Intraspecific Trait Variation and its Effects on Food Chains

Intraspecific Trait Variation and its Effects on food chains Don deangelis University of Miami Coral gables, florida USa Workshop on Nonlinear Equations in Population Biology East China normal University Shanghai, china May2527,2013

Intraspecific Trait Variation and its Effects on Food Chains Don DeAngelis University of Miami Coral Gables, Florida USA Workshop on Nonlinear Equations in Population Biology East China Normal University, Shanghai, China May 25-27, 2013

Intraspecific Variation 1. Traits such as skill at foraging and investment in anti predator defense may vary among individuals within a species population. 2. Traits such as the choice of what sort of habitat to utilize can also vary among individuals of a population Here the effects of both types of variation are examined This intraspecific variation has implications for both fitness strategies within a population and food web dynamics

Intraspecific Variation 1. Traits such as skill at foraging and investment in anti￾predator defense may vary among individuals within a species population. 2. Traits such as the choice of what sort of habitat to utilize can also vary among individuals of a population. Here the effects of both types of variation are examined. This intraspecific variation has implications for both fitness strategies within a population and food web dynamics

. Intraspecific Variation in foraging ability predator avoidance, and other mortality risk Intraspecific variation within populations has been shown to be nearly ubiquitous in nature and to play an important role in community dynamics D I Bolnick, P. Amarasekare, M.S. Araujo, R. Burger, J M. Levine, M. Novak, V H. W. Rudolf, S.J. Schreiber, M. C Urban, and D. A Vasseur, Why intraspecific trait variation matters in community ecology, Trends Ecol. EvoL, 26: 183-192 (2011) D I Bolnick. R. Svanback, J. A Fordyce, L.H. Yang, J M. Davis, C D Hulsey, and M. L. Forister The ecology of individuals: incidence and implications of individual specialization. Amer. Natu,161:1-28(2003). M. Wolf, and F J Weissing, Animal personalities: consequences for ecology and evolution Trends in Ecol. Evol, 27: 452-461 (2012)

I. Intraspecific Variation in foraging ability, predator avoidance, and other mortality risk Intraspecific variation within populations has been shown to be nearly ubiquitous in nature and to play an important role in community dynamics: • D. I. Bolnick, P. Amarasekare, M. S. Araújo, R. Bürger, J. M. Levine, M. Novak, V. H. W. Rudolf, S. J. Schreiber, M. C. Urban, and D. A. Vasseur, Why intraspecific trait variation matters in community ecology, Trends Ecol. Evol,, 26:183-192 (2011). • D. I. Bolnick. R. Svanbäck, J. A. Fordyce, L. H. Yang, J. M. Davis, C. D. Hulsey, and M. L. Forister, The ecology of individuals: incidence and implications of individual specialization. Amer. Natur., 161:1-28 (2003). • M. Wolf, and F. J. Weissing, Animal personalities: consequences for ecology and evolution. Trends in Ecol. Evol., 27:452-461 (2012)

Basic Questions How does this intraspecific variation relate to strategies for fitness of individuals in a population Given the existence of subpopulations having distinct sets of traits or strategies within a population and that there is probably continuous switching of individuals between these subpopulations affect these dynamics?

• How does this intraspecific variation relate to strategies for fitness of individuals in a population? • Given the existence of subpopulations having distinct sets of traits or strategies within a population, and that there is probably continuous switching of individuals between these subpopulations affect these dynamics? Basic Questions

M Predator To investigate trait variation, fN,M fN,M we consider a tri-trophic chain of resource r consumer N, and predator M onsumer 1 The consumer is assumed to m2 n2 have two phenotype subpopulations( with different strategies) and there is some switching back a,RN1 2RN2 and forth between the two

M Predator N1 Consumer 1 N2 Consumer 2 R Resource a2RN2 a1RN1 f2N2M f1N1M m12N1 m21N2 To investigate trait variation, we consider a tri-trophic chain of ‘resource R’, ‘consumer N’, and ‘predator M’ The consumer is assumed to have two phenotype subpopulations (with different strategies) and there is some switching back and forth between the two

This chain resembles the diamond-shaped'chain that has been studied before fN,M e.g., fN,M E.G. Noonburg and p. a Abrams, Transient dynamics limit the effectiveness of keystone predation in N, bringing about coexistence Amer.Natu.165:322-335 (2005) In this case the two a,RN1 consumers are different 2RN2 species, so there is no movement between the two consumer strategies

M N 1 N 2 R a 2RN 2 a 1RN 1 f2 N 2 M f1 N 1 M This chain resembles the ‘diamond -shaped’ chain that has been studied before; e.g., E. G. Noonburg and P. A. Abrams, Transient dynamics limit the effectiveness of keystone predation in bringing about coexistence, Amer. Natur. 165:322 -335. (2005). In this case the two consumers are different species, so there is no movement between the two consumer strategies

A simple set of equations for this system is as follows dR R = rRl 1 K/a,RN RN Resource ba,RN,-d,N,-fN,M-m, N,+m,N, Consumer Phenotype 1 d ba rn, -d,,-f2N2M+mn,N-m, N, Consumer Phenotype 2 dM CfIN,M+df2N,,M Predator Parameters ai di, and fi may differ between the two consumer phenotypes

1 a1RN1 a2RN2 K R rR dt dR  − −      = − 1 1 1 1 1 1 12 1 21 2 1 ba RN d N f N M m N m N dt dN = − − − + 2 2 2 2 2 2 12 1 21 2 2 ba RN d N f N M m N m N dt dN = − − + − cf N M cf N M d M dt dM = 1 1 + 2 2 − m , A simple set of equations for this system is as follows: Parameters ai , di , and fi may differ between the two consumer phenotypes. Resource Consumer Phenotype 1 Consumer Phenotype 2 Predator

There are two equilibrium points for the resource and consumers alone d R1 N12=0M1=0 Kbe R2 0N2 M,=0 Kba However, the equilibrium below cannot exist, as only one species can survive in this model of exploitative competition. The better forager excludes the other. R2 Ka.b

1 0 0 1 2 1 1 1 1 1 1 1 1 1 = =       = = − * * , * , * N M Kba d a r N ba d R 0 1 0 2 2 2 2 2 1 2 2 2 2 2 =       = = = − * * , * , * M Kba d a r N N ba d R There are two equilibrium points for the resource and consumers alone However, the equilibrium below cannot exist, as only one species can survive in this model of exploitative competition. The better forager excludes the other. 1 1 0 2 2 2 2 2 2 2 2 2 2 1 2 2 2 =       = −       = = − * * , * , * M Ka b d a r N Ka b d a r N ba d R

But at least one of the tri-trophic chains is assumed exist; i. e the better forager is poorer at evading the predator d R3 I-ad N32=0M;=如aK (rcf -a, dm) R=K a,d N 、ba2K f Assume that (1)exists; that is, that cfINu-dm>0 This provides a path to the full system if consumer 2 can invade; i.e., if ba2R -d2-f2M;=ba2 K1 d2-(2/0k(1%d This means that the poorer forager can now invade, because the predator suppresses the better forager to some extent

1 1 2 1 1 1 1 3 2 3 1 3 1 1 1 3 1 0 f d (rcf a d ) rcf ba K N M cf d N rcf a d R K m * * , * m , * m = = = − −       = − 1 2 2 2 2 2 2 4 2 4 1 4 2 2 2 4 1 0 f d (rcf a d ) rcf ba K M cf d N N rcf a d R K m * m * , * , * m = = = − −       = − But at least one of the tri-trophic chains is assumed exist; i.e., the better forager is poorer at evading the predator. 1 1 1 − m  0 * cf N , d (1) (2) Assume that (1) exists; that is, that This provides a path to the full system, if consumer 2 can invade; i.e., if 1 1 0 1 1 1 2 2 1 1 1 1 2 3 2 2 3 2 −        − − −       − − = − d ) rcf a d d ( f / f )( ba K rcf a d ba R d f M ba K * * m m This means that the poorer forager can now invade, because the predator suppresses the better forager to some extent

To obtain this solution we also make the assumption that the consumers are in an Ideal Free Distribution at equilibrium, so that m12N,*=m2 N2 This means that the individuals are distributed among the two strategies such that changing will not improve their fitness there is still switching but it is balanced We can find the interior equilibrium point Rs fd-fd b(a,2-a,f M ba,(2d,-fid f b(,fs)fr ad f2[Kba21-a12)-(fd1-f1d2 c(a21-a12 Kb(afi -a,f2) f,r/ Kb(a2fi-a,f2)-(f2d -f,d2)] c(a2fi-a,f2 Kb(a,fi-a,f2)

b( a f a f ) f d f d R * 1 2 2 1 2 1 1 2 5 − − = ( ) 1 1 1 2 2 1 2 1 1 2 1 1 5 f d b( a f a f ) f d f d f ba M * − − − = 2 2 1 1 2 2 2 1 1 2 2 1 1 2 2 1 1 2 2 5 1 Kb( a f a f ) f r[ Kb( a f a f ) ( f d f d )] c( a f a f ) a d N * m , − − − − − − = 2 2 1 1 2 1 2 1 1 2 2 1 1 2 2 1 1 2 1 5 2 Kb( a f a f ) f r[ Kb( a f a f ) ( f d f d )] c( a f a f ) a d N * m , − − − − + − − = To obtain this solution we also make the assumption that the consumers are in an Ideal Free Distribution at equilibrium, so that m12N1* = m21N2*. This means that the individuals are distributed among the two strategies such that changing will not improve their fitness. There is still switching, but it is balanced. We can find the interior equilibrium point