Talk on the use of State-Space Capture-Recapture models and Matrix Analysis to understand the dynamics of posthumous reproduction in guppies. Guppy females store male sperm, which means that males can produce offspring after death.

1. Beyond
Life+me
Reproduc+ve
Success
The
dynamics
of
posthumous
reproduc+on
in
Trinidad
guppies
Andrés
López-­‐Sepulcre

2. Collaborators
General Protocol
Swanne
Gordon
Univ.
Jyväskylä
Finland
•! 3 scales sampled, stored
dry in tubes
•! DNA isolation (enough for
~50 PCRs)
•! Genotype at ~12
microsatellite loci (more
available)
•! Parentage assignment
via CERVUS, PAPA,
PASOS…
Paul
Bentzen
&
Ian
Paterson
Dalhousie
Univ.
Canada
David
Reznick
Univ.
California,
Riverside
USA

3. Sperm
Storage
in
Animals
• Common
in
many
species
• Can
lead
to
posthumous
reproduc+on
• Its
dynamics
in
nature
largely
unknown
• Evolu+onary
significance?

4. Trinidadian
guppy,
Poecilia
re*culata
• Two
dis+nct
phenotypes
associated
to
preda+on
and
resources
• Differences
in
mul+ple
traits
and
ecological
effects
• Several
independent
evolu+onary
events
• Rapid
evolu+on
aSer
transloca+on

5. Experimental
evolu+on
in
the
wild
Reznick et al. 1990. Nature

6. Guppy
Mark
Recapture
• All
individuals
>14mm
individually
marked
• Followed
monthly
• Gene+c
samples
for
pedigree
reconstruc+on

7. Closed
canopy
Capture probabilities
h2 = 0.30
Male
Size
at
Maturity

8. Evolu+on
of
male
size
• Common
garden
Derived
Source
Popula+on

9. Survival
Standard Length (mm)
Survival probability

10. ALIVE Reproduc+on
• Larger
individuals
reproduce
less
…
but
we
had
only
counted
the
live
ones
• Guppy
females
store
male
sperm
• Hot
Propor+on
of
recruits
sired
to
count
in
the
dead?
Standard
Length
(mm)

11. Juvenile
(J)
State
Space
Models
Mature not
reproducing
(M)
Mature
reproducing
(R)
Dead
reproductive
(S)
!J
(1" μ)
!M
(1" #)
!R
!S
!J μ 1 " # ( )
!J μ"
!M"
! 1 " #M ( )$
1 ! "R ( )#
3 months
Conception
! R"R#R
! S"S#S
• Define
model
that
defines
unobserved
biology
Model
includes
transi+on
between
states
Mature
Not
Reproduc+ve
Mature
Reproduc+ve
Dead
Juvenile
Reproduc+ve

12. State
Space
Models
• Overlay
an
observa+on
model
• Data
is
a
result
of
the
observa+on
model
condi+onal
on
the
biology
model
• We
can
es+mate
‘invisible’
biological
parameters
Alive
Alive
Not
Rep.
Observed
Not
Rep
Not
Obs
Alive
Alive
Alive
Zombie
Zombie
Dead
Not
Rep.
Not
Obs.
Reproduced
Observed
Reproduded
Not
Obs
Not
Rep
Not
Obs
Not
Rep.
Not
Obs.

13. Results
●
● ●
●
● ●
●
●
0 1 2 Months 1 2 3 4 5 6 7 8 9 10
reproductive
●
●
(b) Dead males
●
● ●
●
●
●
●
●
● ●
0 1 2 3 4
(c) Females Individual
1 2 3 4 5 6 7 8 9 10
Months dead
Individual contribution to population recruitment (%)
● ● ● ● ●
● ●
●
●
●
1 2 3 4
contribu+on
to
recruitment
…whatever

14. Results
Dead reproductives (S)
Reproductive adults (R)
Non−reproductive adults (M)
Juveniles (J)
2 4 6 8 10 0 50 100 150
Months since introduction Number of males
●
●
●
●
●
●
●
●
●
●
2 4 6 8 10
0.00 0.05 0.10 0.15 0.20 0.25 0.30
Months since introduction
Proportion of new recruits sired by dead males

15. Does
size
macer?
ALIVE DEAD
ALIVE DEAD
Propor+on
of
recruits
sired
Standard
Length
(mm)
Propor+on
of
recruits
sired
Standard
Length
(mm)

16. Thoughts
• How
does
storage
affect
natural
selec+on?
– Maintenance
of
diversity
– ‘Bet-­‐hedging’

17. Thoughts
• How
does
storage
affect
sexual
selec+on?
– Opera+onal
Sex
Ra+o
– Male-­‐male
compe++on
Carotenoid HP
Source
Canopy Open
Proportion showing color

18. Thanks!

19. Sensi+vity
&
Elas+city
Analysis

20. Focal
Experiment
• Individual
based
data
• Monthly
• Phenotype
(pictures)
• Pedigree
and
gene+c
samples
• >15,000
ind,
>10
genera+ons
• ~90%
recapture
rates
• Ecosystem
data
• Physical
variables
• Bimonthly
es+mate
of
compartments
• Annual
15N
drip
Mesocosms
• Ecological
effects
Laboratory
• Common
garden
phenotyping
Structure
of
the
study
Paul Bentzen,
Ian Paterson
(Univ. Dalhousie)

21. Open
canopy
h2 = 0.16
Mature
male
size

22. Reproduc+on
ALIVEDEAD
ALIVEDEAD
Random effects: Groups Name Variance Std.Dev.
FishID (Intercept) 1.06576 1.03236 fSampling
(Intercept) 0.45851 0.67713 Number of obs: 737, groups:
FishID, 107; fSampling, 12Fixed effects:
Estimate Std. Error z value Pr(>|z|) (Intercept)
2.1571 3.4374 0.628 0.5303 SL
-0.5340 0.2004 -2.665 0.0077 ** aliveFALSE
-16.7792 3.6527 -4.594 4.35e-06 ***SL:aliveFALSE
1.0186 0.2124 4.796 1.62e-06 ***
Random effects: Groups Name Variance Std.Dev.
FishID (Intercept) 2.09198 1.44637 Sampling
(Intercept) 0.59734 0.77288 Number of obs: 661, groups:
FishID, 101; fSampling, 12Fixed effects:
Estimate Std. Error z value Pr(>|z|) (Intercept)
-7.97496 4.07333 -1.958 0.0502 .SL
0.01998 0.22781 0.088 0.9301 aliveFALSE
1.26180 3.23465 0.390 0.6965 SL:aliveFALSE
0.02183 0.18019 0.121 0.9036

23. Control
Guppies
(HP)
Natural
resource
levels
Control
Guppies
(HP)
High
resources
(canopy
thinned)
Control
Guppies
(LP)
Control
Guppies
(?)
evolu+on
x2
Experimental
Evolu+on