Grass carp catchability

Introduction

In May 2022, Kris Maxson reached out following-up on in-person conversations regarding our previous work on modeling Smallmouth Buffalo catchability across gears and strata in the Upper Mississippi River using LTRM data. After a few months we regrouped with a focused direction to repeat these catchability analyses for Grass Carp. What follows are analyses that borrow technique and formatting from the Smallmouth Buffalo project deliverables to address similar questions for Grass Carp.

These analyses do not include reach-specific growth questions that we answered for Smallmouth Buffalo, but I would be happy to tackle those next if the eventual Grass Carp research product should include those.

Data considered

I’m using data downloaded from the LTRM website in August 2023, with the following adjustments:

• Filtered to valid summary codes (> 2) and site types (< 2)
• Filtered to contemporary gear types (D, M, F, HS, HL)
• Filtered to relevant strata used for Smallmouth Buffalo (BWC-S, MCB-U, SCB)
• Filtered to the relevant pools where Grass Carp have been caught (LaGrange, Pool 26, and Open River)
• Filtered to 2000-2022. 1990s data seemed more variable. If the goal is to assess which gears/strata to target for contemporary sampling, I figured we should eliminate years where population growth may have impacted inference.
• Assigned a Grass Carp size-class threshold of 300mm to match the Andrew Mathis analysis’ threshold between ‘stock’ and ‘substock’ sized individuals. The LTRM life history database lists 200mm as the threshold between ‘adult’ and ‘juvenile,’ but by analyzing the length-frequency distribution of our data, there is a large gap between small and large individual distributions which contains both 200mm and 300mm. Both seem reasonable so I chose Andrew’s for consistency and management relevancy.
• Substock (juvenile) catch contained a handful of extreme CPUE outliers (10,000+). My modeling approach used a Zero-inflated Poisson (ZIP) distribution, for which parameter estimation is particularly sensitive to outliers. Formal outlier detection in a ZIP scenario is difficult, as most formal methods assume normality or use interquartile range (IQR). Because a ZIP has so many zeros, the IQR itself is 0 (Q1, Q2, and Q3 all equal 0), making boxplots and related outlier thresholds pretty useless. Instead I used a pretty straightforward robust mean estimation technique called ‘Winsorizing,’ wherein a percentile threshold is defined and all values outside of that threshold on the high and low end are forced to the maximum value of the data inside the threshold. In our case, I set the threshold (alpha) to 0.001 to retain 99.9% of the data using the winsor() function from the R package psych (v2.3.6; Revelle 2019). On the low end, no values were changed because we don’t have low-side outliers. On the high end, 0.1% values were changed to 50, which was the maximum observed substock CPUE within the Winsorized range. This obviously isn’t perfect as I’m sure there is value in considering ultra-high catches, but it also doesn’t just throw the outliers away. It allows us to consider all the data in a way that produces meaningful gear- and strata-specific means and confidence intervals for comparison.
• There was no large outlier problem in the stock (adult) CPUE, so I did not Winsorize that data.

All modeling was divided into two subsets, per request: stock-sized (>= 300mm) and substock-sized (< 300mm) individuals. I think it’s reasonable to call these groups ‘adult’ and ‘juvenile’ based on LTRM life-history data as well as analysis of length-frequency data, but we’ll stick with ‘stock’ and ‘substock’ for consistency with the Andrew Mathis analyses.

Kris asked for two main factors to be considered for catchability: gear type and river strata. Where it improved the model, interactions between these factors and pool were examined. This typically only occurred for gear type among the stock individuals.

CPUE modeling

CPUE by gear

All CPUE modeling was performed as generalized linear mixed models with a Zero-inflated Poisson (ZIP) distribution using the function glmmTMB() from the glmmTMB package. The stock and substock models with best fit were defined as follows:

Substock: substock_catch ~ gear + pool + stratum + period + (1|year)
Stock: stock_catch ~ gear * pool + stratum + period + (1|year)

Below you’ll find estimated marginal means and 95% confidence intervals comparing the groups of interest. These should accomplish your goal of accounting for additional factors that the Kruskal-Wallis tests that Andrew Mathis performed did not. Where significant modeling interactions with pool were present, I’ve faceted the plots by pool.

I’m also including pairwise contrasts of the models’ estimated marginal means. These give a sense of statistical significance, though they may show significance where the plots have 95% confidence intervals overlapping due to high sample sizes. Again, where significant interactions with pool existed, I’ve contrasted the gear types within each pool, but not across pools.

Fig. 1. Relative abundance (CPUE) of Grass Carp individuals that are substock (A) and stock (B) sized across gear types in the Upper Mississippi River.

Table 1. Pairwise comparisons of estimated marginal means contrasting CPUE (i.e. catchability) across gear types for substock-sized Grass Carp.

contrast	ratio	SE	df	null	t.ratio	p.value
D / F	14.138	4.471	14569	1	8.377	< 0.001
D / HL	411.572	414.168	14569	1	5.982	< 0.001
D / HS	202.931	145.337	14569	1	7.418	< 0.001
D / M	0.454	0.023	14569	1	-15.810	< 0.001
F / HL	29.111	30.598	14569	1	3.207	0.013
F / HS	14.354	11.164	14569	1	3.425	0.006
F / M	0.032	0.010	14569	1	-10.894	< 0.001
HL / HS	0.493	0.607	14569	1	-0.574	1
HL / M	0.001	0.001	14569	1	-6.769	< 0.001
HS / M	0.002	0.002	14569	1	-8.527	< 0.001

Table 2. Pairwise comparisons of estimated marginal means contrasting CPUE (i.e. catchability) across gear types for stock-sized Grass Carp. Constrasts are made within each pool considered, as the model featured a significant interaction between gear type and pool.

pool	contrast	ratio	SE	df	null	t.ratio	p.value
LG	D / F	2.924	0.505	14580	1	6.208	< 0.001
26	D / F	19.862	14.406	14580	1	4.121	0.002
OR	D / F	1.103	0.395	14580	1	0.273	1
LG	D / HL	0.658	0.060	14580	1	-4.565	< 0.001
26	D / HL	2.514	0.467	14580	1	4.959	< 0.001
OR	D / HL	0.704	0.167	14580	1	-1.479	1
LG	D / HS	2.817	0.418	14580	1	6.974	< 0.001
26	D / HS	27.399	12.627	14580	1	7.183	< 0.001
OR	D / HS	2.352	0.749	14580	1	2.686	0.326
LG	D / M	44.691	15.250	14580	1	11.135	< 0.001
26	D / M	14.549	5.763	14580	1	6.760	< 0.001
OR	D / M	17.722	12.958	14580	1	3.932	0.004
LG	F / HL	0.225	0.044	14580	1	-7.704	< 0.001
26	F / HL	0.127	0.094	14580	1	-2.792	0.236
OR	F / HL	0.638	0.227	14580	1	-1.261	1
LG	F / HS	0.963	0.214	14580	1	-0.168	1
26	F / HS	1.380	1.175	14580	1	0.378	1
OR	F / HS	2.133	0.884	14580	1	1.829	1
LG	F / M	15.284	5.727	14580	1	7.278	< 0.001
26	F / M	0.733	0.598	14580	1	-0.381	1
OR	F / M	16.071	12.499	14580	1	3.571	0.016
LG	HL / HS	4.283	0.661	14580	1	9.424	< 0.001
26	HL / HS	10.899	5.225	14580	1	4.982	< 0.001
OR	HL / HS	3.342	1.056	14580	1	3.817	0.006
LG	HL / M	67.956	23.663	14580	1	12.116	< 0.001
26	HL / M	5.787	2.429	14580	1	4.184	0.001
OR	HL / M	25.178	18.385	14580	1	4.418	< 0.001
LG	HS / M	15.867	5.800	14580	1	7.563	< 0.001
26	HS / M	0.531	0.316	14580	1	-1.064	1
OR	HS / M	7.534	5.729	14580	1	2.656	0.356

CPUE by strata

When comparing strata, we must first subset our data to only one gear type, as the different gear types have fundamentally different levels of effort (not to mention active vs. passive sampling) as well as differential deployment across strata, making it unwise to make comparisons at this level with multiple gears. Daytime electrofishing is deployed most evenly across all strata, and so when making strata comparisons below, we only consider daytime electrofishing data.

Modeling was performed similar to gear comparisons, though no interactions with pool improved the model without causing complicated fit issues. However, this may aggregate over some valuable information. It may be worth noting that, because CPUE values are much higher in the LaGrange pool, pool-aggregated trends may be dominated by the pool-specific trend found in the LaGrange pool. Andrew’s figures may speak to this aspect of the data. Nevertheless, I think leaving out the pool interaction is the appropriate way to model strata comparisons under the current modeling framework. The strata comparison0 model forms considered are as follows:

Substock: substock_catch ~ stratum + pool + period + (1|year)
Stock: stock_catch ~ stratum + pool + period + (1|year)

Fig. 2. Relative abundance (CPUE) of Grass Carp individuals that are substock (A) and stock (B) sized across strata of the Upper Mississippi River. Only daytime electrofishing data is considered to eliminate confounding issues when comparing gears with fundamentally different efforts differentially deployed across strata. No pool interaction was modeled and so only one panel per individual size class is displayed.

Table 3. Pairwise comparisons of estimated marginal means contrasting CPUE (i.e. catchability) across strata for substock-sized Grass Carp.

contrast	ratio	SE	df	null	t.ratio	p.value
(BWC-S) / (MCB-U)	1.784	0.199	4624	1	5.187	< 0.001
(BWC-S) / SCB	1.829	0.196	4624	1	5.636	< 0.001
(MCB-U) / SCB	1.025	0.132	4624	1	0.192	1

Table 4. Pairwise comparisons of estimated marginal means contrasting CPUE (i.e. catchability) across strata for stock-sized Grass Carp.

contrast	ratio	SE	df	null	t.ratio	p.value
(BWC-S) / (MCB-U)	1.858	0.196	4624	1	5.884	< 0.001
(BWC-S) / SCB	0.976	0.084	4624	1	-0.279	1
(MCB-U) / SCB	0.525	0.053	4624	1	-6.383	< 0.001

Length modeling

Length by gear

In the Smallmouth Buffalo analyses, we analyzed fish total length in the same way we analyzed CPUE. These analyses are repeated for Grass Carp below. Length was the response variable for both stock and substock models, but the data were subsetted to the relevant individuals for each size-class model.

Model forms were as follows:

Substock: length ~ gear + pool + stratum + period + (1|year)
Stock: length ~ gear * pool + stratum + period + (1|year)

Fig. 3. Total length (mm) of Grass Carp individuals that are substock (A) and stock (B) sized across gear types in the Upper Mississippi River.

Table 5. Pairwise comparisons of estimated marginal means contrasting total length (mm) across gear types for substock-sized Grass Carp.

contrast	estimate	SE	df	z.ratio	p.value
D - F	-74.556	2.758	Inf	-27.033	< 0.001
D - HL	-6.558	10.370	Inf	-0.632	1
D - HS	-155.612	7.392	Inf	-21.052	< 0.001
D - M	24.921	0.452	Inf	55.122	< 0.001
F - HL	67.999	10.725	Inf	6.340	< 0.001
F - HS	-81.056	7.820	Inf	-10.365	< 0.001
F - M	99.477	2.763	Inf	36.005	< 0.001
HL - HS	-149.054	12.730	Inf	-11.709	< 0.001
HL - M	31.479	10.365	Inf	3.037	0.024
HS - M	180.533	7.387	Inf	24.438	< 0.001

Table 6. Pairwise comparisons of estimated marginal means contrasting total length (mm) across gear types for stock-sized Grass Carp.

pool	contrast	estimate	SE	df	t.ratio	p.value
LG	D - F	6.678	15.070	1590.093	0.443	1
26	D - F	-14.209	77.992	1587.461	-0.182	1
OR	D - F	33.428	35.862	1586.136	0.932	1
LG	D - HL	-99.842	8.930	1603.054	-11.181	< 0.001
26	D - HL	-173.850	19.144	1595.974	-9.081	< 0.001
OR	D - HL	-153.734	23.171	1590.443	-6.635	< 0.001
LG	D - HS	-94.187	14.296	1592.953	-6.588	< 0.001
26	D - HS	-181.801	49.953	1588.096	-3.639	0.013
OR	D - HS	-120.182	33.215	1589.719	-3.618	0.014
LG	D - M	-70.347	34.973	1589.056	-2.011	1
26	D - M	-73.897	42.246	1587.241	-1.749	1
OR	D - M	-153.592	65.694	1593.105	-2.338	0.878
LG	F - HL	-106.521	17.401	1594.405	-6.121	< 0.001
26	F - HL	-159.641	79.606	1588.087	-2.005	1
OR	F - HL	-187.162	35.288	1585.898	-5.304	< 0.001
LG	F - HS	-100.865	20.680	1591.761	-4.877	< 0.001
26	F - HS	-167.592	91.984	1587.884	-1.822	1
OR	F - HS	-153.611	42.699	1587.122	-3.597	0.015
LG	F - M	-77.025	37.681	1588.438	-2.044	1
26	F - M	-59.688	87.850	1587.596	-0.679	1
OR	F - M	-187.020	71.105	1591.587	-2.630	0.388
LG	HL - HS	5.656	14.343	1588.899	0.394	1
26	HL - HS	-7.951	51.395	1585.708	-0.155	1
OR	HL - HS	33.551	32.371	1586.590	1.036	1
LG	HL - M	29.495	35.660	1589.524	0.827	1
26	HL - M	99.953	44.909	1587.889	2.226	1
OR	HL - M	0.142	65.376	1591.472	0.002	1
LG	HS - M	23.840	37.262	1589.084	0.640	1
26	HS - M	107.904	64.365	1587.693	1.676	1
OR	HS - M	-33.409	69.774	1593.030	-0.479	1

Length by stratum

Again, we’ll analyzing by-strata comparisons using daytime electrofishing data only.

Strata comparison model forms are as follows:

Substock: length ~ stratum + pool + period + (1|year)
Stock: length ~ stratum * pool + period + (1|year)

Fig. 4. Total length (mm) of Grass Carp individuals that are substock (A) and stock (B) sized across strata of the Upper Mississippi River. Only daytime electrofishing data is considered to eliminate confounding issues when comparing gears with fundamentally different efforts differentially deployed across strata.

Table 7. Pairwise comparisons of estimated marginal means contrasting total length (mm) across strata for substock-sized Grass Carp.

contrast	estimate	SE	df	t.ratio	p.value
(BWC-S) - (MCB-U)	-12.375	3.750	839.465	-3.300	0.003
(BWC-S) - SCB	-6.636	3.721	838.164	-1.784	0.225
(MCB-U) - SCB	5.739	4.255	837.967	1.349	0.533

Table 8. Pairwise comparisons of estimated marginal means contrasting total length (mm) across strata for stock-sized Grass Carp.

pool	contrast	estimate	SE	df	t.ratio	p.value
26	(BWC-S) - (MCB-U)	71.560	19.159	1000.146	3.735	0.004
LG	(BWC-S) - (MCB-U)	-20.423	11.894	1000.633	-1.717	1
OR	(BWC-S) - (MCB-U)	NA	NA	NA	NA	NA
26	(BWC-S) - SCB	8.627	20.143	1000.762	0.428	1
LG	(BWC-S) - SCB	-64.359	8.947	1005.570	-7.194	< 0.001
OR	(BWC-S) - SCB	NA	NA	NA	NA	NA
26	(MCB-U) - SCB	-62.933	20.213	1001.433	-3.113	0.034
LG	(MCB-U) - SCB	-43.936	11.433	998.119	-3.843	0.002
OR	(MCB-U) - SCB	-16.393	34.891	997.967	-0.470	1

Conclusions

Overall, I think the CPUE inferences are very similar to what Andrew has in his poster. Hopefully these GLMMs provide a level of cross-factor marginalization and modeling sophistication that you were looking for.

The length inferences seem pretty straightforward, too, but I’d be interested in your take.

We can discuss any data/modeling decisions I made, the inferences you think can be drawn from them, and any other changes or additional analyses you’d like to add. I’m happy to chat over Zoom or email, just shoot me a message