The effect of migration on local adaptation in a
coevolving host-parasite system
Andrew D. Morgan1, Sylvain Gandon2 & Angus Buckling1
1
Department of Zoology, University of Oxford, South Parks Road, Oxford OX1 3PS, UK
2
Génétique et Evolution des Maladies Infectieuses, UMR CNRS/IRD 2724, IRD, 911
avenue Agropolis 34394 Montpellier Cedex 5, France
Supplementary information
We used a simulation model to check the robustness of theoretical expectations derived
from general models of coevolution1-3. In particular we looked at the effect of host and
parasite migration on the coevolutionary outcome under situations that approximate our
biological system and our experimental design.
1. The model
We assume that both the host and the parasite are haploid, reproduce asexually, and have
constant and very large population sizes (such that the effect of genetic drift on the
dynamics of gene frequencies is assumed to be negligible). With a probability  h a
bacterium will be in contact with a phage (this parameter thus affects the intensity of
selection for resistance in the host population). Whether or not the phage will infect the
bacteria depends on both the host and the parasite genotypes. Following Agrawal &
Lively4 the genetic determinism of host resistance (or parasite infectivity) is governed by
two biallelic loci which yield four potential genotypes in both the host (H00, H01, H10,
H11) and the parasite (P00, P01, P10, P11). The probability of successful infection  ij of
different parasite genotypes ( i ) on different host genotypes ( j ) is given in table 1. The
specificity of the interaction is governed by several parameters. First, the parameter a
affects the type of interaction4. When a  0 the interaction follows the rules of a
matching allele model (MAM), and when a  1 it follows the rules of a gene-for-gene
model (GFGM). We assume that “1” alleles are resistant alleles in the host (virulence
alleles in the parasite) and the parameter c ( k in the parasite) measures the cost
associated with these alleles (in the absence of these costs the polymorphism is rapidly
lost in a pure GFG model). Second, the parameter  p governs the strength of the
specificity. When  p increases the parasite can infect fewer hosts (see table 1) and,
consequently, this increases selection pressure for infectivity in the parasite. We further
assume that the host and parasite have identical generation times5; phage generation time
is a positive function of bacterial generation time, and minimal generation times are
similar for bacteria and phage in this system.
Parasite virulence V measures the
deleterious effect of parasites on infected hosts (this parameter also controls the intensity
of selection for resistance in the host). Because infected bacteria always die without
reproducing when they are infected we will assume that virulence is maximal in our
model ( V  1 ).
Selection for infectivity in the phage and resistance in the bacteria are described by the
following set of difference equations describing the change in pi  and h j  , the
frequencies of the i th parasite genotype and the j th host genotype, respectively (the
superscript t and t  1 refer to successive generations):
p t 1 i   wPt i  p t i 
h t 1  j   wHt  j h t  j 
where wPt i  and wHt  j  are the relative fitnesses of the i th parasite genotype and the j th
host genotype, respectively, at the t th generation:
4
W i, j h  j 
t
wPt i  
j 1
P
t
WP
4
W i, j  p i 
t
wHt  j  
i 1
H
t
WP
with:
WP i, j   1  a k   ij
v i 
WH i, j   1  ac 
r j 
1    V 
h
ij
and where, vi  and r  j  refer to the number of virulence and resistance alleles in the
parasite and the host, respectively. The mean fitness of the parasite and the host at the t th
generation are:
4
4
W  WP i, j  p t i h t  j 
t
P
i 1 j 1
4
4
W H   WH i, j  p t i h t  j 
t
i 1 j 1
After selection, mutation may occur independently on each locus with probability  H in
the host and  P in the parasite (in our simulations  H   P  10 6 ). Then, depending on
the experimental treatment, migration may occur with a probability mH in the host and
mP in the parasite. Migration takes place just after mutation at each transfer (every 7
generations) among a number max of populations (in our experiment and in our
simulations max  6 ). Migration follows the rules of an island model of dispersal (a
migrant from a given population may reach any of the max  1 remaining populations
with equal probabilities).
2. Measures of adaptation
Different measures can be used to quantify the level of adaptation6-9. In this experiment
we have access to different measures (for both the host and the parasite) based on (1)
local performance, (2) global performance, (3) both local and global performances. We
present these different measures below.
2.1. Local performance
First, we can focus on the performance of each population when placed in its local
environment. In particular the local performance (phage infectivity) of the phage
population, n , is given by:
t
I nn
  p nt i hnt  j  ij
i
j
Note that this measure of adaptation is only based on the ability of the phage to infect
different bacteria genotypes and thus does not depend on the costs of virulence. Note also
that, as in our experiment, phage infectivity is measured just before migration.
Reciprocally, the local performance (bacteria resistance) of the bacteria population, n , is
given by:
t
t
Rnn
  p nt i hnt  j 1   ij   1  I nn
i
j
As for phage performance, this measure of adaptation is only based on the ability of the
bacteria to resist and it does not depend on the costs of resistance. Those measures can
then be averaged over the max different populations of the metapopulation yielding the
 
t
mean local performance of the phage, I 0t   I nn
max , and the mean local
n
 
t
performance of the bacteria, R0t   Rnn
max  1  I 0t .
n
2.2. Global performance
Second, we can focus on the performance of each population averaged over the different
habitats. In particular the global performance of the phage population, n , is given by:


t
I nt   I nm
max     pnt i hmt  j  ij  max
m
m  i
j

 
where the subscripts n and m refer to the different populations.
Reciprocally, the global performance of the bacteria population, n , is given by:


t
Rnt   Rnm
max     pmt i hnt  j 1   ij  max
m
m  i
j

 
Those measures can also be averaged over the max different populations of the
 
metapopulation yielding the mean global performance of the phage, I t   I nt max ,
n
 
and the mean global performance of the bacteria, R t   Rnt max  1  I t .
n
2.3. Local adaptation
One may use a measure of adaptation which takes into account the variability of the
performance in different habitats. This will inform us about the covariation between the
spatial variability of the habitat and the genetic differentiation of the organism under
study. Figure S1 illustrates the fact that two distinct (but related) measures of local
adaptation emerge from classical transplant experiments6-9.
2.3.1 Differential adaptation: .
Differential adaptation depends on the difference between local and global performances
(“home versus away” criteria9). For example, parasite local adaptation is measured as the
difference between infectivity of the phage against sympatric bacteria (from the same
population) and allopatric bacteria (from the other max  1 populations). The local
adaptation of a phage population, n , is thus given by:
max 

t
I nt  I nn
    p nt i hmt  j  ij 
m 1  i
j

mn

max  1
max
I nnt  I nt 
max  1
Reciprocally, the differential adaptation of a bacteria population, n , is given by:
max 

t
Rnt  Rnn
    p mt i hnt  j 1   ij 
m 1  i
j

m n


max
t
Rnn
 Rnt
max  1
max
 I nt 
I nt  Rnt
max  1


Averaging
differential
max
I t   I nt max
n 1
max
  Rnt max
n 1
  R t
max  1

adaptation
over
the
different
populations
yields:
Since I t and R t are redundant we will focus on mean parasite differential adaptation
and simplify the notation: t  I t . We can also average parasite differential adaptation
over both space (6 populations) and time (6 time points: T2, T4, T6, T8, T10, T12):
max

t 1
t
.
max
2.3.2 Local adaptation: .
Local adaptation measures the difference between the performance of local individuals
and immigrants (“local versus foreign” criteria9). For example, the local adaptation of a
phage population, n , is given by:
max 

t
I nt  I nn
    p mt i hnt  j  ij 
m 1  i
j

m n


max
t
I nn
 1  Rnt
max  1
 Rnt

max  1

Reciprocally, the local adaptation of a bacteria population, n , is given by:


max
t
Rnn
 1  I nt
max  1
 I nt
Rnt 

Note the relationship between local adaptation of the parasite (host) and differential
adaptation of the host (parasite).
Averaging local adaptation over the different populations yields:
max
I t   I nt max
n 1
max
  Rnt max
n 1
 R t
Since I t and R t are redundant we will focus on mean parasite local adaptation and
simplify the notation:  t  I t . We can also average parasite local adaptation over both
max
space (6 populations) and time (6 time points: T2, T4, T6, T8, T10, T12):   
t 1
t
.
max
2.3.3 The choice between the two criteria for local adaptation
In this paper we will follow Kawecki & Ebert9 who suggest that the “local versus
foreign” criteria (i.e.,  ) is more relevant than the “home versus away” criteria (i.e.,  )
to detect local adaptation. They argue that the former is a direct evaluation of the driving
force of local adaptation (differential selection within each habitat). The second criteria,
however, may detect a pattern which only emerges because of some intrinsic variability
of the quality of the different habitats.
In our system, the above two measures yield the same average values (i.e.,  t  t ).
They may however have very different variances. In fact there is simple relationship
linking these two variances:
2
 max 
Var    Var    
 Var Rn   Var I n   2CovI nn , I n   2CovI nn , Rn 
 max  1 
For example in our experiment we found a significant effect of the migration treatment
on local adaptation (F4,24 = 3.30, P = 0.027; starting population local adaptation: F1,24 =
3.76, P = 0.06) but a non-significant effect on differential adaptation (F4,24 = 1.02, P =
0.4; starting population local adaptation: F1,24 = 14.70, P = 0.001).
The crucial components linking the variance measures of the two local adaptation
measures are the covariances between global infectivity and local infectivity
( CovI nn , I n  ) and between global resistance and local infectivity ( CovI nn , Rn  ). We
measured these covariances in our unmigrated populations for all time points, and found
significant covariances (P < 0.05) between global resistance and local infectivity in three
out of six time points, but found no significant covariance between global infectivity and
local infectivity in any time point (mean covariances across time = -0.0156 and 0.006,
respectively).
We obtained qualitatively similar results with the other migration
treatments. Thus, in our experiment, global resistance of hosts is a better determinant of
local infectivity than is global parasite infectivity. The variation in resistance among
different host populations may obscure the pattern of local adaptation ( Var  Var )
and hence it is appropriate to measure local adaptation as a difference in parasite
performance within each host populations using the “local versus foreign” criteria.
3. Simulations
Each simulation starts with a random sampling of host and parasite genotypes in the 6
populations. The initial frequencies are obtained after founding each host and parasite
populations with 10 6 individuals with an equal probability to be of any of the four
different genotypes (multinomial distribution). This founding event introduces some
variance in genotype frequency among the different populations. Importantly, this is the
only stochastic event in our simulations. After this initialisation, simulations are
deterministic. For the first 500 generations the 6 populations are evolving independently.
Then, the resulting populations are used under different migration treatments.
4. Results
Fig. 1 presents a single simulation run for three migration treatments. It shows that local
adaptation of individual parasite populations can fluctuate a lot through time. The effect
of the migration treatment is more apparent on the level of local adaptation averaged over
the different parasite populations (i.e.,  t ) : the mean parasite local adaptation is
increased (decreased) when the parasite migrates more (less) than the host.
Fig. S2 presents the effect of different migration treatments and different models of
interaction on the parasite local adaptation when averaged over both space and time (i.e.,
 ). Fig. S2 plots the mean ( standard deviation) of  measured from 1000 simulation
runs for each set of parameter values. It shows that migration promotes local adaptation
for a broad range of parameter values but that the effect of migration decreases when the
underlying model of specificity is closer to a GFGM (when a increases).
We expected to observe a greater homogenising effect of migration in our simulations
(Fig. 1 and Fig. S2). This lack of homogenisation is partly due to the fact that local
adaptation is only averaged over the first 12 transfers after the start of the migration
treatments (because we followed local adaptation for 12 transfers in our experiment).
Averaging over a longer period of time revealed a homogenising effect (not shown).
Another factor explains why high levels of migration do not lead more rapidly to the
synchronisation of the dynamics of gene frequencies among populations (as would be
expected in such island model of dispersal3). In contrast with previous theoretical
models1-3, we allowed 7 intercalary generations between each migration event (as in our
experiment). Those intercalary generations can maintain divergence among populations
despite large migration rates (even when both the host and the parasite migrate).
Additional simulations allowed us to explore the effects of other parameters of this model
(not shown). In particular we found that other values of the costs of resistance and
virulence ( c and k ) did not alter the effects illustrated in Fig. S2. Besides, not
surprisingly, we found that larger values of  h and  p (i.e., higher strength of selection
on host resistance and parasite infectivity) increase the absolute value of  but the
qualitative effect of migration rates illustrated in Fig. S2 remains. Note, however, that for
extreme values of these two parameters (e.g. when  h   p  1 ) the beneficial effect of
migration on local adaptation can vanish. Indeed, in our model (as in our experiment)
local adaptation is measured 7 generations after the migration event. Thus, by the time
local adaptation is measured, selection (when it is intense) can dilute the benefit of
increased genetic variability during those intercalary generations.
References:
1.
Gandon, S., Capowiez, Y., Dubois, Y., Michalakis, Y. & Olivieri, I. Local
adaptation and gene for gene coevolution in a metapopulation model. Proc. R.
Soc. lond. B 263 (1996).
2.
Lively, C. M. Migration, virulence and the geographic mosaic of adaptation by
parasites. Am. Nat. 153, S34-S47 (1999).
3.
Gandon, S. Local adaptation and the geometry of host-parasite coevolution.
Ecology Letters 5, 246-256 (2002).
4.
Agrawal, A. & Lively, C. M. Infection genetics: gene-for-gene versus matchingalleles models and all points in between. Evol. Ecol. Res. 4, 79-90 (2002).
5.
Buckling, A. & Rainey, P. B. Antagonistic coevolution between a bacterium and a
bacteriophage. Proc. R. Soc. Lond. B 269, 931-936 (2002).
6.
Gandon, S. & Van Zandt, P. Local adaptation and host-parasite interactions.
Trends Ecol. Evol. 13, 214-216 (1998).
7.
Gandon, S. & Michalakis, Y. Local adaptation, evolutionary potential and hostparasite coevolution: interactions between migration, mutation, population size
and generation time. J. Evol. Biol. 15, 451-462 (2002).
8.
Kaltz, O., Gandon, S., Michalakis, Y. & Shykoff, J. A. Local maladaptation in the
anther-smut fungus Microbortyum violaceum to its host Silene latifolia: Evidence
from a cross inoculation experiment. Evolution 53, 395-407 (1999).
9.
Kawecki, T. D. & Ebert, D. Conceptual issues in local adaptation. Ecol. Letts. 7,
1225-1241 (2004)
Table 1: Probability of successful infection  ij of different parasite genotypes ( i )
on different host genotypes ( j ). Modified version of the specificity model by
Agrawal & Lively4.
Parasite
Host
H00
H01
H10
H11
P00
1
1 p
1 p
1 p
P01
a  1  a 1   p 
1
1 p
1 p
P10
a  1  a 1   p 
1 p
1
1 p
P11
a 2  1  a 2 1   p 
a  1  a 1   p 
a  1  a 1   p 
1


Figure S1: Schematic illustration showing how a transplant experiment with
parasites sampled in two host populations may result in two different measures
of local adaptation. The differential adaptation (“ home versus away” criterion) of
parasite population 1, 1 , is the difference between local performance and the
performance against allopatric hosts. The local adaptation (“local versus foreign”
criterion) of parasite population 1, 1 , is the difference between local
performance and the performance of immigrant parasites.
Parasite populations
2
1
1
1
2
1
Host populations
Figure S2: Mean parasite local adaptation,  (averaged over 6 populations and
6 time points: T2, T4, T6, T8, T10, T12), for different migration treatments and
different models of interaction (mean  standard deviation obtained from 1000
runs for each set of parameters). Other parameter values (as in figure 1):
 H   P  10 6 , c  k  0.05 ,  H  0.9 ,  P  0.5 .
0.04
0.03
0.02
0.01
0
-0.01
-0.02
-0.03
-0.04
-0.05
mh=10% / mp=0
mh=1% / mp=0
mh=0.1% / mp=0
mh=0 / mp=0
mh=0 / mp=0.1%
mh=0 / mp=1%
mh=0 / mp=10%