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Persistence and fluctuation of Persistence and fluctuation of lateral dimorphism of fisheslateral dimorphism of fishes
Mifuyu NakajimaMifuyu Nakajima, Hiroyuki Mats, Hiroyuki Matsudauda and Michio Hori and Michio Hori, in submiss, in submiss
ionion
K.Morita
Prof.Shirakihara
M.MoriU.CateTown
M.Kai
M.Nakajima lived in Switzerland
Lateral dimorphism of scale eating cichlids in Lake Tanganyika
Righty
Lefty
Hori 1991 Science 267Hori 1991 Science 267
Overview• What is predator specific defense?What is predator specific defense?
• What is antisymmetric predation?
• Is laterality frequency really fluctuate? – If so, what is mechanism of fuluctation?
Prey is not solely victim, but has antipredator traits.
• Vigilance, Schooling, Refuge,
• There may be a trade-off between antipredator effort and other fitness component (e.g., foraging time)
1
2
3
plant
prey
predator
Antipredator effort against predator 1 is …
• [Nonspecific defense] effective against both predator species (types) 1 & 2;
• [Partly-specific] partly effective against 2;
• [Perfect-specific] not effective against 2 at all;
• [overly-specific] riskier against 2 than when it pais no attention to any predator.
Antipredator trait-mediated Exploitative Competition
1
322Increase predator 2
3
Decrease predator 3
Increase vigilance
Exploitative Mutualism (Matsuda, Abrams, Hori. Oikos 1993, 68:549-559)
1
322Increase predator 2
3
Increase predator 3
Watch more against 2
Quiz by Japan Automobile FedarationJAF News, the recent issue
How many points can you watch for simultaneously?
Apparent Competition(Holt, 1979)
1
32
1
Increase predator
Decrease prey 332
Increase prey 2
Apparent mutualism (Abrams & Matsuda 1996 Ecology 77:610-616)
1
32Increase prey 3
32
Increase prey 211
Predator focuses on prey 2
Predator-specific defense enhances
• Coexistence of predators.
• A more complex community strucutre
Matsuda with Abrams & Hori (1994, 1996, Evol. Ecol)
Food web in Lake Tanganyika
Coexistence of laterality dimorphism (antisymmetry)
Fre
qu
enci
es o
f le
ftie
s
Scale eaters in Lake Tanganyika (Hori unpublished)
Year of birth
Overview• What is predator specific defense?
• What is antisymmetric predation?What is antisymmetric predation?
• Is laterality frequency really fluctuate? – If so, what is mechanism of fuluctation?
-10 -5 0 5 10
relative trait values
freq
uen
cyThree types of Asymmetries
(van Valen 1962)
Directive asymmetry (DA)
Fluctuating asymmetry (FA)“Antisymmetry”
Antisymmetry in fishes
• Scale-eating cichlid in Lake TanganyikaScale-eating cichlid in Lake Tanganyika
• Lefties feed on scales of the left side, Lefties feed on scales of the left side, righties feed on scales of the right siderighties feed on scales of the right side
• Frequency dependent natural selectionFrequency dependent natural selection– Hori 1991 Science 267:
• Maintained by predator-specific defenseMaintained by predator-specific defense
Antisymmetry
• Bimodal distribution of laterality in crabs, snails, …
• Maintained by sexual selection
• Few reports of antisymmetry maintained by predation
Mud Fiddler Crabs (Uca pugnax) have antisymmetry in pincers http://www.assateague.com/mud-cr.html
More Story in Fish Laterality….• Another Tanganyikan fish has lateral asymmetAnother Tanganyikan fish has lateral asymmet
ry ry ((Mboko et al. 1998: Mboko et al. 1998: Zool. Sci. 15Zool. Sci. 15))
• A fresh water goby has A fresh water goby has lateral asymmetry lateral asymmetry in a in a Japanese riverJapanese river (Seki et al. 2000: (Seki et al. 2000: Zool. Sci. 17Zool. Sci. 17))
• Many fishes and other aquatic invertebrates have lMany fishes and other aquatic invertebrates have lateral antisymmetry! ateral antisymmetry! (Hori unpublished)(Hori unpublished)
• In these fishes, lefty is dominant heritage. In these fishes, lefty is dominant heritage. • Far too counterintuitive!Far too counterintuitive!• We need more evidence and theoretical reason...We need more evidence and theoretical reason...
Righty predators eat lefty prey, and vice versa.
• Lefties of scale-eating fish feed only on left side sLefties of scale-eating fish feed only on left side scales cales of leftiesof lefties, righties feed only on right side scal, righties feed only on right side scales es of rightiesof righties (Hori 1993 stomach contents, (Hori 1993 stomach contents, unpublunpublished lab experimentished lab experiment). ).
• Circa 75% of the stomach contents of righty and Circa 75% of the stomach contents of righty and lefty piscivorous predators (lefty piscivorous predators (LamprologusLamprologus spp.) spp.) were the lefty and righty, respectively (Hori were the lefty and righty, respectively (Hori unpublished field data).unpublished field data).
Is evidence still short?
Hori et al. (unpublished field data)
# stomach samples Prey PreyR L R L
Predator R 3 12 Predator R 2 6L sp1 L 10 2 L. sp2 L 9 2
R L R LPredator R 2 9 Predator R 3 7L. sp3 L 9 5 L. sp4 L 11 1
Why does a lefty catch a righty?(Michio Hori’s idea)
Definition of Antisymmetric Predation
• Both prey and predator have anti-symmetric traits (laterality);
• “Lefty” predators feed on “righty” prey; “Righty” predators feed on “lefty” prey.
Overview• What is predator specific defense?
• What is antisymmetric predation?
• Is laterality frequency really fluctuate? Is laterality frequency really fluctuate? – If so, what is mechanism of fuluctationIf so, what is mechanism of fuluctation??
Question…
• Does it really fluctuate?– Statistically significant (Hori unpubl)
• Does it really synchronize?
• If so, what mechanism promote fluctuation?
%le
ftie
s
Is evidence still short?
Hori et al. (unpublished field data)
• If frequency fluctuates, this is non-random sampling over several years.
• This is an evidence for either – Existence of antisymmetric predation or– Existence of laterality frequency fluctuation
Two-platoon lineups in MLB
No fluctuation is No fluctuation is reported in the reported in the frequency of lefty frequency of lefty pitchers and pitchers and batters in MLB or batters in MLB or College baseballCollege baseball
Our hypothesis for laterality fluctuation
Persistence and fluctuation in lateral antisymmetry is – Maintained by Antisymmetric
Predation, in analogy to Predator-specific defense
K
A two-trophic level system
yR
zL zR
yL
LRRLL zAy
K
zzr
dt
dz
1
LRL ydmAz
dt
dy][
RLR ydmAz
dt
dy][
RLRLR zAy
K
zzr
dt
dz
1
Lyapunov-type function of the symmetric 4 “population” system
• Trajectories converge the “line” zL+ z
R=2c/Bm (constant).
‡‡‡
‡‡‡
1 log1log1z
z
z
zz
x
x
x
xxL LLRR
2
1 22
( ) 2( ) L Rr Bm z z cd L L
dt B Km
< 0
Laterality frequency fluctuation mediated by antisymmetric predation
prey
predatorIncrease Lefty Predators
time
Fre
qu
enci
es o
f le
ftie
s
Decreasing righty prey = Increasing lefty prey
yL yR
zL zR
The system always has a neutrally stable equilibrium & cyclic orbits with any amplitude.
A = B = C = 1, r = 1, K=10, m=0.8, d=0.05, c=0.15
Any modification makes it stable or unstable.Any modification makes it stable or unstable.
Prey zPrey zRR
Predator xPredator xRR
% R
igti
es
time
Lefty
Rig
hty
Hori 1997
Scale eaters
Piscivores
Omnivory is common in Lake Tanganyika Fish Community
Algal eaters
Extension to Holt and Polis (1997)
x
z
yyz xy
dyy
dtmA z A x d
1 xz yzdz z
r A x A y zdt k
xy xz
dx
dtA y A z xm c
• Where k = K/2
Three trophic levelsThree trophic levels
xL xR
yL yR
zL
zR
• 6 “populations” (3 sp.×{Lefty, Righty}
• X: scale eaters• Y: piscivores• Z: algal feeders• X preys on both y and z.
Does omnivory destabilize or stabilize Does omnivory destabilize or stabilize the antisymmetric predation system?the antisymmetric predation system?
Lefties increase
Righties increase
Righties increase
if X is omnivory, lefties increase
Transition diagram
?
Invasibility analysis
dxR/dt/xR >0 if xR is invasible
xR
yL
Asymmetric equilibrium is always invasible.
0 1 2 3 4 5Axz
0
1
2
3
4
5
zyA ④
①
③②
⑤
Axy=1 m=0.8 K=5 r=1 c=0.5 d=0.5
E dxR/dt dyL/dt
① NE NE NE
② St. - +③ St. + +④ St. + -⑤Unst. + +
A
B
6 “population” dynamic model6 “population” dynamic model
LR R L
dyy
dtmAz Cx d
1L L RR R L
dz z zr Bx Ay z
dt K
LR R L
dx
dtCy Bz xm c
Prey on yRPrey on zR
Prey on zRPreyed by xR
• For For lefties (asexual reproduction model)
Population genetic model (1-locus-2-alleles)
, (1 )ii a i i i i i i
dpp w w p p f g
dt
Righties : allele a: gene frequency pi
Lefties : allele A: gene frequency 1-pi
GenotypesPhenotypic frequency
Fitness
Righty aa pi2 fi
Lefty AA Aa (1-pi2) gi
fx = m Axy Ny (1- py2) + m AxzNz(1-pz
2) – c
Equilibrium gene frequency1 1 1
( , , ) , ,2 2 2
x y zp p p
Phenotypic frequency: 2 2 2 1 1 1( , , ) , ,
2 2 2x y zp p p
From local stability analysis, this is always an unstable focus.
2 2 22 10, 3 2 2 , b b m C xy B xz A yz
3 22 1 0 0b b b
0 5 2 7 (1 )b ABCxyzm m
b0b1-b2 < 0
b0
% R
igh
ties
time
Simulation exhibits a stable limit cycle.
A=1.3 B=0.25 C=1 m=0.8 K=5 r=1 c=0.5 d=0.5
It qualitatively explains the field observation.It qualitatively explains the field observation.
zz
yy xx
We must apply our model to the entire community (Hori unpublished)
Our model results• Under the perfect anti-symmetric pre
dation, no force (“friction”) to stabilize a 1:1 laterality ratio exists.
• Omnivory destabilizes 1:1 laterality ratio and enhances a stable limit cycle (coexistence with fluctuation).– Nakajima, Matsuda, Hori (in review)
Why did laterality evolve?
• Scale-eaters first evolved laterality, because they attack either side scales.
• “Prey” needed to evolve laterality to improve predator-specific defense
• …What story is possible in the absence of scale-eaters???
• Measure quantitative trait in laterality
I don’t know
Lateral dimorphism is
Single-locus Mendellian inheritanceSeen in most of fishes (Hori unpubl)Maintained by antisymmetric predation Fluctuation & coexistence in omnivory[Overly?] predator-specific defenseThis is a new story of Antisymmetry
Competitive exclusion of laterality in amino acids
L-amino acids D-amino acids
Omnivory is probably important for coexistence