573
574
575
Supplemental Material for Carlson et al. “Four decades of opposing natural and
human-induced artificial selection acting on Windermere pike (Esox lucius)”
576
APPENDIX S1
577
578
Recapture probabilities
579
Using the software MARK (White & Burnham 1999), we fit 37 years of CMR data
580
(Haugen et al. 2006) to a multistate model structure known as the Conditional Arnason
581
Schwarz model (Brownie et al. 1993; Nichols & Kendall 1995) to generate estimates of
582
the seasonal recapture probabilities (Table S1). As sampling occasions lasted for 3
583
months, we pooled all captures into a mid-point date within each period, which is
584
equivalent to saying that two individuals captured less than 3 months apart were defined
585
to be captured at the same date.
586
In the current study, we wanted to estimate the seasonal recapture probabilities
587
over the four capture occasions following each spring occasion (the reference occasion,
588
a, at which the individuals were measured). Hence, with respect to the recapture
589
parameters, we fit a combined age and cohort model, where each cohort (i.e., individuals
590
that were measured at the same reference occasion) was estimated to have unique
591
occasion-specific (t) recapture probabilities over the four subsequent occasions following
592
the reference occasion. For occasions beyond the fourth relative occasion the model was
593
constrained to estimate constant seasonal recapture probabilities. Hence, the capture
594
probability model fitted was:
595
 a   t , if t - a  5
Pr( p)  
, if t - a  5
 t .
596
where  and  are coefficients under estimation on a logit scale. The t notion corresponds
597
to constant season-wise estimates. The survival part of the model was constrained so as to
598
vary over time (annual scale) with an additive effect of basin (Pr(S) = basin + t), whereas
599
the dispersal probabilities () were constrained to be basin-specific and constant over
600
time on an annual scale (Pr() = basin, see also Haugen et al. 2006). In total, the model
601
fitted involved 214 parameters, of which 198 were estimable. The logit parameters were
602
estimated by numerically maximizing the log-likelihood function with respect to the
603
parameters using the software MARK (White & Burnham 1999). Owing to data
604
sparseness in the 1980s, all season-specific parameters were constrained to similar for the
605
1980 to 1986 period. The model fitted was over-dispersed, so confidence intervals were
606
adjusted using variance inflation factor ofthat was retrieved from the model’s 2
607
divided by its degrees-of-freedom.
608
Note also that the long lifespan of Windermere pike (up to 17 years, Frost &
609
Kipling 1967) combined with multiple recapture events facilitated our ability to recapture
610
fish that were still alive (see also Fig. S1).
611
612
References
613
Brownie, C., Hines, J.E., Nichols, J.D., Pollock, K.H. & Hestbeck, J.B. (1993). Capture-
614
recapture studies for multiple strata including non-Markovian transitions.
615
Biometrics, 49, 1173-1187.
616
Frost, W.E. & Kipling, C. (1967). A study of reproduction, early life, weight-length
617
relationship and growth of pike, Esox lucius L., in Windermere. J. Anim. Ecol.,
618
36, 651-693.
619
Haugen, T.O., Winfield, I.J., Vøllestad, L.A., Fletcher, J.M., James, J.B. & Stenseth, N.C.
620
(2006). The ideal free pike: 50 years of fitness-maximizing dispersal in
621
Windermere. Proc. R. Soc. Lond. B., 273, 2917-2924.
622
623
624
625
626
Nichols, J.D. & Kendall, W.L. (1995). The use of multi-state capture-recapture models to
address questions in evolutionary ecology. J. Appl. Stat., 22, 835-846.
White, G.C. & Burnham, K.P. (1999). Program MARK: survival estimation from
populations of marked animals. Bird Study, 46, 120-139.
627
Table S1 Using the
Program MARK, we calculated the probability of recapturing an
628
individual given that it was still alive (see Methods). In particular, we calculated this
629
parameter for each of the first four samples following the spring sampling occasion
630
during which body length was measured.
relative recapture occasion
season
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980-1986
631
632
633
634
635
636
637
638
639
640
1
2
3
4
winter
spring
winter
spring
0.18 (0.06)
0.13 (0.03)
0.29 (0.06)
0.23 (0.06)
0.24 (0.09)
0.16 (0.04)
0.14 (0.03)
0.11 (0.03)
0.08 (0.03)
0.28 (0.04)
0.45 (0.05)
0.30 (0.08)
0.44 (0.08)
0.40 (0.07)
0.33 (0.05)
0.24 (0.03)
0.20 (0.03)
0.19 (0.03)
0.35 (0.04)
0.37 (0.06)
0.30 (0.07)
0.37 (0.09)
0.27 (0.06)
0.23 (0.12)
0.20 (0.07)
0.19 (0.07)
0.34 (0.12)
0.21 (0.02)
0.34 (0.11)
0.14 (0.04)
0.14 (0.06)
0.33 (0.10)
0.05 (0.05)
0.16 (0.07)
0.36 (0.07)
0.18 (0.05)
0.24 (0.06)
0.30 (0.05)
0.27 (0.07)
0.09 (0.06)
0.04 (0.04)
0.54 (0.11)
0.23 (0.08)
0.27 (0.06)
0.25 (0.05)
0.20 (0.04)
0.19 (0.05)
0.24 (0.07)
0.16 (0.07)
0.14 (0.09)
0.18 (0.07)
0.13 (0.12)
0.09 (0.06)
0 (Not estimable)
0.02 (0.04)
0.06 (0.02)
0.43 (0.12)
0.18 (0.04)
0.53 (0.12)
0.43 (0.11)
0.44 (0.15)
0.21 (0.07)
0.26 (0.06)
0.16 (0.04)
0.29 (0.06)
0.37 (0.06)
0.44 (0.08)
0.32 (0.12)
0.31 (0.12)
0.61 (0.14)
0.25 (0.08)
0.33 (0.06)
0.28 (0.05)
0.42 (0.06)
0.58 (0.07)
0.37 (0.10)
0.70 (0.12)
0.32 (0.12)
0.53 (0.09)
0.40 (0.18)
0.33 (0.17)
0.32 (0.10)
0.33 (0.22)
0.33 (0.05)
0.25 (0.15)
0.03 (0.02)
0.28 (0.16)
0.26 (0.13)
0.11 (0.10)
0.27 (0.10)
0.21 (0.08)
0.24 (0.06)
0.36 (0.09)
0.19 (0.07)
0.17 (0.08)
0.24 (0.15)
0.25 (0.16)
0.26 (0.21)
0.12 (0.08)
0.07 (0.04)
0.37 (0.08)
0.27 (0.08)
0.28 (0.10)
0.09 (0.06)
0 (0)
0.31 (0.17)
0.25 (0.11)
0.22 (0.2)
0 (0)
0.08 (Not estimable)
0 (Not estimable)
0.05 (0.02)
641
Figure S1 Cumulative
number of recaptures as a proportion of the total recaptures from a
642
given focal spring as a function of the relative recapture event (1 = winter of focal year, 2
643
= following spring, and so on). All fish that were never recaptured were assumed dead for
644
the natural selection analysis and were assigned a fitness of zero. This plot illustrates the
645
importance of multiple recapture occasions to our fitness assignments as all fish that were
646
alive at the end of the period of interest (i.e., at the winter sample in the focal year,
647
relative recapture occasion = 2) were not captured in the winter sample. Rather, many of
648
these individuals were captured during some future sampling event (i.e., relative
649
recapture occasion > 2). Multiple sampling occasions thus minimized the probability that
650
we incorrectly assigned a fish that was alive a fitness of zero. Each line represents the
651
data included in one selection analysis (i.e., one focal year). In particular, we plotted the
652
proportion of new recaptures for every fifth year included in the natural selection analysis
653
(i.e., 1953, 1958, 1963, 1968, 1973, 1978, 1983)
0.0
0.2
0.4
0.6
from a given focal spring
0.8
cumulative number of recaptures as a proportion of total recaptures
1.0
Figure S1
5
10
15
relative recapture occasion
20
25