Generating Survival Estimates

DART offers an online and simplified version of survival and travel times estimates based on programs PitPro and SURPH using first and last detection history generated from the DART database.

The survival estimates are calculated for a population of PIT-tagged fish as defined by the query.

1. The Survival Estimates tool uses Cormack-Jolly-Seber (CJS) estimates. The query results provide estimates and standard errors for the survival and detection probabilities, and the product of the final survival and detection probabilities. The standard error of all estimates are reported in parentheses. The estimate of the overall survival probability, i.e., the product of all the survival estimates, is reported as well.
2. For the CJS estimates to be valid, the following assumptions must be met:
   1. Individuals marked for the study are a representative sample from the population of interest.
   2. Survival and capture probabilities are not affected by tagging or detection. That is, tagged fish have the same probabilities as untagged fish.
   3. All detections are "instantaneous." That is, detection takes a negligible amount of time or distance relative to the length of the reaches between detection events.
   4. The fate of each tagged individual is independent of the fate of all others.
   5. All tagged individuals alive at the beginning of a reach have the same probability of surviving until the end of that reach.
   6. All tagged individuals alive at the beginning of a detection site have the same probability of being detected at that site.
   7. Each individual detected at a particular detection site has the same probability of being removed, and the probability of removal is independent of the survival process.
3. There are several limitations to the Survival Estimates produced by this tool.
   1. Depending on the selection criteria, the survival estimates will tend to over-pool releases.
   2. If you do not define the PIT Tag group specifically by a release site, then different release sites (and travel distances) will be included in the group; hence the assumption that all individuals have the same probability of survival may be violated for the first reach (release point to the first dam). Survival estimates for the other reaches (dam to dam) will be fine.
   3. If the PIT Tag group includes fish released from the same location but at different times, then the estimates will be a weighted average over time as a function of release size. If the probability of survival varies over time, the assumption that all individuals have the same probability of survival may be violated.
   4. The Survival Estimates tool is unable to produce estimates for the last dam because detection efficiency cannot be distinguished from survival for the final reach.
   5. Survival estimates are generated from capture histories for each fish that are based on data downloaded from the PTAGIS database system. The particular data used for these estimates contain only last detections and therefore do not take into account the full detection history for a fish at a given site and may not account for errors in detection sequence recording. This may lead to minor over censoring of the data that in turn may lead to slightly higher standard errors in parameter estimates when compared to systems that use the full detections history of the fish.
   6. Results may be biased low for survival estimates generated during the in-season before the run is complete.

Survival estimates are generated from capture histories for each fish that are based on data downloaded from the PTAGIS database system and aggregated by DART. The particular data used for these estimates contain only last detections and therefore do not take into account the full detection history for a fish at a given site and may not account for errors in detection sequence recording. This may lead to minor over censoring of the data that in turn may lead to slightly higher standard errors in parameter estimates when compared to systems that use the full detections history of the fish.

Survival Estimates require at least 2 detection sites. Generating estimates is a complex process. The greater the number of total fish released, the longer it will take to generate either Survival or Mean Travel Time Estimates.

Note on Last Detection Site pooling Program PitPro allows user configuration for detection site pooling. With the online version, detections below the last site are pooled with the user-selected last site by default, e.g., any detections at the Columbia River estuary pile dike antennas will be pooled with user-selected last site TWX.

Mean Travel Time Estimates

The mean travel times are calculated for a population of PIT-tagged fish as defined by the query.

The travel time estimates are based on the release date for each pit-tagged fish as recorded in the PTAGIS database (and uploaded to the Columbia River DART database) and the first and last detection times at each downstream detection site. Travel Time estimates for release to downstream detection site are calculated using the release time and the time of the first detection at the downstream detection site. Between detection sites travel time estimates are calculated using the time of the last detection at the upstream site and the time of the first detection at the downstream site.

( reach travel time ) / number of unique fish detected at the detection sites

number of unique fish detected at the detection sites / ( (1/reach travel time) )

When dealing with travel times, we are primarily interested in the speed with which fish travel from point A to point B. A good statistic for describing a particular group's speed is the harmonic mean. A harmonic mean is used when working with rates of speed, usually the number of days to travel a set distance. A benefit to using the harmonic mean is that it is more robust in the presence of outliers (i.e., a very fast or slow fish).

FAQ

Question:   I have tags detected at "x" site, why do I get an estimate of 0 detection probability?

Answer:

CJS survival and detection probabilities are estimated by maximizing the likelihood of the observed detection histories. Detection probabilities are estimated by using tags that were detected both above and below a site (thus, known to have passed that site), and calculating the proportion of those that were observed AT that site. The observed count at a dam is then expanded using the detection probability (i.e., observed/(probability of detection)) to estimate the survival probability to that site. For the last reach in model, only the probability of surviving to AND being detected at the last site in the study can be estimated, as there is no information of why a tag was not detected (did the tag fail/fish die before the last site, or did it pass undetected?).

Using tags known to have been above & below each site can create some counter-intuitive estimates, such as estimating zero probability of detection when there were tags detected. This occurs when none of the tags detected at the site were subsequently detected, and are not included in the estimation process. Further, when a site has an estimated near 0% detection probability, the estimated number of tags to have passed that site can be greatly overinflated.

Results that include "nan" or "-inf" are indicators that there is not enough information (detections) to estimate all the probabilities included in the model. Though the "full" model may not be estimable, a user may be able remove detection sites with no detections from the model, recognizing this will result in some estimates representing multiple reaches. Another possible approach would be to pool detection sites (starting at the end and moving upriver) to increase total last detection counts. The interpretation of this last pooled site is be that tags survived to at least the first detection site in the pooled group and were detected.

Example:

Population analyzed: 2021, Chinook, released at METH, all available tags.

Cormack/Jolly-Seber Estimates

(Cormack 1964, Jolly 1965, Seber 1965)

Survival Estimates

Population	Site 1	Site 2	Site 3	Site 4	Overall
webrequest	0.741 (0.0352)	0.745 (0.2852)	inf (nan)	0.000 (nan)	nan (nan)

Capture Probability Estimates

Population	Site 1	Site 2	Site 3	Site 4	Final capture*survival
webrequest	0.532 (0.0262)	0.019 (0.0076)	0.000 (nan)	0.200 (0.1265)	0.007 (0.0048)

Covariance Matrices

	S1	S2	S3	S4	P1	P2	P3	P4
S1	0.00123837	-0.00120561	0	0	-0.000860386	0	0	0
S2		0.0813488	-inf	0	0.000865003	-0.00202818	0	0
S3			nan	nan	0	inf	nan	0
S4				nan	0	0	nan	0
P1					0.00068594	0	0	0
P2						5.82136e-05	0	0
P3							nan	0
P4								0.016

	
Legend:

Main Fields:
	RRH - Rocky Reach Dam
	MCN - McNary Dam
	JDA - John Day Dam
	BON - Bonneville Dam Complex

Final Field:
	TWX - Estuary Towed Array (Exp.)


Survival Reaches:
	1: Release-RRH
	2: RRH-MCN
	3: MCN-JDA
	4: JDA-BON

Capture Sites:
	1: RRH
	2: MCN
	3: JDA
	4: BON

Subset of TagIDs in Population sorted by Outcome at JDA (2=censored, 1=detected, 0=not detected); TagIDs detected at JDA are not detected downstream (BON or TWX) or upstream MCN

tagid	Released	RRH	MCN	JDA	BON	TWX
3DD.003DE65571	1	0	0	2	0	0
3DD.003DE646C7	1	0	0	1	0	0
3DD.003DE64768	1	0	0	1	0	0
3DD.003DE647F9	1	1	0	1	0	0
3DD.003DE648C1	1	1	0	1	0	0
3DD.003DE64AF6	1	0	0	1	0	0
3DD.003DE64BA0	1	0	0	1	0	0
3DD.003DE64BB9	1	0	0	1	0	0
3DD.003DE64D07	1	0	0	1	0	0
3DD.003DE64E90	1	1	0	1	0	0
3DD.003DE64EBA	1	1	0	1	0	0
3DD.003DE651D7	1	0	0	1	0	0
3DD.003DE656C0	1	0	0	1	0	0
3DD.003DE6571F	1	1	0	1	0	0
3DD.003DE65873	1	0	0	1	0	0
3DD.003DE6598D	1	1	0	1	0	0
3DD.003DE63DE1	1	1	0	0	0	0
3DD.003DE64615	1	1	0	0	0	0
3DD.003DE64617	1	0	0	0	0	0

Rerunning the survival estimates request by selecting "Individual Sites" RRH, MCN, BON, and TWX; it is possible to generate survival estimates to Bonneville for the population.

Survival Estimates

Population	Site 1	Site 2	Site 3	Overall
webrequest	0.733 (0.0352)	0.715 (0.2737)	0.573 (0.4215)	0.300 (0.1894)

Capture Probability Estimates

Population	Site 1	Site 2	Site 3	Final capture*survival
webrequest	0.537 (0.0267)	0.020 (0.0082)	0.200 (0.1265)	0.007 (0.0048)

Covariance Matrices

	S1	S2	S3	P1	P2	P3
S1	0.00124105	-0.00117186	0	-0.000880262	0	0
S2		0.0749035	-0.0590233	0.000858832	-0.00208627	0
S3			0.177643	0	0.00167073	-0.0455006
P1				0.000714381	0	0
P2					6.67802e-05	0
P3						0.016

Legend:


Main Fields:
	RRH - Rocky Reach Dam
	MCN - McNary Dam
	BON - Bonneville Dam Complex

Final Field:
	TWX - Estuary Towed Array (Exp.)


Survival Reaches:
	1: Release-RRH
	2: RRH-MCN
	3: MCN-BON

Capture Sites:
	1: RRH
	2: MCN
	3: BON