As a reply to Tom McMahon wrote who wrote: >How does one calculate an error term for multiple population estimates? As >an example, you want to test the hypothesis that fish abundance in two >different habitat types was statistically different.
I thought I would post the summary of the replies to my request for information on sampling fish populations in different waters. I received a number of replies, all of which were addressed to the entire fish ecol notice board and hence I did not post a summary then. However,it may be beneficial to post a summary now to further stimulate discussion on population assessment and detection of significant differences.
Phillip Smith
"I am in my third year of my PhD assessing the impact that zander exert on prey fish in British canals. As part of my investigation I have assessed the fish populations in 5 canals. These canals are narrow (width 914m), shallow (max depth 1.6m) and have been assessed by micromesh (3.0 and 5.0 mm) seine netting. Individual sites (35 m long) have been blocked off with stop nets and the fish present estimated by multiple removal. I have used at least 2 removals on each case and sometimes upto 7. I have also carried out some trials using known populations (in the form of a known number of marked fish introduced into the site prior to depletion).
I have now come to analyse my data and would like to discuss two things:
1. Which of the population estimators are the most accurate (eg Seber and LeCren, Zippin or Carle & Strub). In an attempt to satisfy some of the assumptions of this method I have grouped my catches into species (the dominant species are roach (Rutilus rutilus), bream (Abramis brama), perch (Perca fluviatilis)and gudgeon (Gobio gobio)) and also into three size categories approximately corresponding to different ages (0+, 1+ and 2+ or older). Each species group has its own catchability, high (p=>0.5)for roach & bream and generally low (p=<0.3) for perch and gudgeon. Also,the total number of species/size group caught at each sites varies from >3000 to 0.
So, which estimator is most useful and how does catchability and number of individuals caught affect the accuracy and variance of the population estimate ?
2. Estimates for the abundance of fish in a section of canal depend on within and between site variance. I would like to statistically compare the abundance of each species/size group for each of my 5 canals using analysis of variance and identify any differences by calculation of the least significant difference. Is this a good idea and are there any examples of this in the literature ?
I would like to thank you for reading this and a debate on the use of removal methods to estimate population size would be most interesting."
REPLIES
Phillip: Gary White and collegues at Colorado State University have freeware available that is excellent for estimating population abundance from removal data. You can learn about program CAPTURE, and obtain the software, from http://www.cnr.colostate.edu/~gwhite/software.html
The removal estimator used in program CAPTURE relaxes the assumption of equal capture probability on all occassions, something that is not true with the Zippin, etc. estimators. Goodness of fit tests also help determine if your data are adequately modeled by CAPTURE's estimator. CAPTURE also provides models suitable for mark/recapture studies that do not involve removal.
Have fun.
Charles Gowan Dept. of Biology RandolphMacon College Ashland, VA 23005 8047527293 FAX 8047524724 email: [log in to unmask]
Ram Myers (Fisheries and Oceans, NFLD, Canada) and I have done some fundamental work on population estimation by depletion methods. We have reviewed existing methods and compared a new method we have developped which uses information from all catch sequences simultaneously to estimate the mean and variance of the catchability coefficient. We tested our model with published data of difficult to catch fishes (e.g. darters) in small northern streams as well as tropical fishes in the Amazon. Essentially, this method does better than most at reducing error variance but is still biased (as are all methods unfortunately because of the nature of the data). If you are interested, I can send you some more information on comparison of these methods.
As far as CAPTURE is concerned, I think it is the best available program out there. It estimates probability of capture for each catch event, thereby reducing the error one would get from a single estimate, until the added variance explained in the sequence no longer significantly changes the goodness of fit of the model. This works fine if the probabilities of capture are fairly high and the population size fairly large, but may be more difficult to use in other cases. It also virtually eliminates the risk of estimator failure, but only at a practical level rather than a theoretical modelling level.
> 2. Estimates for the abundance of fish in a section of canal depend on > within and between site variance. I would like to statistically compare the > abundance of each species/size group for each of my 5 canals using analysis > of variance and identify any differences by calculation of the least > significant difference. Is this a good idea and are there any examples of > this in the literature ?
Between site variance is not necessarily error. It may be due to differences in habitat and speciesspecific habitat differences which may be undetectable with the data in hand. You have to be careful how you treat this variance. Grouping sites that are similar and looking at variation in abudance, if you have a time series, would be a good approach. Andre Talbot, PhD Technical Advisor CARICOM Fisheries Resource and Management Program (CFRAMP) Shrimp and Groundfish RAU PO Box 3150, Carenage Post Office Carenage, Trinidad, W.I. Ph:(809) 6344528/4530; Fax: 6344549 Home: (809) 6288375; Home Fax: 6288495
Phil Smith wrote (in part): > 2. Estimates for the abundance of fish in a section of canal depend on > within and between site variance. I would like to statistically compare the > abundance of each species/size group for each of my 5 canals using analysis > of variance and identify any differences by calculation of the least > significant difference. Is this a good idea and are there any examples of > this in the literature ?
Andre Talbot replied (in part): Between site variance is not necessarily error. It may be due to differences in habitat and speciesspecific habitat differences which may be undetectable with the data in hand. You have to be careful how you treat this variance. Grouping sites that are similar and looking at variation in abudance, if you have a time series, would be a good approach.
Dr. Talbot makes a good suggestion about grouping similar sites, but this grouping (stratification) must be done on the basis of an "auxillary variable" like habitattype, *not* on the basis of the population estimates from the sites. Your goal is to reduce amongsite variation, but you cannot do so simply by grouping sites with similar population estimates! Ideally, the stratification would have been done *before* data were collected, then a random sample of sites within each strata measured. Also, since you are estimating populations within sites (not making complete counts), you face a "twostage" sampling situation (you have among and within site variance, as you said). Cochran (1977. Sampling Techniques. 3rd ed. J. Wiley & Sons, NY) provides formulas for estimating parameters (like population abundance) and their variances appropriate for these situations. Bohlin et al. (1989. Electorfishing theory and practice with special emphasis on salmonids. Hydrobiologia 173:943) provides an excellent discussion of the topic with regards to stream fish (see also earlier work by Bohlin cited in the 1989 paper). Hankin and Reeves (1988. Estimating total fish abudnance and total habitat area in small streams based on visual estimation methods. Can. J. Fish. Aquat. Sci. 45: 834844) is also good, as is Hankin (1984. Multistage sampling designs in fisheries research: applications in small streams. Can. J. Fish. Aquat. Sci. 41:15751591).
Or, to really simplify things, you can just use each population estimate in a oneway ANOVA with "canal" as the variable of interest. The problem is that this test will have much less statistical power than those previously described because you will not be reducing variation with stratification. You will also not be partitioning your variance into within site and among site components. However, if the ANOVA indicates a significant difference among canals, then all the extra trouble of stratification and partitioning variance is not necessary to meet your goals.
Another alternative is to simply quit school and live on the streets. I remember that was looking quite attractive to me about the 3rd year into a Ph.D.....
Good luck,
Charles Gowan Dept. of Biology RandolphMacon College Ashland, VA 23005 8047527293 FAX 8047524724 email: [log in to unmask]
In message <[log in to unmask]> Academic forum on fisheries ecology and related topics > ><< I would like to statistically compare the abundance of each species/size > >group for each of my 5 canals using analysis of variance >> > > > >By this do you mean that you would like to compare the abundance of each > >species/size group among the canals, or do you want to compare abundances > >among species/size groups within each canal? > > > I would like to know if the abundance of each species/size group differed > between canals. The reason is that 3 of my canals have an alien piscivore > present and 2 do not and I want to identify any statistically significant > differences in fish community within my 5 canals. ie is there less fish > were the piscivore is present. I did not want to assess if there were any > significant differences in the abundance of each species/size group within > each canal. > > Phil Phil: I delayed jumping into this fray but will make the following observations. First, Tom Kwak ([log in to unmask]) developed some software call POP/PRO that runs on PCs or Macs and can be used to estimate populations via several methods (depletion type and markrecapture). It was described in Ecology of Freshwater Fish (Kwak, T. J. 1992. Modular microcomputer software to estimate fish population parameters, production rates and associated variance. Ecology of Freshwater Fish 1: 7375.
Second, how you go about testing the differences depends on the error you wish to test against. If you simply have say 5 population estimates, one each from 5 canals, then there is no standard way you can use an anova. You have only one estimate (no replication) for each canal. However, each of your canal estimates will have an associated variance or error in the estimator. One can use an approximate confidence interval (e.g., 95%CI = 2*Std Dev  note that since n=1 the standard deviation is equivalent to the standard error) and see if they overlap. This is not super appealing but it is the best approach I know. You really are testing if the estimates are different given your error in estimating each population. Newman and Martin (1993) give some procedures for this.
The other suggestion that was given for instances in which you have either spatial or temporal estimates is to partition the variance into these components. For example, if you have 5 sites at each canal you can compare within canal differences to among canal differences  the estimate for each site is one observation. This procedure ignores any error in the estimates (assumes they are the best estimate and part of the within and between error will include estimation error). Newman and Waters (1989) used this approach to look at temporal and spatial variability in several parameters of a brown trout population. Good luck with your work.
Newman, R. M., and F. B. Martin. 1983. Estimation of fish production rates and associated variances. Canadian Journal of Fisheries and Aquatic Sciences 40: 17291736.
Newman, R. M., and T. F. Waters. 1989. Differences in brown trout (Salmo trutta) production among contiguous sections of an entire stream. Can. J. Fish. Aquat. Sci. 46: 203213.
Ray Newman, Assoc. Prof. PhoneNet: (612) 6255704 Fisheries and Wildlife FAX: (612) 6255299 University of Minnesota Internet: [log in to unmask]
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