Post on 14-Jan-2016
description
Royal Netherlands Institute for Sea Research
1
Seasonal timing of reproduction in the bivalve Macoma balthica: a model study of fitness consequences
NVTB 2008
Jaap van der Meer
2
Question
Timing of reproduction: Make sure the larvae can grow up under optimal food conditions
Spawn just before the spring bloom
Many species don’t do this
An why should they?
Alternative rule: Make sure the bloom occurs at the size of maximum growth
3
System
Semi-chemostat
Seasonal pattern in food concentration of inflowing water
Seasonal pattern in temperature
Standard DEB model
Macoma balthica parameters as estimated by Van der Veer et al. (2006)
R extremely small: 0.012%; background mortality
One spawning event per year
4
60 days after
5000 5010 5020 5030 5040 5050
3.5e
+08
4.5e
+08
5.5e
+08
6.5e
+08
year
popu
latio
n si
ze
5
110 days after
2500 2550 2600 2650
2e+
083e
+08
4e+
085e
+08
year
popu
latio
n si
ze
6
160 days after
0 10 20 30 40 50
2e+
083e
+08
4e+
085e
+08
6e+
08
year
popu
latio
n si
ze
7
Spawning date: bifurcation analysis
-100 0 100 200
2e+
083e
+08
4e+
085e
+08
6e+
087e
+08
days before the plankton peak
popu
latio
n si
zeafter before
8
160 days after
0 1 2 3 4 5 6 7
8.3
8.5
8.7
year
log n
um
bers
0 1 2 3 4 5 6 7
200
400
600
800
year
food
0 1 2 3 4 5 6 7
56
78
year
log n
um
bers
0 1 2 3 4 5 6 7
0.0
0.2
0.4
0.6
year
length
0 1 2 3 4 5 6 7
0100
200
300
year
reserv
es
1200 1400 1600 1800
0.0
0.2
0.4
0.6
e
length
9
Adaptive dynamics
Introduce a mutant that has no effect on the (food) environment, and see whether it can invade
In a k-year cycle of the resident, mutants are introduced during each of k succeeding years
In one run, three types of mutants were introduced: the first
group spawns slightly earlier, the second group does as the residents, the last group spawns slightly later
Mutants
10
12000 12050 12100 12150 12200 12250 12300
1213
1415
16
time in years
log
num
bers
11
Invadability
0 5000 10000 15000 20000
1012
1416
1820
time in years
log
num
bers
after before
12
140 days before the plankton peak
0 200 400 600 800 1000 1200 1400
010
020
030
0
age
repr
oduc
tion
13
140 days before the plankton peak
700 705 710 715 720 725 730
140
150
160
170
180
age
repr
oduc
tion
14
60 days after the plankton peak
0 200 400 600 800 1000 1200
050
100
150
200
250
300
age
repr
oduc
tion
15
60 days after the plankton peak
1050 1060 1070 1080 1090 1100
220
240
260
280
300
age
repr
oduc
tion
16
Individual state
800 1000 1200 1400 1600 1800 2000
0.00
0.05
0.10
0.15
0.20
0.25
0.30
reserves
volu
me
17
Invadability
0 5000 10000 15000 20000
1012
1416
1820
time in years
log
num
bers
after before
18
Preliminary conclusion
Stable strategy: spawn exactly half a year before the food peak
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Next steps
Present survival rule: [E]/[Em] > L/Lm
Resorption of reproductive material
Low R
A-symmetric interference, which decreases the competitive ability of the youngsters