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Location: Green Bay, WI | Shane Mason and I have been talking about the reported growth rates of females in Green Bay. It's interesting, so I thought I would start a thread.
MATH DISCLAIMER!!! Before reading this, please be advised that there is geeky math involved, and much of this material is theoretical. Therefore by proceeding (and presumably, posting afterwards), you acknowledge that you will not mock, ridicule and/or do any of us math geeks bodily harm. Seriously, there may be some moderately heavy math thrown around here, but it *is* in the "Muskie Research" portion of the forum. So here we go...
According to (ex-biologist) Kapuscinski et al (2006), the maximum length that the average female musky can achieve in Green Bay is 1355 mm, or about 53.3 inches. Now we all know of fish caught out there that are larger--but this is the predicted length of the *average* female. That paper also give the von Bertalanffy equation for the female fish as:
Lt = L_inf [ 1 - e^(-0.170t - 0.460)]
Where:
Lt = Length (mm) at time 't' (recall that 25.44mm = 1 inch)
L_inf = Length (mm) at time infinity (maximum theoretical length)
e = irrational constant (base) for the natural log function
t = time (in years)
So given that L_inf = 1355...
Lt = 1355[ 1 - e^(-0.170t - 0.460) ]
So to use this equation, all one needs to do is to plug in values for 't' (in years) and the result will be the length of the fish at that time.
EXAMPLE: t = 10 years
Lt = 1355 [ 1 - e^((-.17 * 10) - 0.460)]
Lt = 1355 [ 1 - e^-2.16]
Lt = 1199 mm = 47.1 inches
So using the given growth model with t= 10 years, the *average* female musky should be about 47.1 inches. That's interesting enough...
But what I found really interesting, is what you can do when you apply a little calculus. You have to take the derivative of the von Bertalanffy equation, and then you can set it equal to various annual growth amounts--then you can determine the growth rate(s) for an average female musky, at the given time (t). I have worked out several examples, but I will leave that for the next post.
So my question to you all, is has anyone read the Kapuscinski paper lately? I thought it might be interesting to see if anyone would like to discuss it--a "journal club" review of sorts.
TB
Edited by tcbetka 5/6/2009 3:33 PM
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| I'll get back with you shortly, Tom  I just saved the .pdf and sent it to myself.
Is there a link you can share with people to look at the article? I don't think most people will have access to the article (I do at the University)... | |
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Location: Green Bay, WI | I don't believe that it's online, unfortunately. I will look around for it some tonight--I do know that the abstract is online of course. But I don't think the whole article is there.
Maybe I could scan the page with the equations on them, if that would help. I was hoping to find a few people that had the article and would be willing to discuss it. And actually, I think discussing the growth model (equations) themselves is the best part about the article--as it is the thing that describes the population. So maybe I can find an article that explains the von Bertalanffy model in general, and is freely available. Then I can just summarize the most salient features from the Kapuscinski article, and possibly scan the page with the equations so people can see them. I will look around.
What I've found to be really neat in this is when you consider the derivative of the growth model for female fish (dLt / dt). It's interesting to calculate the various times (t) by setting 'dLt/dt' (edit) to either 25.44mm (1") or 12.72mm (1/2"), and then determining the corresponding age of the fish at those growth rates.
All of this of course assumes that the model in the paper is accurate--and that's an entirely different discussion. But for the purposes of this thread, I make the assumption that it IS accurate--and certainly represents the most accurate data available at the time of publication. I believe that David Rowe is working on upgrading it, and I will be very curious to see an updated model.
Thanks for your post...
TB
Edited by tcbetka 5/7/2009 10:15 PM
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Location: Green Bay, WI | OK, I have verified my math and can post this.
Recall:
Lt = 1355 [ 1 - e^(-0.170t - 0.460)]
Therefore,
Lt = 1355 - 1355e^(-0.170t - 0.460)
Now, taking the first derivative...
dLt / dt = (-0.170)*(-1355)e^(-0.170t - 0.460), or...
dLt / dt = 230.35e ^ (-0.170t - 0.460)
Ok, someone please check my result there, but I think it's correct. Now the interesting part...
Assume that we want to know the time 't' at which a female musky is growing at a rate of 25.44mm (1 inch) per year. Well, we simply assign dLt the value of 25.44 and solve for 't':
25.44 = 230.35e ^ (-0.170t - 0.460), or...
0.1104 = e ^ (-0.170t - 0.460)
Now,
ln (0.1104) = ln [ e ^ (-0.170t - 0.460)] or...
-2.203 = -0.170t - 0.460
Finally, solving for 't'...
t = 10.25 years
So for the average female musky growing in the population described by that von Bertalanffy growth curve, she is growing 1" per year when she is 10.25 years old. So using some other values:
dLt / dt = 12.72mm per year; t = 14.33 years
dLt / dt = 1 mm per year; t = 29.29 years
Obviously, you cannot equate the derivative (dLt / dt) to ZERO in order to get the absolute minima of the curve--the point at which there is no growth whatsoever. This is because you cannot take the natural log of zero, as it's undefined. So you have to pick a value very close to zero, and I picked 1mm/year, as for intents and purposes...this would be a no-growth condition for the fish. Certainly no appreciable growth.
So the moral of this story is that you can use the model to find a length (Lt) of an 'average' female fish, simply by plugging in a value for the time. Then you can turn around and determine her actual rate of growth, by plugging that same 't' value into the equation for the derivative. When I get a bit more time, I plan to calculate the growth *rate* curves for fish from ages 1 - 25, and plot them. It will be very interesting to see just where there is no significant change in length on an annual basis.
Finally, I once saw a reference (that I cannot find now) describing how a musky basically switches from somatic to gonadal growth, at (edit) some given time. I am not sure if it was a Rod Ramsell article, or just who the author was. But I want to try to find it and compare it to the results from plotting all the growth rates.
Fascinating stuff though...
TB
Edited by tcbetka 5/21/2009 10:36 AM
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Location: Green Bay, WI | I have worked out the lengths at each year, and the corresponding growth rates. I haven't gotten them on the same graph yet, but I created a spreadsheet with the raw data, and two separate graphs. I hope it attaches well. I just need to figure out how to get the raw data to appear in the thread. It's on the spreadsheet, right next to the respective graph.
TB
EDIT: OK, I think this will work. Download the "summary.html" file to your machine, then open it. You should see the raw data to the left of each respective graph. At least it works on my machine--hope it works for everyone else.
Edited by tcbetka 5/6/2009 11:28 PM
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 Summary.html (14KB - 884 downloads)
ScatterPlot1.JPG (45KB - 1200 downloads)
ScatterPlot2b.JPG (47KB - 648 downloads)
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Posts: 444
| Seems to me you could simplify this drastically, You know the average length, average life span, average they grow a year at certain year levels. Seems like a really complex equation to figure out that on average a 40" muskie is #$ years old. | |
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Location: Green Bay, WI | Well, we really *don't* know how long they live... The population is only 19 years old--or, what's left of the 5261 (EDIT, 5/8) fingerlings they stocked in 1989. So we really don't have a clue as to how long they live. But in terms of a complicated equation, the von Bertalanffy model (once developed) is pretty simple actually: Pick a year, plug in the value, crank out an average length. It's simple that is, as long as the model is accurate.
Oh, and we don't know the average yearly growth rate either, unless you simply calculate the length at the years on either end of a given time period, and subtract. But the equation I listed last will do that as well, directly.
But I apologize if I am missing a point you were trying to make. If I am, then please show me how this could be simplified.
Thanks for the post.
TB
Edited by tcbetka 5/8/2009 8:16 PM
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| Unknown variables, #*^@ I hate those...I was thinking average growth rate and how long they live was already determined. I obviously didnt grasp that part.
now can you automate that equation like they do for fractal generators? that would be cool.. | |
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Location: Green Bay, WI | I am not sure how I would go about that, to be honest. And life has been pretty complicated in the last couple of days, so I don't have a ton of time to learn about it. Most of what you see above was calculated some time ago--I just had to verify the math again, once I found the time to revisit the issue.
TB
Edited by tcbetka 5/7/2009 4:46 PM
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Location: Nowheresville, MN | I'm kinda confused too as to what you are looking for.  Remember the model estimates should be applied cautiously to ages outside of the sampled ages used to create the model. For example, I know fish in that system grow fast, but I find it unlikely a 1 year-old fish is 24". | |
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Location: Green Bay, WI | Well, I went back and re-read the paper. The first thing I discovered was that I misquoted the number of fall fingerlings stocked in 1989--it was 5261, not 2200. I edited my previous post to reflect that. The 2200 is (I think) a number I have heard used as basically an average of the number of fingerlings stocked in those early years. But the actual published value is 5261. So in the interest of accuracy, I have edited that number. I apologize for the error.
I made the same observation as you did, regarding where the model starts. I don't think that the model can be considered accurate for the low ages, but I am not sure I can explain why.
But I also recall something I had forgotten from the last time I'd read the article--that the growth model can really only be considered an accurate representation (within a 95% confidence interval) of hatchery-reared fish, stocked into the Fox River. Fish from other areas weren't sampled to any significant degree, and therefore one really cannot generalize as to the applicability of the model to the entire population in the bay. The authors mentioned this very thing in their discussion, and suggested that factors such as diet and water temperature differences between the river and the bay as possible confounding variables. So the equation I've listed above may or may not be accurate for the fish throughout the range in the bay. Also, there were relatively few female fish (62 observations; 17 fish in a known length-age subsample) used in the estimation of the growth model equation I've quoted. That's not a whole lot of fish, but they had what they had and you have to start somewhere.
Furthermore, as I read the paper, it appears that there were only one or two fish above the 50" (1270mm) mark included in the creation of the model. (EDIT: I believe that there was one fish shown in the paper, but Kevin Kapuscinski himself told me that there was another ~51" fish they used as well.) Although there were many more fish included that were under 50", I am not sure how the model would be affected by a higher number of older (10+ yrs) female fish. Our biologist and I have discussed this in the past, as I can't help but think that more fish in the older age groups could only have a positive effect on the accuracy of the model. But it will take some time to collect that data.
In fact I wonder if there really shouldn't be TWO models for the fish sampled? These original fish, stocked into the bay in what could be considered as an "empty niche" of sorts, possibly showed faster-than-expected growth during these early years because of that advantage. But as the entire musky population grows, is it possible that there is a density-dependent effect on the growth of future generations? Indeed another interesting discussion is whether or not there should be two growth models for stocked fish: one for their younger years (where they benefit most from rearing in hatcheries), and another for their later years when they perhaps show a slower growth, more typical of the Great Lakes Strain of muskellunge seen in the Georgian Bay and St. Lawrence River ecosystems?
TB
Edited by tcbetka 5/9/2009 7:43 AM
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Location: Green Bay, WI | tfootstalker - 5/8/2009 8:01 PM
I'm kinda confused too as to what you are looking for. Remember the model estimates should be applied cautiously to ages outside of the sampled ages used to create the model. For example, I know fish in that system grow fast, but I find it unlikely a 1 year-old fish is 24".
I suppose I should actually answer your question...lol.
As to what I am looking for...nothing, really. I simply found it interesting to apply some advanced math to the growth curve, and then take a look at the actual growth rate curve for the aging population. The paper states that there is some concern that these fish grow too fast to achieve record lengths--sort of the "faster growers, but short livers" argument. I have heard this concern referenced several times in fact, used as an argument against the 54" size limit. The argument is that the fish will simply burn themselves out, well before they live long enough to reach record lengths. But in case you haven't already figured it out, I disagree with that idea. There are simply too many confounding variables to be considered, and I just don't believe that we have enough information to make such a statement.
In fact if one considers the range of curve slopes given in the 95% confidence interval cited in the paper, the current model might actually look quite different indeed.
TB
Edited by tcbetka 5/8/2009 9:35 PM
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Location: Rhinelander, Wisconsin | I think a portion of the fast growth/slow growth trophy potential concept has to do with slow, steady growth leading to older, larger fish in that exact combination, not mutually exclusive to maximum expected longevity under less than perfect conditions, I have seen very old muskies in waters here that are trophy sized for that water, but only 45" or less. Low density muskie populations with adequate to excellent forage and limited competition from other fish equal the best growth and potential for the best upper confidence limits at maximum longevity, correct?
If indeed the estimated upper confidence limit on any body of water is to be used either positively or negatively to push for changes in regulations RE: Harvest limits or increased size limits or slot limits, then one needs be aware that there WILL be exceptions to the rule, and those exceptions do not represent the averages on that waterbody as a whole. Tom's math points that out pretty well, I think. What we are seeking on Green Bay is a size limit at 54" to protect the fish from harvest up until they reach that point. Does that mean every female Muskie stocked in BOGB will reach 58"? No. Will every one reach 54"? Probably not. But if a statistically significant number exceed the (based on limited data) upper confidence limit on BOGB we are looking at now, then there will be some very big fish caught...and perhaps harvested as they are over the 54" limit. There's more work to be done educating folks how fragile that system might be, and alienating everyone except those who already support the 'platform' won't get that done.
We (collectively speaking) can alienate the biologists statewide by calling fisheries scientists nitwits and insisting they have not the level of 'common sense' with which we as Muskie anglers are so fortunate to be imbued. I'd suggest the negative rhetoric be toned down, in an attempt to create an atmosphere where EVERYONE pulls in the same direction. Just because 'we' were successful so far in getting changes made on the size limit on BOGB doesn't mean that social pressure from the other sides of things cannot negate the progress, espeially if we collectively drive off any potential allies or neutral parties of note. If I was on the receiving end of some of the rhetoric, I know how I'd respond the next time I'm asked to make a move that is not widely supported by ALL anglers, or by the available data for that matter. I'd especially like to see the higher profile guys spouting less total #*#*, and actually DOING something in concert with the fisheries folks out there....but that wouldn't get as much 'attention', I suppose. What a waste.
Now there's some....common sense.
http://books.google.com/books?id=_qPVXKBSyKgC&pg=PA140&lpg=PA140&dq... | |
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Location: Watertown, MN | Tom
I agree, fish like most living creatures grow in the first 1/3 of their life cycle, humans do not keep growing throughout our lifecycle, we peak then maintain or anctually shrink. So I would expect by years 8-12 muskies should be getting close to their maximum lenght potential.
For the wild card, are the rare super tankers sterile females, and hearing more talk about monster females being sterile and strickly putting all effort to growth and now worrying about reproduction? I know there was 45"+ fish handled this spring that was an absolute tank, she gave no eggs, is she sterile? she was tagged and will see if she gives next year.
Troyz | |
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Location: Green Bay, WI | I do not believe that the largest females are *necessarily* sterile. I just read on TNB's site that the Minnesota DNR harvested about 6 pounds of eggs from a 53" female in Leech Lake this spring--at least I think it was on that forum. I know it was a 53" fish anyway, with 6 pounds of eggs. So I don't think you can make that assumption in any way...
I believe it was biologist Rod Ramsell who wrote an article some time ago, reporting how female fish, after a certain point, devote most of their energy to gonadal development...and not to somatic growth. So that essentially means that the length of the fish would indeed slow at some point--but it does not entirely stop. I have read several references that indicate that fish tend to grow throughout their entire lives. And if you look at the growth curves (Lt and dLt/dt) I've listed above, you can see this. Do they grow the same rate for their entire life? No way. They obviously have to divert more energy to the development of their gonads at some point, but nothing I've ever read indicates that it's a 100% shift.
As to the sterile supertanker question--I think it's likely that some large female fish are better than others (and some are worse) when it comes to reproduction. So what is true for one 45-50" fish isn't necessarily true for the next one. I have never seen anything published that reports this either. Maybe someone else might have a reference.
TB
Edited by tcbetka 5/18/2009 9:31 PM
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Location: Green Bay, WI | I have been reading a very nice article today: Growth and Ultimate Length of Muskellunge from Ontario Water Bodies, by Casselman, Robinson & Crossman. In it, they report (among other things) the von Bertalanffy growth curves for several different populations of muskies, from 12 Ontario water bodies. I'd thought I summarize some of the data here, as I found it quite interesting. These data are for FEMALE fish only.
Recall the general form of the von Bertalanffy growth model...
Lt = L_inf [ 1 - e^-k(t-to) ]
Where:
1) L_inf is the ultimate size that the average female fish can obtain.
2) The K-value represents the rate at which a fish approaches the maximum obtainable size; the higher the value, the faster the rate of growth.
3) Lt is the length at some time 't'
4) 'to' ("t-naught") is some time at which length = 0. Note that this would theoretically be sometime *before* the fish is hatched, and thus it is not observable experimentally.
5) Finally, length in inches = length in mm / 25.44
The interesting thing to note here is that the K-values apparently do not correlate to the size of the fish all that closely (eg; Georgian Bay vs Indian Lake or Lac Seul). I've heard the argument that greater values of K may represent populations that show rapid initial growth, but then do not show longevity. In other words...fast-growers but short-livers. But in the case of Georgian Bay and Green Bay fish, the Georgian Bay fish have a greater value of K than the Green Bay fish, but the oldest fish observed (29-30 years) was indeed in Georgian Bay. There was only one fish of that age apparently, and I initially presumed it was Martin Williamson's 61.25 pound fish. But some research revealed that his fish was caught in November of 2000--a year after this paper was published! So there indeed must have been more than one ~30 year old fish to come out of Georgian Bay. And in fact there were numerous other fish in the 16-24 year age range reported in the article, so it seems as though there are some long-lived female muskies swimming in those waters.
It's a very interesting article that helps explain quite a bit in terms of how to start to learn to interpret these von Bertalanffy growth curves.
EDIT: I should also say that the data from the Green Bay fish was obtained from fish that were sampled by DNR biologists, either by seine nets or electrofishing. However much of the data for the other waterbodies was obtained from anglers via the Cleithrum project. In other words, the Green Bay fish were NOT selected for harvest by anglers, but most of the other fish were harvested (in the 1980's & 1990's). Another important point is that, to my knowledge, most of the populations represented in the 12 waterbodies in Ontario were stable populations that had existed for many years. Contrast this to the Green Bay population, where the majority of fish sampled were from a reintroduction effort that only began in 1989.
These are important facts to keep in mind while comparing the data I've listed below. For one thing, although the Green Bay muskellunge population undoubtedly contains unstocked fish, they most likely did not represent a statistically significant contribution to the results published in the 2006 Kapuscinski (et al) paper. Thus the Green Bay results likely DO NOT represent a stable, mature population...a point I have tried to make several times.
TB
Edited by tcbetka 5/19/2009 8:49 AM
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Location: Rhinelander, Wisconsin | Casselman talked about some of the data in his presentation at the Symposium, IMHO addressing the overall 'trophy' concept in each...and then every muskie water and the claim made at that time that simply planting fish from a waterbody containing large fish will create the same in the stocked waterbody.
Tom, note the Wabigoon data set. That water is so fertile it's amazing, the forage rich and varied, and the Muskies there, spotted fish for the most part, live quite a long time, but do not carry the same UCL that Georgian Bay fish do, by a significant gap. Is it the shorter life span of the sample by 8 years, and is it environment driving that data set?
Of course, Wabigoon and Eagle are considered Trophy fisheries by the Ministry, and carry a 54" limit. I bet fewer muskies are now harvested out of both in a year that what used to be harvested out of Pelican Lake in WI, recently added to the WIDNR list of 50" limit potential trophy waters. | |
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Posts: 272
| Not to take this on a tangent, but since its been brought up.......are "sterile" and "a fish having no eggs" synonyms? Meaning, can a fish be sterile and still have eggs? Like in humans, some may have the right mommy and daddy parts, but just can't conceive?
On those lines, it seems like if a big, super big female, truly put zero energy into producing eggs, she'd get grotesquely huge in a matter of just a couple seasons. That's got to take lots of calories to produce all those eggs.....to have all that put into a fish's weight or length would seem to make for a 80-100# +++?????? fish-zilla in short order. Of which none have ever been caught.
I guess what I'm trying to say is that I'm not sure I buy into the whole "sterile fish equals a super giant" theory. Someone, somewhere would have obtained one. Either by netting, electro, spearing, hit by a boat prop, natural causes..... or angling.
Neat stuff, Tom.
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Location: Green Bay, WI | I don't believe that there really is such a thing as a completely *non-fertile* fish, at least for muskellunge. At least I have never seen a published reference (that I recall anyway) reporting such a thing. Now, I have seen references that indicate that some large fish do not develop as many gametes as their size suggests they should--but that doesn't mean that they do NOT develop eggs/sperm. It only means that they probably don't develop enough gametes to reproduce with any degree of success. Maybe someone else has some additional information they could share, and then I could research it more.
The thing to do I suppose, would be to talk to guys like Joe Fittante and Rick Lax, and other experienced taxidermists, and inquire as to whether or not they can share any observations on the matter. There probably aren't any better folks than these guys, to answer this question.
TB | |
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Location: Green Bay, WI | With regards to Steve's last post, I wanted to share a thought...
In the Casselman paper on page 288, they hypothesized that in order to explain why the Georgian Bay fish weren't found to be larger (despite their apparently longevity), there might be TWO different "stocks" of muskellunge: a "bay" stock with a higher growth potential, and a more riverine stock with lower potential. I firmly believe this to be true--and in fact feel that it's *exactly* what we are seeing in the population in Green Bay.
The fish that tend to frequent the Fox River and southern bay most of the year, tend to be a more "riverine" fish. But I believe that there are many fish that indeed spend most of their lives in the open bay (certainly outside University Bay), and thus may have a much more significant growth potential than the riverine population. In fact this could certainly explain why there seems to be such an increase in the number of LARGE females caught in the fall--they simply migrate towards the mouth of the Fox River to follow the forage, thus exposing themselves to angling efforts.
While I freely admit that I cannot prove this theory, I have spoken to literally hundreds of anglers who fish Green Bay--many whom have fished it for 10-15 years, and report seeing or catching very large fish well north of the University Bay area at the south end of Green Bay. It hasn't been until the last 5-7 years that larger fish have been seen in any significant number, in the areas most frequently fished by the majority of anglers.
So I suggest that if this IS true and (for whatever reason) we aren't seeing these larger fish in the sampling nets to any significant degree, then the data that has been used to formulate the von Bertalanffy model for these BoGB fish is, in fact, *not* representing the entire population at all. And of course this becomes a problem because the management plan thus far is being predicated on that very model. I for one would very much like to see a telemetry study conducted on some Green Bay fish. Catch some of these supertankers in the fall, tag them and then follow them. Not only could we gain tremendous insight as to just how much these fish migrate throughout the year, but we could also start to get a feeling for the degree of delayed mortality that's occurring out there.
But in my opinion, until we really know for certain just how much migration there is between the riverine and lacustrine portions of the bay system, we really won't know just how much protection these fish really need...
TB
Edited by tcbetka 5/19/2009 9:48 AM
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| tcbetka - 5/19/2009 9:45 AM
Catch some of these supertankers in the fall, tag them and then follow them. Not only could we gain tremendous insight as to just how much these fish migrate throughout the year, but we could also start to get a feeling for the degree of delayed mortality that's occurring out there.
TB
All that, and a million other questions could be answered. For instance, are the fish here in the fall because of the bait movements, or because the river smell imprinted on them when they were stocked, so like salmon....they think they're going 'home' to spawn? Would/Is the Bay's shad movement enough of a draw to bring in fish from other parts of the bay? How far? Would fish stocked here come later if there were no shad? Would they come back at all if the shad pop crashed? Do they dispurse after the fall run to spawn elsewhere in the lower bay, or are the U-Bay fish here to spawn only, and, oh by the way, just happened to run into a herd of shad? Do some go elsehwere in the bay after munching on shad in October? Do any? How many? Where do they go?
In other words, are they going elsewhere during the summer that they would they rather be all the time, and are just returning because they were 'born' here? I'd guess probably. Would they do better being stocked somewhere else? Would we have better spawning success if we stocked fish elsewhere? Would they come to the the mouth and into the river anyway even if stocked (hopefully someday successfully hatched) elsewhere? Would their offspring come to the Fox for food or other reasons?
....and, where does the white go when the snow melts?
-Eric | |
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Location: Green Bay, WI | A point of clarification is in order here...
Bytor pointed out that the true age of Williamson's fish was about 18 years old. In fact this is correct--I confirmed that with Larry Ramsell today. I initially mis-read Larry's email where he was talking about Ken O'Brien's fish (which was 29 +/- 1 years old), and thus I got the two fish confused. So thanks to Troy for clearing this up!
TB
Edited by tcbetka 5/21/2009 4:36 PM
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| many of the green bay fish were from st clair. the genetics should show females over the 52-53 inch range. as long as the forage base is strong theres definately tankers there. . thru recent years we are seeing 55 class fish here., and yes for a shallow basin weights and sizes are upswinging. could it be release ethics?? | |
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Location: Green Bay, WI | I think there were eggs from LSC fish only one year, as I recall. It isn't in the Kapuscinski (et al) paper, but I seem to recall our biologist telling us that at a talk he gave last fall. I am positive that the vast majority of the fish came from the Indian Spread Chain in northern Michigan (not the UP), but I cannot put my fingers on a number for you right now. I'd have to re-watch his talk in the video section of this site, in order to get the number. But by the sound of it, there was an issue with getting more eggs from LSC fish, so that only lasted a year or so.
But for giggles, I will dig up the growth model for LSC, Georgian Bay and the Larry, and plot them out. It'll take a bit of work, so I'll have to wait until the weekend--but I have been going to do it, and just never got around to it yet. Now that fishing season is here, there's another excuse *not* to finish all those things I've been meaning to get to...lol.
TB | |
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Location: Green Bay, WI | I received some updated data from our local fisheries biologist about two weeks ago. The data included the newest growth model for the population in the bay of Green Bay, through 2009. To his knowledge, this is the latest revision of the growth model that exists. Therefore I have calculated the average length at age of female muskellunge in this population, using both the original model (2005, referenced above) and the newest model. The results are shown in the two tables I am attaching to this post.
An interesting thing occurs when you evaluate the growth rate equations using the values of 1" (25.4 cm), 0.5" (12.7 cm) and 0.04" (0.1 cm) effective growth per year. While the new growth model indicates that a female musky is slightly older when she is growing at 1" per year, she is actually slightly younger when she is growing at 0.5" per year; and when she has essentially stopped growing (rate = 0.1 cm/yr).
1.0" per year growth rate: 10.26 years (2005 model); 10.32 years (2009 model)
0.5" per year growth rate: 14.34 years (2005 model); 14.22 years (2009 model)
0.04" per year growth rate: 29.29 years (2005 model); 28.49 years (2009 model)
TB
Edited by tcbetka 5/20/2012 6:42 AM
(FemaleMuskyLengths_GRB.jpg)
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FemaleMuskyLengths_GRB.jpg (135KB - 1036 downloads)
GrowthRates.jpg (128KB - 902 downloads)
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