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Scale eaters in Lake Tanganyika (Hori unpublished)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