Session B1- Sample size and statistical considerations for the estimation of American shad upstream fish passage efficiency

Transcription

1 University of Massachusetts - Amherst ScholarWorks@UMass Amherst International Conference on Engineering and Ecohydrology for Fish Passage International Conference on Engineering and Ecohydrology for Fish Passage 2011 Jun 27th, 10:20 AM - 10:40 AM Session B1- Sample size and statistical considerations for the estimation of American shad upstream fish passage efficiency Stephen H. Arnold HDR/DTA Alan Wells HDR Follow this and additional works at: Arnold, Stephen H. and Wells, Alan, "Session B1- Sample size and statistical considerations for the estimation of American shad upstream fish passage efficiency" (2011). International Conference on Engineering and Ecohydrology for Fish Passage This Event is brought to you for free and open access by the The Fish Passage Community at UMass Amherst at ScholarWorks@UMass Amherst. It has been accepted for inclusion in International Conference on Engineering and Ecohydrology for Fish Passage by an authorized administrator of ScholarWorks@UMass Amherst. For more information, please contact scholarworks@library.umass.edu.

2 Sample Size and Statistical Considerations for the Estimation of American Shad (Alosa sapidissima) Upstream Passage Efficiency at the York Haven Hydroelectric Project Stephen H. Arnold, HDR DTA, Portland, ME and Alan W. Wells, Ph.D., HDR, Pearl River, NY June 27, 2011

3 West Branch Susquehanna River Williamsport Scranton Wilkes-Barre Lewistown Sunbury Susquehanna River Huntingdon Juniata River P E N N S Y L V A N I A M A R Y L A N D Harrisburg Susquehanna River 1904 York Haven 1931 Safe Harbor 1910 Holtwood 1928 Conowingo Chesapeake Bay

4 Restoration Goal: 2 Million Adult Shad Above York Haven Dam Seine haul mouth of Susquehanna River, late 1800 s

5 Fish Passage Current 1991 Conowingo lift 1997 Safe Harbor lift 1997 Holtwood lift 2000 York Haven ladder York Haven Fish Ladder Earlier Efforts Trap and Transport of shad from Conowingo to above York Haven > 200,000 shad Phased-out Conowingo Dam

6 Susquehanna River American Shad Passage , , , , , ,000 80,000 60,000 40,000 20, Conowingo Holtwood Safe Harbor York Haven

7 Shad Upstream Passage Efficiency as Ratio of Downstream Dam Passage 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Holtwood Safe Harbor York Haven

8 Safe Harbor

9 Annual Flow Data (cfs) Susquehanna River Flows USGS Harrisburg Gage Annual Flow Duration Curve Safe Harbor York Haven % 10.00% 20.00% 30.00% 40.00% 50.00% 60.00% 70.00% 80.00% 90.00% % Percent Exceedance

10 Susquehanna River Safe Harbor to York Haven Reach

11 York Haven

12 York Haven Project Layout

13 York Haven East Channel Fishway

14

15 Provide a statistically valid estimate of the passage efficiency* of American shad at the York Haven fish ladder. How many fish must be tagged? How many seasons must the study be repeated? *Passage Efficiency Rate (PER) = number passing divided by the number desiring to pass.

16 But what is, statistically valid? Robson and Regier (1964)* suggest the following standards (α = 0.05): ±50% for preliminary studies ±25% for management studies ±10% for careful research studies * Robson, D.S. and H.A. Regier (1964). Sample size in Petersen markrecapture experiments. Trans. Amer. Fish. Soc., 93:

17 N Simple Problem? PR= P YH /P SH Numeric Results for Two-Sided Confidence Intervals for One Proportion Confidence Interval Formula: Exact (Clopper-Pearson) Sample Confidence Size Target Actual Proportion Lower Upper Width if Level (N) Width Width (P) Limit Limit P = References Fleiss, J. L., Levin, B., Paik, M.C Statistical Methods for Rates and Proportions. Third Edition. John Wiley & Sons. New York. Newcombe, R. G 'Two-Sided Confidence Intervals for the Single Proportion: Comparison of Seven Methods.Statistics in Medicine, 17, pp ± CI % N N vs C.I. Width with C.L.=0.95 P=0.080 C.I. One Proportion C.I. Width

18 YH/SH Ratio YH/SH vs Year Year

19 LN(York_H aven) LN(Safe_Harbor) P YH = P SH n = 10; r 2 = 0.888

20 YES Is k > 1000? Randomly Select Number Passing at Safe Harbor (P SH ) YES YES Is i > N Years? Is j > N Tags? k = k+1 NO NO Select, with Replacement, Random Record from Table 1 with Replacement NO Duplicate and Store the i th Record 1 j = j+1 i = i+1 2 Store calculated probability from regression model Summarize Results and Print Year Bootstrap Analysis P SH , , , , , , , , , , , ,994

21 95% CI = exp( x ln(years) x ln(tags), R 2 = 0.968

22 Sample Size Increase Resulting from Year-to-Year Variation Design Annual N Total N for ± 25% CI Binomial years years years years years years years years Incorrect, does not account for year-toyear variation in YH/SH. Increasing penalty for fewer years sampled.

23 Findings Demonstrated a significant relationship between the number of shad passing Safe Harbor and the number passing York Haven Probability of passage at York Haven (YH/SH) increases with number of shad passing Safe Harbor density-dependent passage efficiency..??? Substantial increase in sample size needed to account for year-to-year variation with penalty for decreasing study years Able to successfully propose and support statistically valid study design Able to put short term results available during the FERC regulatory timeframe into proper statistical context

24 QUESTIONS?