This example could be useful:

https://www.researchgate.net/publication/230683323_Population_Dynamics_of_the_Andean_Lizard_Anolis_heterodermus_Fast-slow_Demographic_Strategies_in_Fragmented_Scrubland_Landscapes

Article Population Dynamics of the Andean Lizard Anolis heterodermus...

Hi Nina - can you not derive population estimates from each habitat using your CMR-data each month? This will provide CIs to illustrate the variability over time. I think mark-recapture is a far better way to look at this than relying on an index like the number caught per trap effort per month, as such indices ignore detectability entirely (and there is likely to be a range of factors that affect how trappable your small mammals are that vary throughout the year). I think open mark-recapture models would be the best way to go.

I hope this helps.

Matt

Hi Nina,

depending on your sampling design, I hope for you that you think about the Robust Design sampling.

It is a useful sampling design, especially for small mamals like rodent. There are several models depending on whether your population is closed or open. You can do your analyses with the MARK software or directly in R with the Rmark package.

Do not hesitate to ask me if you need more informations.

A small look at "Analysis and Management of animal population" by Williams, Nichols and Conroy 2002 will also help you

Cheers,

Guillaume

Yes, I agree use the robust design. Both MARK and Rmark are freeware.

And here is the book on how to use MARK,

http://www.phidot.org/software/mark/docs/book/

chepter 15th is on robust design.

Good luck!:)

Hi, Nina. You can just use the GLM, considering the number as DV has a binomial or Poisson distr., and years, month and habitat types as predictors (IVs). (Do you read in russian? :-) )

Таблица 4. Модели изменчивости обилия мелких млекопитающих в окрестностях Карабашского медеплавильного комбината (Челябинская обл.); октябрь, 2008 г. GLM: биномиальный отклик. MinCAIC =943.7

Предикторы K -2LL ΔCAIC w

Зона + ЗонаНаправление 5 900.11 0.00 0.638

Зона 3 918.93 1.38 0.319

Зона + Направление + ЗонаНаправление 6 897.12 5.73 0.036

Зона + Направление 4 917.99 9.16 0.007

Участок =0,9 10 885.67 29.15 3E-07

ЗонаНаправление 3 956.63 39.08 2E-09

Направление + ЗонаНаправление 4 955.4 46.57 5E-11

Константа# 1 988.05 53.07 2E-12

Направление 2 987.97 61.70 3E-14

Линия =0,74 30 826.17 144.03 3E-32

Примечание: w(Зона)=1, w(ЗонаНаправление)=0.674, w(Направление)=0.043.

Ops... :-( One moment pls.

Yes!

Hi Nina,

Your question is somewhat vague and a serious, clarifying answer requires more information like:

What is the objective of your study?

Quality of your data?

Do you have data on age or stage structure? proportions of males vs females, sexually mature vs imatures, etc? If you do comparing such structures could be interesting. A tip, read about evenness and Gini coeficients

Have you got data enabling to estimate vital rates for the full life cycle? Comparing asymptotic population growth rates, their sensitivities and elasticities would be interesting.

If, not, have you got data enabling estimating the vital rates related to the fate of the individuals alive (survival related rates)? In such case you can use Markov chain analysis to estimate (and compare) life trajectory related events as age of first reproduction, life espectancy, etc. Again, sensitivities and elasticities might also be interesting.

There are several interesting papers refering population performance not so much depending on the habitat but on its central vs peripheric location. As well as temporal floctuations not associated to season but to population's intrinsic properties.

Good luck

Along with mean density per environment, why don't you try comparing the coefficient of variation of density across time among environments? I guess you should do this for each species separately. That way, instead of differences in abundance you test differences in degree of population fluctuation - I'm assuming you have proper replication within forest types...

Thanks a lot for all your answers!

@ Vasco Vieira: My objective lies in evaluating the role of small mammal populations as hosts for ticks in different forest habitats in Germany. Therefore, I need some kind of tool to assess small population fluctuations in time and space. Data is taken monthly (from March to October) with equal capture effort. I have records on species, sex, weight and age class. As I am collecting CMR-data I do have information about the fate in case of survival and recapture of a given individual.

@ Matt Hayward & Guillaume Souchay: Thanks a lot for your input. I already had a look at open population models recently and was a bit confused which one to chose...So, in my case you would recommend me to rather use robust models than e.g. CJS or Manly-Parr? As I have no experience with this kind of analysis so far, it is a bit difficult to decide which one fits my data.

My focus is the detection of population trends within and between years and of course within the different forests in order to in turn find some relationship to tick population dynamics in these area(s).

A few more questions: Can I compare cyclic and non-cyclic populations in this way? I guess I should separate small mammal species, right (as there are voles, mice and insectivores...)

Hi Nina,

It seems from the answer you gave to Matt and Guillaume that you are interested in looking at what is happening in the tick populations over time and the interaction between their dynamics and those of their hosts - the various small mammals. You might find the books by Royama (1996) Analytical Population Dynamics and Turchin (2003) Complex Population Dynamics of some value. One issue I see is that unless you have sufficiently long time series of observations you will find it difficult to separate intrinsic population effects,such as density dependence, from stochastic effects arising from environmental noise. If I was in your position I would try to formulate a model for the interaction between the parasite and host populations in either a differential or difference equation framework and then think about how your observations can be used to inform you about the parameters of the model.

Yours,

N

Hi Nina,

First, you should sum up your protocol to choose what kind of model to use. Is your study over several years, how many capture occasions per year/month/ ...

Depending on your sampling design, you will able to use one or the other kind of analysis, and to assess different questions.

Second, how are you going to assess your parasite population trend ? Do you have information about parasite load at each capture? Independent data from other studies ?

I agree with Neil about try to formulate the relationship between host and parasites, and to see if you can estimate the parameter of the model.

Here are two examples of relationship between host and parasites population trends. Cattadori, I. M., D. T. Haydon, and P. J. Hudson. 2005. Parasites and climate synchronize red grouse populations. Nature 433:737-741.

Redpath, S. M., F. Mougeot, F. M. Leckie, D. A. Elston, and P. J. Hudson. 2006. Testing the role of parasites in driving the cyclic population dynamics of a gamebird. Ecology Letters 9:410-418.

Cheers,

Guillaume

As far as I understand, I think that the robust design models do not fit my capture protocol. Sampling - so far - took place from May until October last year and March until October this year (and hopefully will continue March until October next year). takes place on a monthly basis for two consecutive nights. They are placed in the evening, and checked the next morning and evening plus the morning the day after.

@Guillaume: I think of it the "other way round": How does the presence/dominance/species composition/density...of small mammals influence the tick population in a given habitat over time?

@ Neil: Yes, you are absolutely right about my intention. Could you give me some advice on how I can formulate the relationship between host and parasite populations?

All the best, Nina

Hi Nina,

just saw your question. Did you make some progress regarding these problems? Can you provide more details about number of traps per night/site, trapping design (square, line, etc.) , number of caught animals? I am afraid with only two nights you can not do much more then Chapman Estimate with Variance (http://en.wikipedia.org/wiki/Mark_and_recapture) and Minimum Number Alive.

You may find some information regarding this at: https://www.researchgate.net/publication/232701402_Habitatansprche_Strukturbindung_und_Raumnutzung_von_Vgeln_und_Sugetieren_in_forstwirtschaftlich_genutzten_und_ungenutzten_Kiefern-und_Buchenwldern?ev=prf_pub

and in my very outdated paper at: https://www.researchgate.net/publication/233859494_Ein_Blick_in_die_Zukunft_Mark-Recapture_Experimente_zur_Schtzung_der_Abundanz_und_berlebensraten_in_Kleinsugerpopulationen?ev=prf_pub.

For open population models POPAN (http://www.cs.umanitoba.ca/~popan/), although outdated, might be a good choice. A good start anyway is to have a look on the pages from Kenneth Burnham, Kenneth H. Pollock (http://www4.ncsu.edu/~pollock/st506.html; http://www4.ncsu.edu/~pollock/pdfs/Pollock%20et%20al%20Mono1990.pdf) and Gary C. White. The primer about closed populations is a must for each student starting in this field. You can find it at: https://www.researchgate.net/publication/243763546_Capture-recapture_and_removal_methods_for_sampling_closed_populations.

However, guess the main problem might be your sampling approach making it difficult to apply more sophisticated models. Therefore, try to keep it simple first.

All the best,

Reinhard

Article Habitatansprüche, Strukturbindung und Raumnutzung von Vögeln...

Article Ein Blick in die Zukunft: Mark-Recapture Experimente zur Sch...

Article Capture—Recapture and Removal Methods for Sampling Dosed Populations

You can try simple logit regression: logit(y1/y0)~all your predictors (year, season, place ... etc) ;-)

Dear Reinhard,

thank you for your detailed answer! So far, I have progressed in terms of heaving read several publications, book chapters etc.

At the moment I mainly use # individuals per hectare or # individuals per trap night (corrected for non-target captures or empty traps) but I am not relly satisfied and still looking for a more precise way to estimate abundance.

A few more details about the setting:

Trapping is done monthly at four sites (May-Oct 2012, March-Oct 2013, March-now 2014). Each site has three square grids with 5x5 traps each, so a total number of 75 traps is checked three times per session. Animals are marked individually before release. The number of trapped animals varies greatly between sites and years.

Where would you recommend me to start?

Do you think it was possible to include non-target captures, possible dead-recoveries and assumingly unequal trappability over time?

All the best,

Nina

Dear Nina,

1. the main problem is your sampling approach. You have only a very few nights to make a good estimate. Unfortunately most people don't read the relevant literature before a study :(. Normally you should model your data and make a guess what you can get and what you would need for the results you want. OK, it doesn't make sense to discuss this, you did your fieldwork already. So, my recommendation is: don't expect too much, use a simple method / model for the population estimate.

2. because the number of trapped individuals varies grately you will have probably problems to make an estimate for every month, at least with the more sophisticated models. Chapman Estimate should still work. The primer I recommended is really good to learn about all the problems related to CMR in closed populations. But you should know, your sampled grid is (compared to your habitat, if you have not habitat islands) probably rather an open population.- so you will violate the assumptions anyway. However, if you have used same approach everywhere you can compare at least on the same basis but you can not make comparisons of abundance, density in absolute numbers and with results of other people. Or at least you should be aware of the problems caused by the violation of the assumptions.

3. The differences you found in numbers are normal for German forests. You can get only very good results with: a) a very high effort in terms of trapping / sessions (5 and more nights or trapping actions), b) high numbers of traps ( and repetitions per trapping station -> e.g. approach from Sykora 4 traps per station (to avoid trap blocking by the first catch) / 4 x 4 (or more) stations) A good choice for traps is also the "Finnish Redbacked Vole trap" one can catch more then one animal with at the same time. Such an effort is very (too) high for only one person.

4. What do you mean with non-targeted captures? I think if you focus on small mammals you are interested in all of those species, or? I guess with life traps you won't have caught birds!? Dead recoveries on your site you can use, e.g. there are options to correct for in MARK. Regarding the other assumptions like heterogeneity, unequal trapping etc. you need good data and more then only two or three trap nights per session, and you shouldn't mix the species.

5. The different species (probably Myodes glareolus, Apodemus flavicollis, Apodemus agrarius, Microtus agrestis) have different cycles. If you work only for two or three years it is to short to get good time series. However, at least you can compare the population size at same time to make an inference about number of animals, habitat and ticks.

6. I will sent you the small mammal part of our report from the HASTRA project (http://www.gnl-kratzeburg.de/projects/hastra/) where the paper I mentioned above is based on (https://www.researchgate.net/publication/232701402_Habitatansprche_Strukturbindung_und_Raumnutzung_von_Vgeln_und_Sugetieren_in_forstwirtschaftlich_genutzten_und_ungenutzten_Kiefern-und_Buchenwldern?ev=prf_pub). There we made simiar analyses and I described the methods, results and also problems ;) more in detail.

7. So my recommendation is: use the relevant literature from small mammals and forestry in Germany to get ideas about habitat related densities, calculate your densities with simple but robust methods (Chapman, MNAA; the so called "robust" approach you can use only for a larger period of e.g. 3 months with your data), use regression to relate the densities to your environmental variables (like recommended by Ivan above) and to the ticks. And befor I forget, do simple descriptive statistics first to get an idea about the distributions in your data.

Best wishes,

Reinhard

Article Habitatansprüche, Strukturbindung und Raumnutzung von Vögeln...

Dear Reinhard, 

1. My sampling approach is based on previous studies focusing on tick burdens of small mammal hosts: https://www.researchgate.net/publication/10842066_Spatiotemporal_variation_in_a_Lyme_disease_host_and_vector_black-legged_ticks_on_white-footed_mice?ev=prf_pub

But as trapping success over time varied a lot within and between sites I started looking for alternatives.

2. Would you recommend me to rather use a closed population model to keep it simple and violate the assumptions of closeness or should I rather use an open population model like Jolly-Seber, Manly-Parr or similar because of the dynamic behaviour of small mammal populations? My central aim is to compare the small mammal population dynamics between sites and years with respect to tick burden, pathogen prevalence etc. So I rather claim to assess relative abundances not absolute numbers - but of course I still wanted to do it "the right way", not just follow the methodical approach  someone else had used before without questioning if the method really fitted my data. 

3. Yes, this is why I decided to only use one trap per trapping station. I've started sampling after a mast year resulting in high small mammal abundance followed by a strong decline the year after in three out of four sites. Could you think of some habitat features that might buffer this effect?

4. Yes, of course I am interested in all small mammal species, but in fact we also captured toads and a songbird (once), but most often there are slugs that enter the traps and release the closing mechanism of the trap thereby altering the number of available traps.

5. Yes, I agree.

6. Thank you.

Best wishes and thank you for all of your suggestions.

Nina

Article Spatiotemporal Variation in a Lyme Disease Host and Vector: ...

Dear Nina,

sorry for my late answer. 

to 1.

I just checked the sampling approach from Goodwin et al. 2001 you mentioned above. They did it very well in regard to their aim: 1. two plots (repetitions) per site, 2 traps per station (to trap additional animals even if one trap has already caught an animal, necessary if population density is high), 3. more than 100 stations (higher probability to catch enough animals even if the population density is low), 4. simple statistics (Minimum Number Alive - MNA,  appropriate to their two nights approach).

Of course with this sampling approach (1.-3.) and 5 nights they would have the chance to get really good estimates with more sophisticated models. However, as you can see from their first figure, even with this high effort they had sites and seasons with very low or even zero numbers. However, I am wondering about a mismatch between their description of methods (trapping in April/May and November) and the figure showing July and January?!

to 2.

If you have only two consecutive nights you can use a closed population model because the probability of "demographic" emigration/immigration (birth, dead) is rather low. However, because your grid is not to big in terms of trapping stations (less then a quarter compared to the approach from Goodwin) you have a higher probability of immigration and emigration. That's a disadvantage.

I would suggest following, use MNA first, additionally use Chapman Estimator if you have only two nights and if you have more nights you can run closed models vs. open ones - in he case (season) you have higher numbers on all plots).

That should be not to difficult because if you have prepared the data well it should be easy to provide the capture histories. With these histories you should be able to run more or less all classes of models, e.g. in MARK.

I prefer to use a relational data bases for such aims (e.g. like PARADOX, MS Access etc.). If it is designed well you are very flexible with all types of data structures needed. You can create it with the queries/sql, partly in combination with a spread sheet in the second step, or use R (in combination with RMARK).

Today it isn't a big deal anymore to make these calculations with a PC and the software mentioned already. You can compare the results and discuss them in a broad manner. You can also chose between a conservative scenario and a rather optimistic one.

So you will have a lot of oportunities to relate the population densities to your tick data. Maybe some of your parmeters will correlate very well, others not. I am curious about the results.

If you are very limited in time (like most PhDs) use MNA first to get results, and try to do the more sophisticated/complicated things in the second step. If you get good results already with MNA then you should focus on your mice - tick - problem first. I guess it will take also some time to chose and set up the regression models for the mice - tick - problem. The more sophisticated analyses could be reveal some more details in the second step. But with this approach you will not get lost in too much unnecessary (related to your problem) stuff. It's another thing if you are interested in the small mammals ecology first.

3. here I can't give a really good answer without any detailed knowledge about the habitat, landscape. Please keep in mind that each population has their own history, there must be no autocorrelation if your sites are really distinct.

4. Because you have only one trap per station it could be really important to relate the numbers of bycatch / closed traps to your catches of small mammals. By the way, what kind of baits did you use?

All the best and good luck,

Reinhard