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 9-14m),
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
Randolph-Macon College
Ashland, VA  23005
804-752-7293
FAX 804-752-4724
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 species-specific 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) 634-4528/4530; Fax: 634-4549
Home: (809) 628-8375; Home Fax: 628-8495

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 species-specific 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 habitat-type, *not* on the basis of the population estimates
from the sites.  Your goal is to reduce among-site 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
"two-stage" 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 173:9-43) 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: 834-844) is also good, as is Hankin (1984.  Multistage
sampling designs in fisheries research: applications in small streams.  Can.
J. Fish. Aquat. Sci. 41:1575-1591).

Or, to really simplify things, you can just use each population estimate in
a one-way 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
Randolph-Macon College
Ashland, VA  23005
804-752-7293
FAX 804-752-4724
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 mark-recapture).  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: 73-75.

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:
1729-1736.

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: 203-213.



Ray Newman, Assoc. Prof.             PhoneNet: (612) 625-5704
Fisheries and Wildlife               FAX:      (612) 625-5299
University of Minnesota              Internet: [log in to unmask]

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           Chance favors only the prepared mind  -Pasteur