Host migration strategy is shaped by forms of parasite

1602 | Journal of Animal Ecology SHAW et Al.

Despite the growing body of literature on these topics, migration

research often fails to consider the role of parasites (including bac‐

teria and viruses, as per Pedersen, Jones, Nunn, & Altizer, 2007), in

influencing either the movement decisions or the costs and benefits

of migration in (potential) hosts. This oversight is surprising given

that migratory animals are often exposed to novel environments

and conspecifics as they travel and thus may be under stronger se‐

lection pressure to evolve strategies that help them deal with in‐

fection. Recent empirical evidence indicates that hosts can, indeed,

adjust migration in response to infection (Halttunen et al., 2018;

Hegemann et al., 2018). However, the ecological and evolutionary

dynamics driving such infection‐induced host movement remains

understudied.

When parasitism is considered in the context of migration, re‐

searchers have tended to focus on its negative consequences in

terms of increased parasite transmission (Elfving et al., 2010; Fèvre,

Bronsvoort, Hamilton, & Cleaveland, 2006; Waldenström, Bensch,

Kiboi, Hasselquist, & Ottosson, 2002; Wesolowski et al., 2012). For

instance, increased movement of infected individuals can lead to the

spread of otherwise localized diseases such as the West Nile virus

and Ebola (Altizer, Bartel, & Han, 2011). By virtue of their increased

geographic range, migratory individuals may also be at greater risk

of encountering and acquiring new parasites (Alerstam et al., 2003;

Koprivnikar & Leung, 2015; Waldenström et al., 2002). Some stud‐

ies have found greater parasite diversity in migratory birds and

mammals than in residents, suggesting that migrating species face

a higher infection risk than species that do not migrate (Figuerola &

Green, 2000; Koprivnikar & Leung, 2015; Teitelbaum, Huang, Hall,

& Altizer, 2018). Exposure to new infections, compounded by the

costs of long‐distance movement, may, therefore, represent import‐

ant barriers to the evolution and stability of migratory behaviour.

In addition to increasing transmission, host migratory move‐

ments may also reduce the spread of parasites in several non‐mu‐

tually exclusive ways. For one, physiological costs resulting from

infection can amplify the cost of movement. As a result, infected

individuals may be less likely to survive the migration journey, thus

reducing the prevalence of infection in a population (“migratory

culling”, Bradley & Altizer, 2005). For example, migratory monarch

butterflies (Danaus plexippus) have a lower prevalence of the proto‐

zoan parasite Ophryocystis elektroscirrha than resident populations

(Altizer,Oberhauser,&Brower,2000;Satterfield,Maerz,&Altizer,2015). This is likely because infected individuals have reduced flight

performance and efficiency compared with healthy individuals and

therefore higher mortality along the migration route (Bradley &

Altizer,2005).Migrationcanalsoallowindividualstoescapepara‐sites by spatially or temporally separating them from infected con‐

specifics or habitats (Altizer et al., 2011; Loehle, 1995; Zuk, 1991).

“Migratoryescape”fromparasitesasanaddedbenefitofmigrationis well documented in ungulates infected with ectoparasites such

asticks(Folstad,Nilssen,Halvorsen,&Andersen,1991;Mysterud,Qviller,Meisingset,&Viljugrein,2016;Qvilleretal.,2013).Themi‐gration of susceptible juveniles away from infected adults (“migra‐

tory allopatry”) also benefits a variety of fish species (Krkošek et al.,

2007; Poulin et al., 2012) and has been hypothesized as a selective

force in the evolution of the larval phase experienced by many coral

reef fishes (Strathmann et al., 2002). By moving between environ‐

mentally distinct habitats, migration may also promote recovery

from infection if parasites are unable to survive changes to their

host's internal or external environment during the migration (“migra‐

tory recovery”, Shaw & Binning, 2016). For example, when salmon

lice (Lepeophtheirus salmonis) intensities increase in the marine envi‐

ronment, sea trout (Salmo trutta) return from migration to freshwater

streams earlier in the season, ridding them of these harmful ecto‐

parasites (Birkeland & Jakobsen, 1997). Indeed, both the ecto‐ and

endoparasite communities of many fish hosts change dramatically

over the course of migration across strong environmental gradients

such as salinity (Thieltges, Dolch, Krakau, & Poulin, 2010).

Despite this growing body of literature, deriving general relation‐

ships underlying host migration in the context of parasites is difficult.

First and foremost, these behaviours are the result of a long history

of evolutionary interactions, which can make it difficult to disentan‐

gle cause and effect by observing wild populations alone. Second, by

virtue of the distances and time‐scales covered, empirical studies of

migratory species across their annual cycles are inherently difficult

(Bowlin et al., 2010). This has led to a sampling bias whereby some

migratory populations or species are well studied, with a paucity of

research on the majority of migratory organisms. Third, the sites

visited by migrants throughout their journey differ in a number of

biotic and abiotic factors other than parasite risk or exposure. Thus,

attributing movement decisions to specific causes can be difficult

(Avgar, Street, & Fryxell, 2014). Finally, dramatic differences in host

life‐history and parasite transmission dynamics can make it challeng‐

ing to generalize across studies from a few focal species. The rec‐

ognition that parasites are likely important in driving long‐distance

movement patterns coupled with these challenges associated with

studying of migratory species has created to a significant knowledge

gap in our ability to predict the effects of ongoing environmental

change on migration and infection risk (Altizer et al., 2011).

Theoretical approaches can be useful in understanding com‐

plex ecological interactions. For instance, mathematical models

allow researchers to systematically vary some parameters while

holding others constant, which can provide important insights

into the relative importance of each factor in influencing ob‐

servedpatternsinnature.Modelscanalsocapturethedynamicalaspects of a system (i.e. population changes, infection status and

trait evolution) through time, which may be opaque in empirical

studies with few time points (Lloyd‐Smith et al., 2009). Observing

the dynamics of a model can help one understand feedbacks pres‐

ent in the system, such as indirect effects of model parameters

acting through population size. In this way, theoretical studies are

an important complement to empirical research that can be used

both to generate insight into biological processes and to generate

testable predictions amenable to field and laboratory research

(Servedio et al., 2014).

Here, we develop a mathematical model to explore the ef‐

fect of parasites on the evolution of migration in previously

| 1603Journal of Animal EcologySHAW et Al.

residential species. We draw on case studies of host–parasite

systems with migratory hosts (Table 1), to ground our theory

and to showcase the breadth of our model. Our goal is to under‐

stand under what conditions parasites can drive host migration,

in the absence of any other factor favouring migration. We take

this approach not because we think parasites are the sole factor

driving migration, but rather to start with the simplest possible

scenario by considering one factor at a time, as many empirical

and theoretical studies do. We consider how transmission mode,

costs of migration and infection, and the spatiotemporal dynam‐

ics of infection and recovery influence the evolution of migration

in our model. We show that transmission mode and costs matter

for both the evolution of migration and for extinction risk of the

host population. We find that partial migration can emerge in

one of two ways.

2 | MATERIAL S AND METHODS

2.1 | Model development

In our modelling framework (Figure 1; Table S1), we assume a popu‐

lation of susceptible (S) and infected (I) individuals, where a fraction

of the population (θ) migrates seasonally between two different

environmentswhiletherestofthepopulation(1−θ) remains in the

first environment year‐round. We use a combination of discrete and

continuous time in our model (Johns & Shaw, 2016; Shaw & Binning,

2016): each year is made up of discrete seasons, related to migration,

during which population dynamics (mortality, reproduction) and in‐

fection dynamics (transmission, recovery) each occur continuously.

Within this framework, we determine when migration evolves across

a breadth of scenarios. Full model code is available from Dryad

(Shaw, Craft, Zuk, & Binning, 2019).

First, we vary the spatiotemporal patterns of infection dynam‐

ics by varying the season and environment in which recovery and

transmission occur. For most of the host–parasite systems we con‐

sider (Table 1), hosts could be reinfected by the same parasite, and

thus, we assume infection dynamics according to an SIS (suscepti‐

ble‐infected‐susceptible) model. In this model, individuals that be‐

come infected moved from being susceptible (S) to being infected

(I), and individuals that recover from infection move from being

infected and infectious (I) to being susceptible again. Specifically,

we consider the following cases, recovery occurs (a) never, (b) only

in environment #1, (c) during the movement phase of migration

(transit) or (d) only in environment #2 (Figure 1). We model tran‐

sit explicitly since a number of processes can alter infection dy‐

namics during the transit phase (Daversa, Fenton, Dell, Garner, &

Manica,2017),whicharenotcapturedbymodelsfocusingsolelyon the two environments. We assume that transmission only oc‐

curs in environment #1. We do not consider possibilities where

transmission only occurs during transit or in environment #2, since

introducing a parasite that is only transmitted during migration to

an otherwise residential population (i.e. a population remaining in

environment #1 year‐round) would never be expected to favour

the evolution of migration. We do not include exposure to new

parasites in environment #2; considering this would shift when mi‐

gration occurs, but previous work suggests that migration can still

be favoured even with exposure to new parasites (Shaw, Sherman,

Barker, & Zuk, 2018). We leave the exploration of other combina‐

tions of transmission (e.g. transmission in environment 1 and in

transit) for future work.

Next, we vary transmission mode, considering “indirect”, “den‐

sity‐dependent” and “frequency‐dependent” transmission (Keeling

& Rohani, 2008). With indirect transmission, susceptible individuals

become infected as they pick up parasites at transmission rate β from

the environment. In this case, the infection dynamics are given by

In contrast, with both density‐dependent and frequency‐depen‐

dent transmission, infection occurs via host‐to‐host contact when

susceptible individuals acquire a parasite at transmission rate β

by coming into contact with infected individuals. With density‐

dependent transmission, the infection risk for a susceptible in‐

dividual increases with population density and overall infection

dynamics are given by

(Begon et al., 2002). With frequency‐dependent transmission, the

infection risk for a susceptible individual does not change with pop‐

ulation density, but increases with the frequency of infected indi‐

viduals in the population. For this transmission mode, the overall

infection dynamics are given by

(Begon et al., 2002). In addition to transmission, our model also in‐

cludes the possibility of recovery from parasite infection. We assume

that infected individuals recover from infection (and become suscep‐

tible again) at a constant rate γ, with infection dynamics given by

Finally, we vary cost currency, that is whether the costs of migra‐

tion and infection are paid in terms of fecundity or survival. The form

of infection cost can have indirect effects that shape evolutionary out‐

comes. For example, infection‐induced mortality can lower average life

span changing the selective pressure on migration (Shaw & Binning,

2016). A parasite that reduces survival will also lower infection preva‐

lence in the population (compared to one that reduces fecundity) which

could also change selective pressures on hosts. We consider four cost

scenarios: (a) migration and infection both reduce survival, (b) migra‐

tion and infection both reduce fecundity, (c) migration reduces survival

while infection reduces fecundity or (d) vice versa (migration reduces

(1a)dS∕dt=−�S

(1b)dI∕dt=�S.

(2a)dS∕dt=−�SI

(2b)dI∕dt=�SI

(3a)dS∕dt=−�SI∕(

S+ I)

(3b)dI∕dt=�SI∕(

S+ I)

(4a)dS∕dt= �I

(4b)dI∕dt=−�I.

1604 |

Jou

rnal o

f An

imal E

co

log

yS

HA

W e

t A

l.

TA B L E 1 Host–parasite examples representing different systems where recovery either does not occur or occurs in specific locations and could be modelled with one of three transmission modes

Transmission type Recovery location Host Parasite Details Environmental gradient References

Indirect, βS None Plains zebra (Equus

burchelli)

Anthrax (B.

anthracis)

Zebra die from anthrax; non‐migra‐

tory groups maintain the disease in the

environment

No environmentally me‐

diated recovery known

Zidon et al. (2017)

Env #1 Violet‐green swal‐

lows (Tachycineta

thalassina)

Bird mites (Acarina) In breeding environment, birds sun more

when they are infected with ectoparasites

Increased temperature Blem and Blem (1993)

Transit Anatid ducks Helminths Host gut chemistry/physiology changes

during migration causing a loss of parasites

Changed internal

environment

Buscher (1965)

Env #2 Red deer (Cervus

elaphus)

Ticks (Ixodes ricinus) Tick prevalence is lower on migratory deer,

esp. those that migrate higher in altitude

Increased altitude Mysterudetal.(2016)

European flounder

(Platichthys flesus)

Marinecopepods(Lepeophtheirus

pectoralis)

Parasite dies as fish migrate from salt to

brackish water

Decreased salinity Boxshall(1974);Möller(1978); Thieltges et al.

(2010)

Density‐dependent, βSI None Harbour seals

(Phoca vitulina)

Phocine distemper

virus (Phocine

morbillivirus)

Virus is transmitted in both breeding and

post‐breeding environments



Swinton, Harwood, Grenfell,

and Gilligan (1998)

Env #1 Violet‐green swal‐

lows (Tachycineta

thalassina)

Feather lice (Bruelia

sp.)

In breeding environment, birds sun more

when they are infected with parasites

Increased temperature Blem and Blem (1993)

Transit NA NA

Env #2 Sea trout (Salmo

trutta)

Monogeneanectoparasite

(Gyrodactylus

derjavini)

Parasite only occurs in freshwater, dies

when fish migrates to the sea

Increased salinity Mo(1997)

Frequency‐dependent,

βSI/(S + I)

None Waterfowl Avian influenza

viruses

Environmental virus reservoir gives rise to

indirect transmission



Rohani, Breban, Stallknecht,

and Drake (2009)

Env #1 NA NA

Transit Alpine newt

(Ichthyosaura

alpestris)

Chytrid fungus

(Batrachochytrium

dendrobatidis, Bd)

Intensity of Bd infections decreased in

newts moving overland between ponds

Decreased humidity Daversa,Manica,Bosch,Jolles, and Garner (2018)

Env #2 Common toads

(Bufo spinosus)

Chytrid fungus

(Batrachochytrium

dendrobatidis)

Infection is cleared when toads migrate to

terrestrial winter burrows

Decreased humidity Daversa,Monsalve‐Carcaño,Carrascal, and Bosch (2018)

Note: Manyoftheseexamplescouldbemodelledundermultipletransmissionmodeformulations.Thislistisnotexhaustivebutratherintendedtoseedinsightsintowhensomeofthesebiologicallyrelevant scenarios might occur. NA: no example found.


fecundity, infection reduces survival). To model reduced survival from

infection, we assume a survival rate (σ) of

for infected individuals during each season (i.e. individuals die at rate

1−σ), where σS is the survival rate susceptible individuals and μI is

thesurvivalcostofinfection(0≤μI≤1).Tomodelreducedsurvivalfrom migration, we assume a survival rate of

for migrants during the transit seasons of migration, where μM is

the survival cost ofmigration (0≤μM ≤ 1). For scenarioswhereboth migration and infection incur survival costs, we assume that

infected migratory individuals pay both survival costs during

transit with survival rate

and then pay only the cost of infection during the non‐transit seasons

of migration (i.e. while in environment 1 or environment 2).

We assume that reproduction only occurs during the breeding

season in the breeding environment (i.e. season 1 in environment 1).

To model reduced fecundity from infection, we describe the repro‐

ductive rate (n) of infected residents as

where nSR is the reproductive rate of susceptible residents and φI is

thefecunditycostofinfection(0≤φI≤1).Similarly,tomodelreducedfecundity from migration, the fecundity rate of susceptible migrants is

where φM is thefecunditycostofmigration (0≤φM≤1).Forsce‐

narios where both migration and infection incur fecundity costs, we

assume that migratory infected individuals pay both fecundity costs;

that is, their reproductive rate is

The maximum rate of potential offspring production is then

(i.e. the number of individuals of each type present multiplied by their

per capita reproduction rate). The actual rate of offspring produced

accounts for density dependence and is given by

where N is the number of offspring and δ is the strength of density

dependence. For simplicity, we ignore vertical transmission and as‐

sume that all newborns are born susceptible. See supporting infor‐

mation for full population dynamics equations.

To determine the migration fraction (value of θ) that evolves

for each set of parameters, we analysed our model using numeri‐

cally simulated adaptive dynamics (Best et al., 2017; Bowers, White,

Boots, Geritz, & Kisdi, 2003). These simulations required tracking

the number of individuals of each migration strategy and infection

status. We considered 21 migration strategies (θ = 0, 0.05, 0.1, …,

1) and two infection statuses (S and I), and thus, we had a total of

42 different types to track. Each simulation had two time‐scales: a

shorter “burn‐in” period with just ecological dynamics followed by a

longer period with evolutionary dynamics. So, first we simulated the

transmission, movement and population dynamics of the population

until it reached an ecological equilibrium, where the overall popula‐

tion size did not change by more than 0.1 from year to year (roughly

103 years).

Second, we ran a repeated mutation‐simulation process for 104

iterations, of 10 years each. This was generally enough to ensure

convergence of the population to an evolutionary equilibrium (i.e.

little change in the variance of strategies across iterations). We iden‐

tified “non‐converged” simulations as those where the variance in

strategies changed by more than 2 over the last 5,000 iterations of

(5a)�I= (1−�I)�S

(5b)�SM=

(

1−�M

)

�S

(5c)�IM=

(

1−�M

) (

1−�I

)

�S

(6a)nIR=(

1−�I

)

nSR

(6b)nSM= (1−�M)nSR

(6c)nIM=

(

1−�M

) (

1−�I

)

nSR.

(6d)b=nSRSR+nIRIR+nSMSM+nIMIM

(6e)dN∕dt=b[1−�(

SR+SM+ IR+ IM

)

]

F I G U R E 1 Modellingframework.Afractionθ of susceptible (S) and infected (I) individuals migrate from environment #1 to #2 (throughathirdtransitenvironment)andbackwhiletherest(1−θ) stay resident in environment #1. Transmission (β) and recovery (γ) rates can vary with environment and season (τ) in the annual cycle; survival (σ) and reproduction (b) can vary with infection and migration status as well as season. See Table S1 for parameter definitions


the simulations. To mutate the strategies, we first picked one strat‐

egy at random in proportion to its relative abundance in the pop‐

ulation to be the mutator, θ'. Then, we chose at random whether

mutation increased (θ'' = θ' + 0.05) or decreased (θ'' = θ' −0.05)themigrationfraction (withtheconstraint0≤θ''≤1).Wemovedonesusceptible individual with the mutator strategy (θ') to be a suscep‐

tible individual with the new strategy (θ''), and similarly one infected

individual with θ' to be an infected individual with θ'', at the end

of the breeding season, before migration. We simulated the trans‐

mission, movement and population dynamics of this population for

10 years. Since population size is continuous in our model (and never

goes to exactly zero), we removed any low‐density strategies that

had fewer than one surviving individual. At the end of each simula‐

tion, we quantified the final distribution of migration strategies that

evolved in each population.

2.2 | Simulations

For all simulations, we used the same baseline parameters for sus‐

ceptible resident (non‐migratory) individuals, and only varied param‐

eters relating to infection and migration. For a baseline, we assumed

a population of relatively long‐lived individuals with sufficient repro‐

duction to maintain a viable population of an intermediate size. We

assumed the survival rate of susceptible residents (σSR) was 0.95 per

year. We assumed the reproductive of susceptible residents (nSR)

was 2 offspring per year and that the strength of density depend‐

ence in fecundity (δ) was 0.001. A susceptible resident population

(with no infection or migration) with these parameter values reached

an equilibrium population size of 1,000 individuals (S*). We also as‐

sumed that each “season” (i.e. phase of migration) lasted ¼ of the

year (τj = 0.25).

We are interested in conditions under which an initially resi‐

dent (non‐migratory, θ = 0) population evolves to be migratory in

response to a newly introduced parasite. Thus, we started each

simulation with 100 susceptible individuals and one infected in‐

dividual with strategy θ = 0, and zero individuals with all other

strategies.

Comparing across different transmission modes in a meaning‐

ful way requires careful choice of parameter values. Our aim was

to vary the relative time‐scales of transmission and recovery. To

do this, we first set the recovery rate (γ) to be 10, corresponding

to approximately 90%–99% of infected individuals recovering when

recovery occurs during migration or in transit. Next, we defined ρ

as the ratio of the transmission and recovery time‐scales (ρ = β/γ).

We primarily used ρ = 2 to emulate a pathogen where the transmis‐

sion rate exceeds recovery rate, and then also ran simulations with

ρ values of 0.4–0.5 (recovery exceeds transmission) and 10 (trans‐

mission far exceeds recovery) for comparison. We then set transmis‐

sion rates for indirect and frequency‐dependent transmission to be

βIN = βFD = ρ γ. Finally, we set the transmission rate for density‐de‐

pendent transmission to be βDD = βFD/S*, normalizing by population

size to account for the difference between frequency‐ and density‐

dependent transmission.

We considered a wide range of parameter values. We ran sim‐

ulations for all combinations of the four transmission‐recovery

scenarios (no recovery, recovery in environment #1, in transit or in

environment #2); three transmission modes (indirect, density‐de‐

pendent or frequency‐dependent); three ρ values; and four cost

scenarios (migration and infection each either reduce survival or

fecundity) mentioned above; along with eleven different values of

infection cost (μI or φI = 0, 0.1,…, 1); and eleven values of migration

cost (μM or φM = 0, 0.1,…, 1), for a total of 17,424 simulations (shown

in Figures S1–S9 where each dot is one simulation). Thus, this model

builds on a framework we previously developed for the evolution

of migration in response to infection (Shaw & Binning, 2016), by ex‐

ploring a much broader range of biological conditions. Here, we ex‐

plore several recovery scenarios (instead of just assuming recovery

happens in environment #2), of transmission (instead of just indirect)

and cost scenarios (instead of assuming migration and infection both

reduce survival, with a potential extra fecundity cost to infection).

3 | RESULTS

Typically, the population reached a single movement strategy, ei‐

ther full residency (θ = 0, Figure 2a, grey dots in Figures S1–S3) or

full migration (θ = 1, Figure 2b, black dots in Figures S1–S3). Rarer

outcomes included coexistence of two distinct strategies (Figure 2c)

and evolution of an intermediate strategy (0 < θ<1,Figure2d).Mostrarely, some simulations never converged (Figure 2e, stars in Figures

S1–S3), suggesting that the selection gradient is extremely shallow

for these parameter combinations.

3.1 | Cost scenarios

The type of cost currency (in terms of reduced survival or fecundity)

mattered (Figure 3). When migration and infection costs were paid in

the same currency, the less costly activity was generally favoured (stay

and pay infection cost or migrate and pay migration cost). When the

currencies differed, the option with the fecundity cost was favoured

across the widest range of conditions. In other words, migration was

favoured across the broadest range of parameter space when migra‐

tion reduced fecundity while infection reduced survival (Figure 3a);

across an intermediate range of parameter space when both migra‐

tion and infection reduced survival (Figure 3b) or both reduced fecun‐

dity (Figure 3c); and across the narrowest range of parameter space

when migration reduced survival while infection reduced fecundity

(Figure 3d). This was true for all three transmission modes considered

(Figures S1–S3), as long as individuals can recover from infection at

some point during migration (in transit or in environment #2).

3.2 | Transmission mode and extinction

Extinction risk differed by transmission mode. Populations only

went extinct under a sufficiently high cost of infection (for both cur‐

rency types). For indirect transmission, extinction occurred when


either the fecundity cost of infection was 1, or if the survival cost

of infection was 0.5 or greater (Figures 3 and 4a,b). In viable popula‐

tions, migration was favoured only if it was sufficiently less costly

than infection. For frequency‐dependent transmission, the results

were almost identical to those for indirect transmission (Figure 4c,d).

In contrast, for density‐dependent transmission, populations almost

never went extinct (Figure 4e,f, Figure S2). Instead, populations re‐

mained viable and exhibited partial migration for intermediate costs

of infection.

3.3 | Density‐dependent transmission favours partial migration

Partial migration, where the population evolved neither full resi‐

dency nor full migration, but something in between, only occurred

if parasite transmission was density‐dependent (Figure 4). Partial

migration evolved in one of two ways: either the entire population

evolved to have the same intermediate strategy (e.g. Figure 2d) or

two distinct strategies evolved and coexisted in the population (e.g.

Figure 2c). Generally, a single intermediate strategy evolved when‐

ever recovery from infection was possible, regardless of where

recovery occurred (e.g. Figure 5a). In contrast, if individuals never

recovered from infection, coexistence of two strategies was a pos‐

sible form of partial migration (Figure 5b).

3.4 | Impact of transmission and recovery time‐scales

The above results did not change substantially with different val‐

ues of ρ (the ratio of transmission to recovery time‐scales). Instead,

there were only two small differences in outcome. First, increas‐

ing ρ increased host extinction risk. Simulations with larger values

(ρ = 10; Figures S4–S6) had extinction for a broader range of param‐

eter values whereas simulations with smaller values (ρ = 0.5; Figures

S7–S9) had extinction for a narrower range of parameter values,

compared with the above results. Second, increasing ρ shifted the

boundary between migration and residency. With density‐depend‐

ent transmission, simulations with larger values (ρ = 10) were more

likely to show full migration where the above simulations had partial

migration, and simulations with smaller values (ρ = 0.5) were more

likely to show partial migration where the above simulations had full

migration.

4 | DISCUSSION

Migrationandinfectioncaninteractinavarietyofways,yetderiv‐

ing general principles regarding these interactions is challenging,

F I G U R E 2 Evolution of strategies over time. Simulation examples showing the number of individuals with each migration strategy in the population over evolutionary time (in thousands of iterations) showing (a) full residency (θ = 0), (b) full migration (θ = 1), (c) coexistence of distinct strategies (full migration and an intermediate strategy), (d) intermediate strategy and (e) a still evolving strategy. Differences in the population numbers across panels (darkness of grey) arise through differential mortality

0 5 10

1

0.5

00 5 10

1

0.5

0

0 5 10

1

0.5

00 5 10

1

0.5

0

0 5 10

1

0.5

0

>100

50

0

(a) (b)

(c) (d)

(e)

Str

ate

gy (

)

Iteration (Thousands)

Number of

individuals

F I G U R E 3 Cost type influences when migration is favoured. The average evolved migration strategy (θ) as a function of the cost of migration (x‐axes) and the cost of infection (y‐axes). White areas indicate a non‐viable population, black is full migration, light grey is no migration, and medium grey is intermediate strategies. Infection reduces either survival (a, b) or fecundity (c, d), and migration similarly reduces either fecundity (a, c) or survival (b, d). Parameters: indirect transmission with recovery in environment #2 and ρ = 2

0 0.5 1

0

0.5

1

0 0.5 1

0

0.5

1

0 0.5 1

0

0.5

1

0 0.5 1

0

0.5

1

1

0.5

0

(a) (b)

(c) (d)

Fe

cu

nd

ity

Su

rviv

al

Infe

ctio

n c

ost

Fecundity Survival

Migration cost


due to both the length of time over which migration evolves and

the diversity of the organisms involved. Here, we develop a gen‐

eral modelling framework to study these interactions, enabling us

to both simulate long time‐scales and encompass a large range of

empirical systems. We show that selective pressures from a para‐

site can favour the evolution of host migration and that the out‐

come is influenced by the spatiotemporal dynamics of infection

and recovery from infection, the currency of costs associated with

each migration and infection, and the parasite transmission mode.

Specifically, migration was most likely to evolve when migrants

could recover from infection either during transit or in the envi‐

ronment #2 they travelled to and when migration reduced host

fecundity while infection reduced host survival. Partial migration

only evolved when parasite transmission was density‐dependent.

Our simulation results match previous analytic work (i.e. Figure 3b

here vs. figure 2a in Shaw & Binning, 2016) when infection cost is

low. However, when infection cost is high, simulated populations

went extinct before migration could evolve, an outcome that was

not captured in the analytic model which did not account for the

rate of evolution.

The migration strategy that evolved was shaped by the currency

inwhich costs in ourmodelwere paid.Migrationwasmost easilyfavoured when the migration cost was in terms of fecundity, rather

than survival, and when the infection cost was in terms of survival.

For instance, migrants can experience reduced fecundity relative

to residents due to delayed arrival at breeding sites and/or reduced

competitiveness upon arrival (i.e. Red‐spotted newts; Notophthalmus

viridescens viridescens; Bloch & Grayson, 2010). Conversely, migra‐

tion was least likely to be favoured when the migration cost was in

terms of survival, while the infection cost was in terms of fecundity.

Thus, reducing fecundity was a weaker selective pressure than re‐

ducing survival, although the strength (or direction) of this result may

depend on our assumption that density dependence acts through

fecundity not survival. Such conflicting selection pressures are com‐

mon in natural populations (Schluter, Price, & Rowe, 1991) and can

explain variation in life history among taxa. A challenge in comparing

across types of life‐history costs is that different costs may be paid

at different times. For example, individuals commonly die at any time

of year (continuous survival cost) but are often seasonal breeders

(discrete fecundity cost). Alternatively, survival could be based on

whether an individual travelled to a sufficiently good overwintering

spot during migration (discrete survival) but fecundity could depend

on the total resources accumulated through the year, varying with

infection status and migratory behaviour (continuous fecundity cost).

Table 1 highlights a variety of empirical systems that could

represent some of the patterns we found in the model. For some

pathogens, hosts do not recover in a specific location; migratory and

non‐migratory hosts alike could die instead of recovering (e.g. zebra

and anthrax, Zidon, Garti, Getz, & Saltz, 2017) or the environment

does not play a role in recovery (e.g. viral infections such as morbil‐

livirus or influenza). For other pathogens with recovery, hosts often

recover by utilizing some sort of environmental gradient. For exam‐

ple, hosts can modify their behaviour in their breeding environment

F I G U R E 4 Transmission mode shapes extinction and partial migration. The average evolved migration strategy (θ) as a function of the survival cost of migration (x‐axes, μM) and the survival cost of infection (y‐axes, μI) with ρ = 2. Transmission is indirect (a, b), frequency‐dependent (c, d) or density‐dependent (e, f), and recovery either does not occur (a, c, e) or occurs in environment #2 (b, d, f). White areas indicate a non‐viable population, black is full migration, light grey is no migration, and colours are intermediate strategies, and stars indicate simulations that had not fully converged (due to low selection gradients)

0 0.5 1

0

0.5

1

0 0.5 1

0

0.5

1

0 0.5 1

0

0.5

1

0 0.5 1

0

0.5

1

0 0.5 1

0

0.5

1

0 0.5 1

0

0.5

1

1

0.5

0

(a) (b)

(c) (d)

(e) (f)

NO RECOVERY ENV #2 RECOVERY

IND

IRE

CT

FR

EQ

.-DE

P.

DE

NS

.-DE

P.

Infe

ctio

n c

ost (s

urv

iva

l)

Migration cost (survival)

F I G U R E 5 Two forms of partial migration. The number of individuals with each migration strategy in the population at the end of simulations (y‐axis, θ) as a function of the fecundity cost of migration (φM, x‐axes) for two scenarios: (a) recovery from infection occurs in environment #2, and (b) there is no recovery from infection. Partial migration occurs either as (a) an intermediate strategy (0 < θ < 1) or as (b) the coexistence of two distinct strategies. Parameters: density‐dependent transmission, infection has a survival cost of μI = 0.8 and ρ = 2. [Correction added after online publication on 16 August 2019: Figure 5 replaced].

0 0.5 1

1

00 0.5 1

1

0

100

50

0

(a) (b)

Migration fecundity cost

Full

migration

No

migration

Number of

individuals


to discourage parasites by sunning themselves (e.g. birds and lice,

Blem & Blem, 1993). Hosts can also recover in transit to the migra‐

tory grounds (e.g. ducks and helminths) or at the migratory grounds

(e.g.flounders loseparasitesaswaterdecreases insalinity,Möller,1978). However, note that the same parasite can be modelled with

different transmission modes under different ecological circum‐

stances (e.g. chytrid fungal infections in amphibians); thus, the de‐

tails of the biologically relevant available data should drive choice of

transmission mode.

The transmission modes (corresponding to different types of

parasites) influenced extinction risk as well as the type of migration

that evolved. Parasites with density‐dependent transmission (e.g.

gastrointestinal helminths and sea lice, Arneberg, Skorping, Grenfell,

& Read, 1998; Jansen et al., 2012) almost never drove populations

extinct. The exceptions occurred when infection with a parasite led

to an extreme reduction in fecundity (Figures S2, S5 and S8). This

matches existing theory suggesting that density‐dependent trans‐

mission should not drive a host population extinct, except in a few

cases, including when the pathogen reduces host fecundity while

having little effect on survival (De Castro & Bolker, 2004; O’Keefe

& Antonovics, 2002). For example, trematode infection in pulmon‐

ate snails can result in reduced fecundity while having no impact on

survival (Keas & Esch, 1997). Parasites with frequency‐dependent

transmission typically caused population extinction when infection

sufficiently reduced either fecundity or survival. This result builds

on existing literature, suggesting that diseases with frequency‐de‐

pendent transmission can drive a population extinct (De Castro &

Bolker, 2004).

Partial migration, where only a fraction of the population mi‐

grates, only emerged when parasite transmission was density‐de‐

pendent. With density‐dependent transmission, any factor that

reduces population density will, intuitively, reduce the transmis‐

sion rate per individual as well. Thus, partial migration, which splits

the population spatially during part of the year, reduces transmis‐

sion for non‐migrant individuals enough that it balances the cost

of staying in an environment with parasites. This result is analo‐

gous to previous theoretical findings that density dependence (in

survival) during the season where migrants and non‐migrants are

apart can favour partial migration (Kaitala, Kaitala, & Lundberg,

1993). In contrast, with either frequency‐dependent or indirect

transmission, reducing population density has no effect on per in‐

dividual transmission rates, and thus, partial migration (as a mixed

strategy at the population level) is never favoured as a strategy:

only full migration or no migration evolves. Partial migration can

also be viewed as a mixed strategy at the individual level; our

past work showed that slow rates of transmission and recovery

can favour occasional migration by long‐lived individuals (Shaw &

Binning, 2016).

In our model, partial migration occurred in two distinct ways: a

monomorphic population with an intermediate migration strategy

or a dimorphic population with two coexisting strategies. The first

outcome is equivalent to individuals being flexible in their migratory

strategy across years while the second corresponds to individuals

adopting a fixed strategy throughout their lives; both of these out‐

comes are exhibited by freshwater roach (Rutilus rutilis) populations

(Brodersen et al., 2014). Dimorphic partial migration (which has the

potential to lead to speciation on long enough time‐scales) only oc‐

curred when there was no recovery from infection.

There are a number of future directions that could be developed,

building on the work presented here. First, given that migration/res‐

idency is not a binary trait, one could consider degrees of migration

(distance, diversity of habitats visited) to tease apart the aspects of

migration that most influence infection (Gutiérrez, Rakhimberdiev,

Piersma, & Thieltges, 2017). One could also consider trade‐offs in

host strategies for dealing with parasites: for example, investing

in tolerance versus resistance (Råberg, 2014). One could also con‐

sider evolving parasite behaviour, or even co‐evolution between

hosts and parasites, drawing on ideas from the dispersal literature

(e.g. Lion & Gandon, 2015; Lion, van Baalen, & Wilson, 2006) and

exploring the impact of a virulence‐transmission trade‐off for par‐

asites. Finally, since infection is rarely the only factor selecting for

migration, future work could determine how migration propensity

depends on the combination of infection and other factors that se‐

lect for or against migration.

Disease ecologists and wildlife epidemiologists traditionally

focus on parasite transmission between individuals and populations;

understanding transmission helps us not only understand when and

where certain individuals are more likely to get infected than others

but also allows us to assess future impacts on population dynam‐

ics and better design preventative or reactive control strategies.

Here, we show that transmission matters beyond the population

scale and can influence broader phenomena such as the evolution

of migration. Given growing concern about climate‐driven disease

emergence (Altizer, Ostfeld, Johnson, Kutz, & Harvell, 2013), under‐

standing how movement of hosts and their interactions with para‐

sites change as environments change is a pressing problem that is

ripe for research (White, Forester, & Craft, 2018).

ACKNOWLEDG EMENTS

We thank the CEID group at UGA for early feedback on results

and anonymous reviewers for suggestions. We acknowledge the

Minnesota Supercomputing Institute (MSI) at the University ofMinnesotaforprovidingresourcesthatcontributedtotheresearchresults reported within this paper (http://www.msi.umn.edu). This

material is based in part upon work supported by the National

Science Foundation under Grant No. DEB‐1654609. S.A.B. is sup‐

ported by the Natural Sciences and Engineering Research Council

of Canada.

AUTHORS’ CONTRIBUTIONS

A.K.S.,M.E.C.,M.Z.andS.A.B.conceivedofthestudy;A.K.S.devel‐opedandanalysedthemodel;M.E.C.andS.A.B.compiledtheem‐

piricalexamples;andA.K.S.,M.E.C.,M.Z.andS.A.B.contributedtowriting and editing the final manuscript.


DATA AVAIL ABILIT Y STATEMENT

Simulation code and data are available from the Dryad Digital

Repository https ://doi.org/10.5061/dryad.nc0f501 (Shaw et al., 2019).

ORCID

Allison K. Shaw https://orcid.org/0000‐0001‐7969‐8365

Meggan E. Craft https://orcid.org/0000‐0001‐5333‐8513

Sandra A. Binning https://orcid.org/0000‐0002‐2804‐9979

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SUPPORTING INFORMATION

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Host migration strategy is shaped by forms of parasite