What follows are updates of our previous efforts to assess relationships between invasive carp densities and body condition (relative weight) of invasive carp as well as native, abundant planktivores. This update adds 2022 MAM data to our 2019-2021 analyses. The goal of these analyses are to determine the value of MAM for assessing the impact of invasive carp, and by extension, invasive carp harvest on the native fish community.

Based on our conversation, it would seem we have two major hypotheses:

1. invasive carp density is inversely correlated with invasive carp body condition
2. invasive carp density is inversely correlated with body condition of native planktivores, putatively due to competition for consumptive resources

It would seem there is one offshoot hypothesis from this work directly applicable to management:
3. If a relationship exists between invasive carp desnity and native planktivore body condition, can one predict with any useful precision the density of invasive carp from native fish body condition metrics?

Next steps depend largley on what you’d like to do. I had developed the outline of a paper that this could be a part of, which we discussed late last year. Or maybe you just wanted this as discussion material for MRWG meetings and MAM financial support. If you’re interested in it being developed further, I can work this up for Pool 26. I may also eventually incorporate LTEF data, although I’m not certain I love that idea, for reasons that I explain at the end of the document.

I’m limiting the analysis of invasive carp to just Silver carp and Grass carp, as they represent the vast majority of individuals in the system during these years. These proportions remain relatively unchanged since adding 2022 data. Hereby, when I say ‘Invasive carp’ I mean Silver and Grass carp combined.
SPECIES_CODE n percent
BHCP 42 0.05
GSCP 20553 24.16
SVCP 64472 75.79

Per our conversation, I’m also limiting the analysis to adult Invasive carp. The LTRMP life history database uses 193mm as the cutoff for Silver carp adults and 200mm for Grass carp adults, and after analysing the MAM data I’ve bumped it up to 200mm for our combined grouping of both spp. 2022 data reinforces this cutoff.

Does Invasive carp density negatively correlate with Invasive carp body condition

Because relative body weight is my choice metric for body condition, I’m eliminating any fish that weren’t measured exactly for both length and weight. I’m using strata weights to compile designed-based, annual, pool-wide estimates for Invasive carp daytime electrofishing catch, both in terms of number of fish (CPUE) and biomass (kgPUE). I’m only using Period 3 fish for both body condition and pool-wide abundance estimates because the majority of P1/P2 fish are not directly weighed and I don’t want to rely on modeled weights when the goal is to compare actual weights to model predictions (i.e. relative weight)

One could also apply strata weights to the fish, and may be data-driven reasons to do so in some pools, as both length and length’s relationship to weight seem to vary significantly by strata in certain pools. This seems to be true for both SVCP and a couple native planktivore’s. However, these trends seem pool-specific, not universal, with some strata high in some pools and low in others. See breakdowns for both Invasive carp spp. and Gizzard shad below.

Although these may be statistically significant differences, the fact that trends aren’t universal across pools makes me less convinced that correcting body condition by strata weights is going to solve some big issue here. If we’re ignoring size differences among strata, we can then lump in LTEF size data or maybe even commercial harvest size data alongside the MAM size data and not worry that LTEF/harvest is “oversampling” MCB fishes. If it’s not IRBS or fisheries-in-general convention to strata-weight the fish sizes as well as the abundance, my choice would be to ignore the size and condition differences between strata and lump everything together.

For now, I’m just going to analyze the MAM data because that’s what I had on hand to start and am most familiar with. This only provides 3 years of data but eliminates issues of biased abundance from pool-wide MAM abundance estimates and mostly-MCB LTEF abundance estimates. I haven’t modeled the differences in abundances among strata, but I think it’s safe to assume those are likely different. More on that later…

Finally, here’s my attempt at answering our first question. I’m modeling using the formula abundance estimate ~ body condition to test for correlations, but I’m plotting the data on the opposite axes because it seems a more intuitive cause-and-effect, to me at least. For body condition, I’m using the LTRM life history database’s length-weight relationship parameters for Silver carp even though I’m modeling both Silver and Grass carp, but the parameters are very similar for both species.

First I’ll plot abundance estimates by pool and year, to get a sense of the abundance data we’re using.

Note the large standard error bars on the Starved Rock CPUE values. This may be important later, so below I’ll also plot the average of the Variance, Standard Error of the Mean, and Coefficients of Variation for each pool’s annual CPUE estimates. You’ll notice that Starved Rock has much higher Variance and SEM than other pools, but a lower CV. 2022 data generally support our inferences from 2019-2021.

Now the plots that test our first hypothesis, in the style of Coulter et al. (2018):

After adding 2022, a generalized linear mixed model using Pool as a random effect still shows a pretty clear trend between Invasive carp relative weight, with the exception of 1) the Starved Rock outliers we discussed earlier and 2) the Marseilles pool from 2022. The relationship with Invasive carp biomass, however, seems to be deteriorated by 2022 points from multiple pools (all except Peoria). I’m posting the model summary using number of fish below, because it has a better model fit. Including Year as an effect did not improve model fit for either variable. The effect of Wr on CPUE is not significant with the 2022 Marseilles point included, but becomes significant when that point is excluded.

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: Gamma  ( log )
## Formula: n_weighted_mean ~ mean_weight_r + (1 | POOL_REACH)
##    Data: modeling_data
## 
##      AIC      BIC   logLik deviance df.resid 
##     65.5     69.7    -28.7     57.5       17 
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.1886 -0.5854 -0.1434  0.5919  1.8112 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev.
##  POOL_REACH (Intercept) 1.0237   1.0118  
##  Residual               0.3574   0.5978  
## Number of obs: 21, groups:  POOL_REACH, 6
## 
## Fixed effects:
##               Estimate Std. Error t value Pr(>|z|)
## (Intercept)      4.614      4.359   1.058    0.290
## mean_weight_r   -4.558      3.967  -1.149    0.251
## 
## Correlation of Fixed Effects:
##             (Intr)
## mean_wght_r -0.990

I think there good evidence to suggest a relationship between Invasive carp body condition and Invasive carp abundance here, even though it’s difficult to visualize due to the random effect at play and contains a handful of points that appear to be influenced heavily by an outside factor. We can plot GLM predictions conditioned on random effects, which give me a sense that, even though it’s a significant relationship, the confidence intervals are wide making any predictions of abundance from body weight rather uninformative. Below i’ve plotted those predictions (on the response scale, not the log scale), with and without confidence intervals. The model’s average predictions are dragged upward by the four points disucssed earlier. We should discuss if you think there is a biological or methodological reason for these points and whether that is reason enough to omit them.

Is invasive carp density inversely correlated with body condition of native planktivores?

Let’s take a look at a few, relatively abundant fishes that might be competing directly with invasive carps, specifically Emerald Shiner (ERSN), Gizzard Shad (GZSD), Bigmouth Buffalo (BMBF), and River carpsuckers (RVCS). I’m also going to throw in common carp (CARP).

I’ve removed all pools that have zero for Invasive carp. I could add a small constant to these pool x year combinations in which we didn’t catch carp so that their log10 values appear on the plots and in the models, but these generally had body condition values that spanned the range of the relative weight data for each species. This could compromise any claims that there is a correlation, because theoretically these species should have very high body condition values. I’ll revisit this point at the end.

I also removed pool x year combinations for which no individuals of the given native species were captured and/or weighed.

There seems to be some evidence for negative correlations between Invasive carp abundance and body condition of some native planktivore species. None of the relationships are very clean, though. In some cases, I had trouble getting generalized linear mixed models (GLMM) to converge, possibly because the random effect of Pool may have been an overfit. In these cases, I refit generalized linear models (GLM) where Pool was removed as an effect. In general, adding Year as a fixed effect did not improve model fits.

One peculiar result is the positive correlation between Invasive carp abundance and body condition of river carpsucker. This species is listed as a ‘Planktivore/Detritivore’ in the LTRM life history database and are one of the most abundant species in the MAM data that have ‘Planktivore’ as the first identifier for their guild entry .

Similar to the plots of Invasive carp body condition, much of the native planktivore data also suggest that Starved Rock does not fit the pattern as well as the other pools. I’m not sure why this is. I’m rarely in favor of throwing data out unless there’s very good reason to do so, but let’s just examine these plots without Starved Rock for the sake of exploring the data.

Removing Starved Rock seems to strengthen our evidence for a trend and result in better model fits in general. However, this feels a bit like cherry-picking unless we have a biological or methodological reason to do so, in my opinion. Perhaps the fact that the average annual SEM (how far the sample mean is likely to be to the true mean) of these estimates is nearly triple the next highest pool gives us pause on the reliability of our CPUE estimates for estimating the true abundance of Starved Rock? Is that enough to throw away this pool that has the highest abundance of carp? Sort of a judgement call, I guess. Although, when corrected for the high mean CPUE, the Coefficient of Variation is actually the lowest in Starved Rock, giving us a sense that the samples we take there are proportionally closer to the sample mean than in other pools.

2022 does little to strengthen or weaken these trends, with the exception of 2022 Peoria for River carpsuckers. There appears to be an extremely high Wr point at a mid-sized abundance level here. Upon further investigation, this point is highly influenced by one individual with a weighted of 521g and length of 310mm, giving a Wr of 1.3. With a total of 9 RVCS captured in Peoria in 2022, normally this large fish wouldn’t dominate the average, but the Wr’s are weighted by the availability of the strata in which they were caught, much in the same way annual pool-wide abundance estimates are calculated. Because this was the only individual Rivercarpsucker caught in the Peoria backwater in 2022, and because the backwater makes up the vast majority of the sampling area in Peoria, it is weighted nearly 100x higher than the 7 individuals caught in the side channel and 3x higher than the 1 individual caught in the main channel. Because a disproportionate effect can be made by one fish, maybe we should revisit weighting the averages in this design-based way.

I also took a look at a few benthivores. Jason and I went back and forth a few times on this, and the MAM results seem to be the opposite of what he was seeing with LTEF, where carp abundance seemed to positively correlate with benthivore Wr. For MAM, there are weak negative correlations for a couple species. I’ll plot those benthivores below (omitting Starved Rock, for consistency): Smallmouth buffalo, Freshwater drum, and Channel catfish.

Some weak trends there for Smallmouth buffalo and Channel catfish that might be cleaned up if we had reason to omit a few outliers. Perhaps those outliers are similarly due to outsized weighted average effects from strata-specific catches. If you decide you want this worked up in more detail, that would be a place I would start. There’s probably nothing at all here for Freshwater drum.

Finally let’s include pool x year combinations in which we did not catch Invasive carp. Theoretically there were carp present, just below our detection threshold. Therefore, I will add a small constant (0.01) to both the CPUE and kgPUE values so they can fit the log-link framework of our generalized linear modeling.

I’ll add Starved Rock back in for completion, and we’ll go back to just the original set of native planktivore species you requested.

As you can see, adding in pool x year combinations where no carp were caught as some arbitrary, low abundance number removes all significant relationships from Invasive carp abundance and native planktivore body condition. Emerald shiner is not present in this group of plots because of a technical issue, but I’ll plot those below.

As with the other planktivores, ERSN also lacks a relationship with these added ‘below-detection’ Invasive carp abundances. So we have a decision to make. Is it reasonable to leave out these ‘below-detection’ pool x year combinations? Or misleading? It’s my opinion that we don’t know what these abundances are. They’re likely to not actually be zero, just below detection, and so plotting/modeling them as zero is not accurate. In addition, the log-link in the model requires that we add a small constant to every value. How far to the ‘left’ of the non-zero points that these ‘zero’ points appear is dependent on the value of that small added constant. Because we’re running regression, these ‘zero’ points on the left side of the graph have very high leverage on the modeled trend, and because their position is somewhat arbitrary because of the arbitrary added constant, I don’t feel super comfortable including them.

If we assume it’s reasonable to exclude pool x year combinations where no Invasive carp were caught, and we have valid reason to eliminate Starved Rock (two big ‘ifs’) we can return to our result that, for many of the highly abundant planktivores (and common carp), there is a significant, negative relationship between Invasive carp abundance and native planktivore body condition. Otherwise, it’s a stretch to say there’s much of a correlation between Invasive carp abundance and body condition of any fishes except Invasive carp themselves.

As for the follow-up hypothesis about predicting invasive carp abundance from native planktivore relative weight, I’m not sure even the significant relationships are strong enough to do so with any real level of certainty, but we can go down that analytical path if you’d like.

There are a few next-steps in this analysis. I could add LTEF data, either just the relative weights of planktivores or add in the LTEF carp abundance estimates as well. However, because carp abundance is likely significantly different by habitat type (I haven’t run those GLMs yet but I think that’s a fair assumption) and because LTEF mostly samples main-channel habitat, the LTEF, main-channel estimates may not be comparable to the MAM, pool-wide estimates. Plus, in pools (like Peoria) where the backwater dominates the available habitat and therefore has extremely high strata weighting, the addition of LTEF main-channel individuals might not influence the annual, pool-wide Wr averages since they will be extremely downweighted relative to the backwater values. I have to think through that a bit more and maybe pick your brain on using those data in tandem. Otherwise I may analyze the LTEF data separately from the MAM data.

Overall, I don’t think the 2022 data change our insights very much, although they do bring to the forefront the issue of outliers influencing/obscuring trends. Design-based (i.e. strata-weighted) Wr estimates seem to inflate our risk of having extreme outliers, and so maybe we should revisit if it makes sense to allow a small number of individuals to dominate what are supposed to be values representative of an entire year and pool of fishes.

I’m happy to talk through this more with you at your convenience.