Modelling Ranavirus Transmission in Populations of Common Frogs (Rana Temporaria) in the United Kingdom

viruses

Article Modelling Ranavirus Transmission in Populations of Common Frogs (Rana temporaria) in the United Kingdom

Amanda L.J. Duﬀus 1,* , Trenton W.J. Garner 2, Richard A. Nichols 3 , Joshua P. Standridge 1 and Julia E. Earl 4 1 Department of Mathematics and Natural Sciences, Gordon State College, Barnesville, GA 30204, USA; [email protected] 2 Institute of Zoology, Zoological Society of London, London NW1 4RY, UK; [email protected] 3 School of Biological and Chemical Sciences, Queen Mary, University of London, London E1 4NS, UK; [email protected] 4 School of Biological Sciences, Louisiana Tech University, Ruston, LA 71272, USA; [email protected] * Correspondence: aduﬀ[email protected]

Received: 10 April 2019; Accepted: 4 June 2019; Published: 15 June 2019

Abstract: Ranaviruses began emerging in common frogs (Rana temporaria) in the United Kingdom in the late 1980s and early 1990s, causing severe disease and declines in the populations of these animals. Herein, we explored the transmission dynamics of the ranavirus(es) present in common frog populations, in the context of a simple susceptible-infected (SI) model, using parameters derived from the literature. We explored the eﬀects of disease-induced population decline on the dynamics of the ranavirus. We then extended the model to consider the infection dynamics in populations exposed to both ulcerative and hemorrhagic forms of the ranaviral disease. The preliminary investigation indicated the important interactions between the forms. When the ulcerative form was present in a population and the hemorrhagic form was later introduced, the hemorrhagic form of the disease needed to be highly contagious, to persist. We highlighted the areas where further research and experimental evidence is needed and hope that these models would act as a guide for further research into the amphibian disease dynamics.

Keywords: transmission modelling; susceptible-infected (SI) models; emerging infection; ranavirosis; Iridoviridae; disease dynamics

1. Introduction Ranaviruses are double-stranded DNA viruses in the Iridoviridae family that can infect ectothermic vertebrates [1] and are found worldwide [2]. Ranaviruses cause systemic hemorrhaging and edema in amphibian, reptile, and ﬁsh hosts [3]. In amphibians, mortality can occur in only three days in very susceptible host species and life history stages [4], resulting in die-oﬀs of both adults and larvae, in Europe [5,6], and tadpoles and metamorphs, in North America [7,8]. Ranaviruses have been shown to alter amphibian population dynamics, with declines of the common frog (Rana temporaria) in the United Kingdom [9] and whole amphibian communities in Spain [10]. Additionally, population simulation models have shown that ranaviruses could potentially cause the local extinction of populations of three, highly susceptible species of the United States anurans [11,12]. However, these models do not include the transmission dynamics, which are not well-understood and could potentially alter host population dynamics. Farrell et al. [13] modeled host population declines in the case of the highly pathogenic Ambystoma tigrinum virus (ATV), but they found that extinction of host populations would not occur even in the cases where the host population was severely reduced. These diverse conclusions

Viruses 2019, 11, 556; doi:10.3390/v11060556 www.mdpi.com/journal/viruses Viruses 2019, 11, 556 2 of 13 showed that there were many different possible outcomes of ranavirus infections that influenced disease dynamics, and they appeared to be system-specific. Mathematical models are helpful tools for understanding transmission dynamics and the persistence of pathogen and host populations [14,15]. Models might help determine which transmission conditions are most likely, given the information about disease dynamics in wild populations. In the case of the ranavirus, Brunner and Yarber [16] developed a model which suggested that ranavirus transmission from water and scavengers are likely minimal in most circumstances. Previous attempts have also been made to formalize the transmission dynamics at, both, the species level [17] and at the community level [18]. Most models have been based on North American amphibian populations or communities. The dynamics of amphibian–ranavirus systems in the UK, the ranavirus–common frog (Rana temporaria) system, are distinctly different from those in North America and thus require specific investigation. Here, we developed susceptible-infection (SI) models for ranavirus infection in common frogs, in the UK. The ranavirus–common frog system in the UK differs from the infection/disease dynamics seen in North American anuran species, because infections in eggs or tadpoles of wild populations are absent, for the most part [19,20], despite experimental evidence that tadpoles can be infected and have died with signs of ranavirosis. Given this information, the route of transmission in common frogs is most likely among adults. With the benefit of long-term data sets on the persistence of ranavirus infections in common frogs, we know that the ranavirus can persist in adult frog populations for many years [9] and involves at least two distinct disease syndromes (hemorrhagic and ulcerative) with variations in the prevalence of disease, across sites and years [21]. We, therefore, developed SI models to test the hypothesis that ranaviruses have the potential to remain in the UK common frog populations, under various conditions, with only horizontal transmission between adults. We examined scenarios with host population declines that included both ranavirus syndromes.

2. Basic Model Formulation In the simplest case, we used an SI model with no recovery, based on the high mortality rate associated with ranavirus infection. We followed the method for developing mathematical models described by Otto and Day [22]. The population consisted of recruits (AR), susceptible individuals (AS), and infected individuals (AI) and mortality occurred at two different rates—natural mortality (MN) and mortality due to disease (MD). We assumed that the adult population size remained constant (i.e., mortality was fully compensated irrespective of the cause of death), all recruits to the population were susceptible to the ranavirus, and all individuals were equally susceptible to infection. The contact rate (Ψ) was defined as the number of different individuals that one animal physically contacts, the likelihood of transmission (σ) was the probability of transmission given the physical contact, and R0 was the basic reproductive rate of the virus. We used a discrete time model, because common frogs aggregate annually for breeding and we assumed that transmission primarily occurred from contacts during breeding. We also assumed that mortality due to disease occurred primarily during summer; ranavirus-associated mortality peaks between mid-July and mid-August, after breeding, has previously been concluded [20]. (See Figure1 for a schematic view of the important life history events and timing.) Based on the above assumptions, we developed the following equations:

As(t + 1) = As(t) σΨ As(t) A (t) M (t) + A (t) (1) − · · I − N R

A (t + 1) = A (t) + σΨ As(t) A (t) [M (t) + M (t)] (2) I I · · I − N D R = σΨ As(t)/[M (t) + M (t)] (3) 0 · N D To determine under what conditions the ranavirus would remain or spread in a population, we modiﬁed Equation (3) by removing MD (t) to assume a successful introduction:

Ro = σΨ As/M (t) (4) · N Viruses 2019, 11, x FOR PEER REVIEW 3 of 14 Viruses 2019, 11, x FOR PEER REVIEW 3 of 14 Viruses 2019, 11, 556 3 of 13 Ro = σΨ·As/MN(t) (4) Ro = σΨ·As/MN(t) (4) TheThe importantimportant interactionsinteractionsinteractions in inin this thisthis equation equationequation are areare between betweenbetweenσ σσand andandΨ Ψ,Ψ and,, andand this thisthis relationship relationshiprelationship needed neededneeded to to be explored, graphically, to determine when the conditions for Ro ≥ 1 exist. If we assume a beto explored,be explored, graphically, graphically, to determine to determine when thewhen conditions the conditions for Ro for1 exist. Ro ≥ If 1 we exist. assume If we a population assume a ≥ population size of 99 (AS), with an initial introduction of one infected individual (AI) and an MN of sizepopulation of 99 (A sizeS), withof 99 an(AS initial), with introduction an initial introduction of one infected of one individual infected individual (AI) and an (A MI) Nandof an 20% M [N23 of] 20% [23] (although other estimates do exist [24]), values of σ and Ψ under which Ro ≥ 1 are illustrated (although20% [23] (although other estimates other estimates do exist [24 do]), exist values [24]), of σ valuesand Ψ ofunder σ and which Ψ under Ro which1 are illustrated Ro ≥ 1 are inillustrated Figure2. ≥ Toinin Figure testFigure ifsimilar 2.2. ToTo testtest assumptions ifif similarsimilar areassumptionsassumptions valid at a are smallerare validvalid population atat aa smallersmaller size, populationpopulation we repeated size,size, the wewe process repeatedrepeated using thethe process using alternative values for AS = 49 and MN = 10% (i.e., 5 individuals/annum) and introduced alternativeprocess using values alternative for AS =values49 and for M ANS == 4910% and (i.e., MN 5 = individuals 10% (i.e., 5/ annum)individuals/annum) and introduced and one introduced infected individualoneone infectedinfected (total individualindividual population (total(total size populationpopulation 50; Figure sizesize2). 50;50; FigureFigure 2).2).

FigureFigure 1.1. AnnualAnnual cycle cycle of of important important life life history history events events for for commoncommon frogsfrogs ((RanaRana temporariatemporaria)) andandand importantimportant eventsevents forfor ranavirusranavirus infectionsinfections andand diseases,diseasdiseases,es, forfor thesethese animals.animals.animals. Boxes Boxes shaded shaded in in blueblue areare thosethose thatthat occuroccur in in thethe aquaticaquatic environment, environment, green greengreen boxesboxes areare those those that that straddlestraddle the the land and and water, water, greygrey boxesboxes occuroccur atat anan unknownunknown location,location, andand mauvemauvmauvee boxesboxes areare lifelife historyhistory eventsevents thatthat areare knownknown toto happenhappen onon bothboth thethe landland andand inin thethe water.water.

FigureFigure 2.2. TheThe interaction interaction between between σσ andand ΨΨ, under, under which which Ro R≥o 1, when1, when AS = A 99S =and99 an and MN an = 20% MN (upper= 20% Figure 2. The interaction between σ and Ψ, under which Ro ≥ 1,≥ when AS = 99 and an MN = 20% (upper (upperdashed-curve) dashed-curve) and when and the when initial the conditions initial conditions of AS = 49 of and AS =an49 M andN = 10% an M(lowerN = 10% curve), (lower where curve), Ψ is dashed-curve) and when the initial conditions of AS = 49 and an MN = 10% (lower curve), where Ψ is where Ψ is the contact rate and σ is the likelihood of transmission for the model. thethe contactcontact raterate andand σσ isis thethe likelihoodlikelihood ofof transmissiontransmission forfor thethe model.model. After establishing the conditions which permit ranavirus persistence, we next examined the AfterAfter establishingestablishing thethe conditionsconditions whichwhich permitpermit ranavirusranavirus persistence,persistence, wewe nextnext examinedexamined thethe behaviorbehavior ofof AASS andand AAII underunder potentialpotential biologicallybiologically relevantrelevant conditions.conditions. We usedused experimentalexperimental datadata behavior of AS and AI under potential biologically relevant conditions. We used experimental data from ranavirus exposures in the literature, to estimate σ (Table1). It is important to note that the data fromfrom ranavirusranavirus exposuresexposures inin thethe literature,literature, toto estimateestimate σσ (Table(Table 1).1). ItIt isis importantimportant toto notenote thatthat thethe datadata σ usedused toto estimateestimate σ waswas extremelyextremely variable;variable;the theviral viraltiters titersused usedin inthe theexperiments experiments range range from from TCID TCID5050 used1 to estimate2 σ was extremely variable; the viral titers used in the experiments range4.2 from6.2 TCID50 ofof 10101 toto 10102 mLmL forfor virusvirus obtainedobtained fromfromcrude crude organ organ homogenates homogenates to to TCID TCID5050of of 10 104.2 toto 10106.2 mL,mL, forfor of 101 to 102 mL for virus obtained from crude organ homogenates to TCID50 of 104.2 to 106.2 mL, for virus produced via tissue culture [25]. This variability made the biological relevance of our estimates virusvirus producedproduced viavia tissuetissue cultureculture [25].[25]. ThisThis variabilityvariability mademade thethe biologicalbiological relevancerelevance ofof ourour estimatesestimates less than ideal; however, these are the best estimates that can be made with the available data. lessless thanthan ideal;ideal; however,however, thesethese areare thethe bestbest estimatesestimates thatthat cancan bebe mademade withwith thethe availableavailable data.data.

Viruses 2019, 11, x FOR PEER REVIEW 4 of 14

Table 1. Estimates for σ derived from the literature. Note: Experiments where the exposure was via

Viruses 2019inoculation, 11, 556 have not been included in these estimates. No distinction has been made between the4 of 13 types of ranavirus-associated disease that the virus was derived from. Development of disease data,

TCID50 and type of experiment information are summarized from Cunningham et al. [25]. (HS = TableHemorrhagic 1. Estimates and forUSσ = derivedUlcerati fromve forms the literature.of ranavirosis.). Note: Experiments where the exposure was via inoculation have not been included in these estimates. No distinction has been made between the types Development of of ranavirus-associated disease that the virus was derived from. Development of disease data, TCID50 Disease Disease Estimate and type of experiment information are summarizedType of Experiment/Exposure from Cunningham et Type al. [25 ]. (HS = HemorrhagicTCID50 No. with Total No. Prevalence of σ and US = Ulcerative forms of ranavirosis.). Disease Exposed Development of Disease Immersion with virus from naturally Disease 1 3 20 15% Type of Experiment/Exposure Type Estimate of0.15σ TCID10 /mL No. with Total No. Prevalence disease tissue, with and without bacteria 50 Disease Exposed Immersion with virus from naturally 102/mL HS Immersiondisease tissue with virushomogenate from naturally to animals 93 20 20 15%45% 0.15 0.45 101/10mL1.5/mL diseasewith tissue,skin wounds, with and without with and bacteria without Immersion with virus from naturally US bacteria 102/mL HS 9 20 45% disease tissue homogenate to animals with 0.45 101.5/mL2 US skin wounds, with and without bacteria 10 /mL HS 9 10 90% Immersion in virus from culture 0.90 101.5/mL 102/mL HS 9 10 90% Immersion in virus from culture 0.90 101.5/mLUS US 5.6 ImmersionImmersion in in virus virus from from virus virus culture culture to to 105.610to to 55 5 5 100% 1 1 animalsanimals with with wounded wounded skin skin 106.210/mL6.2/mL ImmersionImmersion in virus from in virus tissue from homogenate tissue 22 5 5 40% fromhomogenate naturally diseased from animals naturally to animals diseased 0.40 0.40 103/mL103/mL animalswith to animals wounded wi skinth wounded skin

EstimatesEstimates of ofΨ Ψwere were unavailable, unavailable, so so we we arbitrarily arbitrarily chose choseΨ Ψ= =0.3 0.3→0.60.6 (Figure (Figure3). 3). We We ignored ignored sex sex → speciﬁcspecific contact contact rates, rates, as as male–male male–male contact contact rates rates are are extremely extremely high high and and polyandry polyandry is is common common [ 26[26].]. Additionally,Additionally, Teacher Teacher et al.et [al.9] [9] found found that that the medianthe median population population size ofsize common of common frogs wasfrogs 31 was for those31 for placesthose whereplaces ranaviruseswhere ranaviruses have emerged have emerged in the UK, in the so weUK, used so we an used ATotal anof A 30Total (Figure of 30 (Figure4). 4).

Figure 3. Predicted values of AS with varying values of Ψ while other values remained constant at: Figure 3. Predicted values of AS with varying values of Ψ while other values remained constant at: σ σ = 0.3; MN = 0.2; and MD = 0.75. The starting population composition is AI = 1 and AS = 99 and time = 0.3; MN = 0.2; and MD = 0.75. The starting population composition is AI = 1 and AS = 99 and time is in is in years. AS is the number of susceptible individuals, Ψ is the contact rate, σ is the likelihood of years. AS is the number of susceptible individuals, Ψ is the contact rate, σ is the likelihood of transmission, MN is the natural mortality rate, and MD is the mortality rate associated with ranavirosis. transmission, MN is the natural mortality rate, and MD is the mortality rate associated with ranavirosis.

Viruses 2019, 11, 556 5 of 13 Viruses 2019, 11, x FOR PEER REVIEW 5 of 14

FigureFigure 4. The 4. The average average expectation expectation of of the the ranavirus ranavirus dyna dynamicsmics in in a apopulation population of adult of adult common common frogs frogs (Rana temporaria) through time (years). (Ψ = 0.45; σ = 0.3; MN = 0.2; MD = 0.775; starting population (Rana(Rana temporaria temporaria) through) through time time (years). (years). ( Ψ(Ψ= =0.45; 0.45;σ σ == 0.3;0.3; M NN == 0.2;0.2; M MD D= 0.775;= 0.775; starting starting population population comprised of AI = 1 and AS = 29.) AI is the number of infected individuals, AS is the number of comprised of AI = 1 and AS = 29.) AI is the number of infected individuals, AS is the number of susceptible individuals, Ψ is the contact rate, σ is the likelihood of transmission, MN is the natural susceptible individuals, Ψ is the contact rate, σ is the likelihood of transmission, MN is the natural mortality rate, and MD is the mortality rate associated with ranavirosis. mortality rate, and MD is the mortality rate associated with ranavirosis. Since ranaviruses have emerged recently in the UK, and common frogs and the severity of the Since ranaviruses have emerged recently in the UK, and common frogs and the severity of disease is affected by climate change, it is unlikely that the disease dynamics have reached an the disease is aﬀected by climate change, it is unlikely that the disease dynamics have reached an equilibrium ([27,28]; Figure 4). Using an estimated σ of 0.3 (from data from Table 1), an average MD equilibrium ([27,28]; Figure4). Using an estimated σ of 0.3 (from data from Table1), an average M of of 0.775, an average Ψ value of 0.45, and an Atotal of 30 [9] with the initial conditions of an As of 29 and D 0.775,an an A averageI of 1, we Ψfoundvalue that of the 0.45, interaction and an A betweentotal of 30 AS [ 9and] with AI requires the initial greater conditions than 60 ofyears an Atos stabilizeof 29 and an AI ofto 1, wepost-epidemic found that dynamics the interaction (Figure between 5). These A resuS andlts AsuggestI requires that, greater under thanthe present 60 years conditions, to stabilize to post-epidemicranavirus dynamicsin populations (Figure of5 ).common These results frogs suggestcan be that,sustained under theentirely present through conditions, adult–adult ranavirus in populationstransmission. of common frogs can be sustained entirely through adult–adult transmission.

Figure 5. Illustration of the predicted values for AS with diﬀerent disease-induced mortality rates, while other values remained constant at: Ψ = 0.45; σ = 0.3; MN = 0.2; the starting population comprised

of AI = 1 and As = 29. As is the number of susceptible individuals, Ψ is the contact rate, σ is the likelihood of transmission, MN is the natural mortality rate and MD is the mortality rate associated with ranavirosis. Viruses 2019, 11, x FOR PEER REVIEW 6 of 14

Figure 5. Illustration of the predicted values for AS with different disease-induced mortality rates, Viruses 2019, 11, 556 6 of 13 while other values remained constant at: Ψ = 0.45; σ = 0.3; MN = 0.2; the starting population

comprised of AI = 1 and As = 29. As is the number of susceptible individuals, Ψ is the contact rate, σ 2.1. Factoringis the inlikelihood Population of transmission, Decline MN is the natural mortality rate and MD is the mortality rate associated with ranavirosis. In UK common frogs, ranavirosis has caused an 81% decline in some affected populations, over a 10 year2.1. periodFactoring [9 in]; thisPopulation appears Decline to be a clear violation of the assumption in the model that population size remainsIn UK constant. common Teacher frogs, ranavirosis et al. [9] foundhas caused that an the 81 declines% decline in in these some populations affected populations, were proportional over to theira 10 year size period (i.e., the [9]; this larger appears the population,to be a clear violation the larger of the the assumption decline experienced).in the model that Thispopulation is possibly consistentsize remains with the constant. assumption Teacher that et all al. adults [9] found are equally that the susceptible, declines in when these a ranaviruspopulations first were invades a population.proportional Contrarily, to their size larger (i.e., the declines larger the in largerpopulation, populations the larger might the decline be due experienced). to density-dependent This is transmissionpossibly consistent of the virus. with This the assumption scenario can that also all accountadults are for equally the di susceptible,fferences among when a individuals, ranavirus first in their invades a population. Contrarily, larger declines in larger populations might be due to density- susceptibility to the ranavirus. dependent transmission of the virus. This scenario can also account for the differences among However, Teacher et al. [29] report that populations of common frogs maintain allelic diversity individuals, in their susceptibility to the ranavirus. through theHowever, immigration Teacher of et adults al. [29] from report nearby that populations ponds. This of immigrationcommon frogs has maintain two potentially allelic diversity important consequencesthrough the for immigration the emergence of adults of ranavirosis: from nearby (1)ponds. the populationThis immigration of adult has frogstwo potentially in the aff ected populationimportant will consequences remain susceptible for the emergence to infection of ranavi becauserosis: of (1) the the homogenizing population of adult effect frogs of immigration; in the thus,affected the immigration population ofwill susceptible remain susceptible individuals to mightinfection dilute because the prevalenceof the homogenizing of the resistance effect of genes, as longimmigration; as the immigrants thus, the immigration come from of susceptible susceptible populations;individuals might and dilute (2) immigration the prevalence might of the bolster populationresistance numbers genes, as and long reduce as the immigrants the observed come decline. from susceptible Consequently, populati theons; estimatesand (2) immigration of population declinemight due bolster to ranavirosis population thatnumbers were and made reduce by the Teacher observed et al.decline. [9] might, Consequently, in fact, the be estimates underestimates. of population decline due to ranavirosis that were made by Teacher et al. [9] might, in fact, be In addition, Campbell et al. [30] have found that the population structure shifts from older adult frogs underestimates. In addition, Campbell et al. [30] have found that the population structure shifts from to proportionallyolder adult frogs more to proportionally juveniles, with more a much juveniles, smaller with total a much population smaller sizetotal in population the affected size populations. in the Theseaffected smaller populations. populations These have smaller also populations been shown ha tove bealso more been susceptibleshown to be tomore stochastic susceptible events, to via populationstochastic modelling events, via [30 population]. For simplicity, modelling we [30]. assumed For simplicity, that declines we assumed of 81% overthat declines a 10 year of period,81% as seenover by Teachera 10 year et period, al. [9], as correspond seen by Teacher to a steadyet al. [9], annual correspond decline to a of steady 8.1%. annual Under decline such conditions,of 8.1%. it takesUnder the model such conditions, approximately it takes 65 the years model to approximat stabilize, withely 65 all years adults to stabilize, in the population with all adults suff inering the from ranaviruspopulation infections suffering (Figure from6 ranavirus). infections (Figure 6).

FigureFigure 6. Illustration 6. Illustration of of the the predicted predicted dynamicsdynamics of of aa common common frog frog population population,, with with the ranavirus the ranavirus

factoringfactoring in an in annualan annual population population decline decline of of 8.1% 8.1% forfor adult common common frogs. frogs. (Ψ ( Ψ= 0.45;= 0.45; σ = σ0.3;= M0.3;N =M 0.2;N = 0.2; MD = 0.775; starting population comprised of AI = 1 and AS = 29; time is in years.) As is the number of MD = 0.775; starting population comprised of AI = 1 and AS = 29; time is in years.) As is the number susceptible individuals, Ψ is the contact rate, σ is the likelihood of transmission, MN is the natural of susceptible individuals, Ψ is the contact rate, σ is the likelihood of transmission, MN is the natural mortality rate, and MD is the mortality rate associated with the ranavirosis. mortality rate, and MD is the mortality rate associated with the ranavirosis.

2.2. Accounting for Different Disease Syndromes Ranavirosis in the UK common frogs presents as two syndromes which are not mutually exclusive. The ulcerative form of the disease is characterized by ulcers of the skin and the skeletal muscle, and sometimes necrosis of the digits, while the hemorrhagic form of the disease is characterized by internal hemorrhages, most commonly involving the gastrointestinal and reproductive tracts ([21]; Viruses 2019, 11, 556 7 of 13 personal observation). Adult common frogs exposed to a tissue homogenate derived from skin ulcers only developed the ulcerative form of the disease (with a prevalence of ~30%; See Table2;[ 25]). Conversely, adult frogs exposed to a virus isolate obtained from skin ulcers generated both ulcerative and hemorrhagic signs of the disease, while virus isolated from a hemorrhage caused the hemorrhagic form of the disease in exposed adults [25]. These, and other data, indicate that ranaviruses associated with different pathologies in the UK might have different transmission rates [25]. Our estimates of σ for both the ulcerative and hemorrhagic forms can be found in Table2. If we take the view that infection using viral isolates derived from the cell culture does not mimic the natural process, the other estimates from Table2 would be preferred, in which case, we estimated σ for the ulcerative and hemorrhagic syndromes as 0.33 and 0.20, respectively.

Table 2. Estimates for σ derived from the literature, taking into account the diﬀerent disease syndromes and type of syndrome that the virus was obtained from. U indicates the ulcerative form of the disease; H is the hemorrhagic form. The estimate of σ is simply the prevalence of the disease based on the presence of the signs of disease when the experiment terminated. The average estimate of σ is simply the mean of the estimates for each type of virus used for exposure. Development of disease data and type of experiment information are summarized from Tables 3–5 of Cunningham et al. [25].

Development of Disease Type of Experiment/ Average Estimate of σ Exposure Type σ No. with U No. with H No. with U & H Total Exp. Estimate of Immersion with virus from 2 0 0 5 naturally disease tissue with 0.4 bacteria (Ulcerative) Immersion with virus from 0.36 1 0 0 5 naturally disease tissue without 0.2 bacteria (Ulcerative) Immersion with virus from naturally disease tissue to animals 2 0 0 5 0.4 with skin wounds with bacteria (Ulcerative) Immersion with virus from naturally disease tissue to animals 0 0 0 5 0 with skin wounds without bacteria (Ulcerative) Immersion in virus isolated from 2 2 0 5 naturally diseased animals from 0.8 virus culture (RUK 13, Ulcerative) Immersion with virus from 0 0 0 5 naturally disease tissue without 0 bacteria (Hemorrhagic) Immersion with virus from 0.44 0 0 0 5 naturally disease tissue with 0 bacteria (Hemorrhagic) Immersion with virus from naturally disease tissue to animals 1 1 1 5 0.6 with skin wounds with bacteria (Hemorrhagic) Immersion with virus from naturally disease tissue to animals 0 3 1 5 0.8 with skin wounds without bacteria (Hemorrhagic) Immersion in virus isolated from naturally diseased animals from 1 2 1 5 0.8 virus culture (RUK 11, Hemorrhagic)

We investigated three scenarios applying different values of σ, where the first two versions explored the two syndromes in isolation (ulcerative form, AU, and hemorrhagic form, AH, present, respectively, in Figure7A,B), represented by Equations (5)–(9) for the initial frequencies and Equations (10)–(14) at time (t). Then we developed a new series of equations for when both disease syndromes are present and including individuals that show signs of both forms of the disease, AU+H. For simplicity, we Viruses 2019, 11, 556 8 of 13 assumed that all animals are equally susceptible to both forms of the disease (Figure8) and that there was no difference in the disease-induced mortality rate between syndromes:

A (t) = A (i) [σ Ψ A (i) A (i) + σ Ψ A (i) A (i) + σ Ψ A (i) A (i)] M (i) + A (i) (5) S S − 1 · S · U 2 · S · (U+H) 3 · S · H − N R A (t) = A (i) + [σ Ψ A (i) A (i)] [σ Ψ A (i) A (i) + σ Ψ A (i) A (i)] [M (i) + M (i)] (6) U U 1 · S · U − 1 · U · H 3 · H · U − N D(U) A (t) = A (i) + [σ Ψ A (i) A ] + [σ Ψ A (i) A (i)] + [σ Ψ A (i) A (i)] (U+H) (U+H) 2 · S · (U+H) 1 · U · H 3 · H · U (7) [M (i) + M (i)] − N D(U+H) A (t) = A (i) + [σ β A (i) A (i)] [σ β A (i) A (i) + σ β A (i) A (i)] [M (i) + M (i)] (8) H H 3 · S · H − 1 · U · H 3 · H · U − N D(H) As(t + 1) = A (t) [σ Ψ A (t) A (t) + σ Ψ A (t) A (t) + σ Ψ A (t) A (t)] M (t) + A (t) (9) S − 1 · S · U 2 · S · (U+H) 3 · S · H − N R A (t + 1) = A (t) + [σ Ψ A (t) A (t)] [σ Ψ A (t) A (t) + σ Ψ A (t) A (t)] U U 1 · S · U − 1 · U · H 3 · H · U (10) [M (t) + M (t)] − N D(U) A (t + 1) = A (i) + [σ Ψ A (i) A ] + [σ Ψ A (i) A (i)] + [σ Ψ A (i) A (i)] (U+H) (U+H) 2 · S · (U+H) 1 · U · H 3 · H · U (11) [M (i) + M (i)] − N D(U+H) A (t + 1) = A (t) + [σ Ψ A (t) A (t)] [σ Ψ A (t) A (t) + σ Ψ A (t) A (t)] H H 3 · S · H − 1 · U · H 3 · H · U (12) [M (t) + M (t)] − N D(H) Viruses 2019, 11, x FOR PEER REVIEW 9 of 14

σΨ·As(t)·AU(t) A)

AR(t) As(t) AU(t) MN(t)

MN(t) MD(t)

σΨ·A (t)·A (t) B) s H

AR(t) As(t) AH(t) MN(t)

MN(t) MD(t)

Figure 7. Diagrammatic representations of the transmission dynamics of the ranavirus when only the AS or AH causingFigure 7. Diagrammatic isolate of the representations ranavirus is of present. the transmissi (A) Whenon dynamics only of the the ulcerative ranavirus when form only of the ranavirus is presentA withinS or AH causing the population. isolate of the (ranavirusB) When is present. only the (A hemorrhagic) When only the ulcerative form of form the disease of the ranavirus is present in the population.is present All of within the variables the population. present (B) areWhen the only same the hemorrhagic as described form above of theand disease all is have present a time in the component population. All of the variables present are the same as described above and all have a time associated with them. Where As is the number of susceptible individuals, Ψ is the contact rate, σ is the component associated with them. Where As is the number of susceptible individuals, Ψ is the contact likelihood of transmission, MN is the natural mortality rate, and MD is the mortality rate associated rate, σ is the likelihood of transmission, MN is the natural mortality rate, and MD is the mortality rate with ranavirosis.associated with ranavirosis.

Viruses 2019, 11, 556 9 of 13 Viruses 2019, 11, x FOR PEER REVIEW 10 of 14

σ3Ψ·As(t)·AH(t)

σ2Ψ·As(t)·AU+H(t) AR(t)

σ3 Ψ·As(t)·AH(t) σ1Ψ·As(t)·AU(t)

As(t) AU(t) AU+H(t) AH(t)

σ1Ψ·As(t)·AU(t)

MN(t) MN(t) MD(U)(t) MN(t) MD(U+H)(t) MN(t) MD(H)(t)

FigureFigure 8. 8. IllustrationIllustration of of the the complex complex transmission transmission dy dynamicsnamics of of the the ranavirus, ranavirus, when when both both of of the the observedobserved disease disease syndromes syndromes are are present present in in the the popula population.tion. Dashed Dashed lines lines are are used used to to make make the the disease disease syndrome-specificsyndrome-speciﬁc vectors vectors of of the the transmission transmission easier easier to to follow. follow. The The box box sizes sizes are are not not representative representative of of thethe number number of of individuals individuals in in each each category. category. The The order order of of the the boxes boxes does does not not indicate indicate when when the the given given diseasedisease syndrome syndrome was was introduced. introduced. All All parameters parameters have have time time components components associated associated with with them. them. A Ass isis thethe number number of of susceptible susceptible individuals, individuals, ΨΨ isis the the contact contact rate, rate, σσ isis the the likelihood likelihood of of transmission, transmission, M MNN isis thethe natural natural mortality mortality rate, rate, and and M MDD isis the the mortality mortality rate rate associated associated with with ranavirosis. ranavirosis.

UnderUlcerative the assumptions Syndrome that AS = 28 → 14, AH = 1 → 14, with the introduction of 1 → 5 AU, MD(U) = MD(H) = 0.775, σ1 = 0.3, σ3 = 0.25, Ψ = 0.45, and MN = 0.2, based on the RO values, AU and AH should RoU = σ1Ψ [AS(t) + AH(t)]/MN(t)+MD(U)(t) + MD(H)(t) (13) not coexist over the long term. It does not matter if AU is introduced into a population with AH or vice-versa (Figure 9). Both of these disease syndromes co-occur in nature [21] and in experimental Hemorrhagic Syndrome infections [25].

RoH = σ3Ψ [AS(t) + AU(t)]/MN(t) + MD(H)(t) + MD(U)(t) (14)

Under the assumptions that A = 28 14, A = 1 14, with the introduction of 1 5 A , S → H → → U MD(U) = MD(H) = 0.775, σ1 = 0.3, σ3 = 0.25, Ψ = 0.45, and MN = 0.2, based on the RO values, AU and AH should not coexist over the long term. It does not matter if AU is introduced into a population with AH or vice-versa (Figure9). Both of these disease syndromes co-occur in nature [ 21] and in experimental infections [25]. Increasing the number of AU individuals in a population requires a higher transmission rate at each contact, for A to become established (i.e., Ro 1). However, establishment does not guarantee H ≥ coexistence over the long term. While at ﬁrst this might seem counter intuitive, it can be explained as follows—when there are more AU individuals in the population there is a greater overall mortality rate because MD(U) >> MN. Hence, there are actually fewer individuals to infect. Even when all of the population (n = 29) is composed of A individuals, A can become established (σ 0.85; U H 3 ≈ see Figure 10). Although this is a high transmission rate, it is not unlikely in the situation where animals have broken skin (see [25]; adult common frogs with broken skin are more likely to become infected), which is characteristic of the ulcerative form of the ranaviral disease. The above analysis demonstrates that the two disease syndromes could persist in the short term, in the same population, by adult-to-adultFigure 9. Ro values transmission, for the introduction albeit under of one conditions AH individual which into have a population been estimated of AS = 28 from and data AU = that 1 are incomplete(MD(U) = M andD(H) not= 0.775, necessarily Ψ = 0.45, biologicallyMN = 0.2). AS is relevant, the number based of susceptible on the diﬀ individuals,ering Ro values. Ψ is the contact rate, σ is the likelihood of transmission, MN is the natural mortality rate, and MD is the mortality rate associated with ranavirosis.

Increasing the number of AU individuals in a population requires a higher transmission rate at each contact, for AH to become established (i.e., Ro ≥ 1). However, establishment does not guarantee

Viruses 2019, 11, x FOR PEER REVIEW 10 of 14

σ3Ψ·As(t)·AH(t)

σ2Ψ·As(t)·AU+H(t) AR(t)

σ3 Ψ·As(t)·AH(t) σ1Ψ·As(t)·AU(t)

As(t) AU(t) AU+H(t) AH(t)

σ1Ψ·As(t)·AU(t)

MN(t) MN(t) MD(U)(t) MN(t) MD(U+H)(t) MN(t) MD(H)(t)

Figure 8. Illustration of the complex transmission dynamics of the ranavirus, when both of the observed disease syndromes are present in the population. Dashed lines are used to make the disease syndrome-specific vectors of the transmission easier to follow. The box sizes are not representative of the number of individuals in each category. The order of the boxes does not indicate when the given disease syndrome was introduced. All parameters have time components associated with them. As is

the number of susceptible individuals, Ψ is the contact rate, σ is the likelihood of transmission, MN is

the natural mortality rate, and MD is the mortality rate associated with ranavirosis.

Under the assumptions that AS = 28 → 14, AH = 1 → 14, with the introduction of 1 → 5 AU, MD(U) = MD(H) = 0.775, σ1 = 0.3, σ3 = 0.25, Ψ = 0.45, and MN = 0.2, based on the RO values, AU and AH should not coexist over the long term. It does not matter if AU is introduced into a population with AH or Virusesvice-versa2019, 11 (Figure, 556 9). Both of these disease syndromes co-occur in nature [21] and in experimental10 of 13 infections [25].

Viruses 2019, 11, x FOR PEER REVIEW 11 of 14 coexistence over the long term. While at first this might seem counter intuitive, it can be explained as follows—when there are more AU individuals in the population there is a greater overall mortality rate because MD(U) >> MN. Hence, there are actually fewer individuals to infect. Even when all of the population (n = 29) is composed of AU individuals, AH can become established (σ3 ≈ 0.85; see Figure 10). Although this is a high transmission rate, it is not unlikely in the situation where animals have broken skin (see [25]; adult common frogs with broken skin are more likely to become infected), which is characteristic of the ulcerative form of the ranaviral disease. The above analysis Figure 9. Ro values for the introduction of one AH individual into a population of AS = 28 and AU = 1 demonstratesFigure 9. R thato values the two for the disease introduction syndromes of one could AH individual persist in into the a populationshort term, of in A Sthe= 28same and population, AU = 1 (M(MD(U) == MMD(H) = 0.775,= 0.775, Ψ =Ψ 0.45,= 0.45, MN = M 0.2).= A0.2).S is the A numberis the number of susceptible of susceptible individuals, individuals, Ψ is theΨ contactis the by adult-to-adultD(U) D(H) transmission, albeit underN conditionsS which have been estimated from data that are contactrate, σ is rate, theσ likelihoodis the likelihood of transmission, of transmission, MN is MtheN isnatural the natural mortality mortality rate, rate,and M andD is M theD is mortality the mortality rate incomplete and not necessarily biologically relevant, based on the differing Ro values. rateassociated associated with with ranavirosis. ranavirosis.

Increasing the number of AU individuals in a population requires a higher transmission rate at each contact, for AH to become established (i.e., Ro ≥ 1). However, establishment does not guarantee

FigureFigure 10.10. Ro values forfor thethe introductionintroduction ofof oneone AAHH individual to populationspopulations with didifferingﬀering numbersnumbers ofof AAUU,, while the total population size remains constantconstant atat 30.30. TheThe numbernumber associatedassociated withwith eacheach lineline indicatesindicates thethe numbernumber of of A AUUindividuals individuals present present in in the the population. population. (M (MD(U)D(U)= = 0.775,0.775, ΨΨ= = 0.45,0.45, MMNN == 0.2) AAss isis thethe numbernumber ofof susceptiblesusceptible individuals,individuals, Ψ isis thethe contactcontact rate,rate, σσ isis thethe likelihoodlikelihood ofof transmission,transmission,

MMNN is the natural mortality rate,rate, andand MMD isis the the mortality mortality rate rate asso associatedciated with ranavirosis. 3. Discussion 3. Discussion Transmission dynamics are key to understanding host and pathogen persistence. In amphibian Transmission dynamics are key to understanding host and pathogen persistence. In amphibian ranavirus systems, transmission can occur through direct contact, from scavenging, from virus particles ranavirus systems, transmission can occur through direct contact, from scavenging, from virus persisting in the environment, and even between vertebrate classes, as seen in laboratory experiments. particles persisting in the environment, and even between vertebrate classes, as seen in laboratory However, there is little understanding of the transmission routes that are most important in natural experiments. However, there is little understanding of the transmission routes that are most communities. In North America, ranavirus transmission appears to be primarily through direct contact important in natural communities. In North America, ranavirus transmission appears to be primarily with minimal transmission from water and scavenging, in most circumstances [16]. Our model is through direct contact with minimal transmission from water and scavenging, in most circumstances consistent with these results, demonstrating that the ranavirus(es) present in the UK common frog [16]. Our model is consistent with these results, demonstrating that the ranavirus(es) present in the populations might persist in the short-term through horizontal, adult-to-adult transmissions alone. UK common frog populations might persist in the short-term through horizontal, adult-to-adult When the declines of 8.1% per annum—observed by Teacher et al. [9] in the common frog transmissions alone. populations where ranavirosis have emerged—are factored into the model, it took approximately When the declines of 8.1% per annum—observed by Teacher et al. [9] in the common frog populations where ranavirosis have emerged—are factored into the model, it took approximately 65 years for all adults in the population to become infected. This model did not take into account immigration, which has been noted by Teacher et al. [29] or the change in population structure that is caused by the emergence of ranavirosis, as described by Campbell et al. [30]. These additional factors, along with the effects of climate change [28], might change the outcomes of the models, and perhaps even require adjustments to the model parameters. Strict adult-to-adult transmission of ranaviruses appears to be relatively rare. It is likely to have occurred in a mass mortality event of over 1000 adult and metamorphic water frogs (Pelophylax spp.) in the Netherlands, caused by a strain of Common Midwife Toad Virus (CMTV) [31]. In this case, there were also common newts (Lissotriton vulgaris) involved in the mortality event [31], but they made up only approximately 1% of the animals killed, and ranavirus transmission to the newts might be best

Viruses 2019, 11, 556 11 of 13

65 years for all adults in the population to become infected. This model did not take into account immigration, which has been noted by Teacher et al. [29] or the change in population structure that is caused by the emergence of ranavirosis, as described by Campbell et al. [30]. These additional factors, along with the effects of climate change [28], might change the outcomes of the models, and perhaps even require adjustments to the model parameters. Strict adult-to-adult transmission of ranaviruses appears to be relatively rare. It is likely to have occurred in a mass mortality event of over 1000 adult and metamorphic water frogs (Pelophylax spp.) in the Netherlands, caused by a strain of Common Midwife Toad Virus (CMTV) [31]. In this case, there were also common newts (Lissotriton vulgaris) involved in the mortality event [31], but they made up only approximately 1% of the animals killed, and ranavirus transmission to the newts might be best attributed to pathogen spillover. In North America, reports of adult anurans infected with ranavirus are rare (e.g., only one adult wood frog [18]); morbidity and mortality events tend to occur in the tadpole stage. However, in the UK, adult-only mortality and morbidity events are typical, therefore, adult-to-adult transmission must play a major role in the transmission, which is consistent with our model results. This is an important finding since, there often is a lack of tadpoles in the ponds at the time of the adult mortality events [20]. However, other species might act as a reservoir of hosts that can infect common frogs [32], such as common toads, common newts (Lissotriton vulgaris) and the introduced common midwife toad (Alytes obstetricans). Future models and studies should explore interspecies transmission and subsequent population dynamics, especially since the presence of other species, namely common toads (Bufo bufo), can reduce disease risk in common frogs [5,27]. Our models showed that both disease syndromes can co-exist in the short term, despite competition between the ranavirus(es) associated with the different disease syndromes. This is not surprising if there are multiple strains of ranavirus present in the population. Exposure to different ranaviruses has been shown to result in enhanced viral infectivity in larval amphibians in the USA [33], and it is possible that this same pattern is occurring in the adult UK common frogs. The susceptibility of the host might depend on which ranavirus strain (ulcerative or hemorrhagic) is first introduced into the population. A similar effect has been previously observed in tadpoles exposed to Frog virus 3 (FV3) and Ambystoma tigrinum virus [33]. This might be the case in the UK, because there are at least two different types of ranaviruses present [27]. CMTV-like and FV3-like ranaviruses have been previously identified in the UK populations of common frogs [27]; however, no association with the distinct disease syndromes were found in this study. In a previous study, molecular differences between two of the isolates (RUK 11 and RUK 13) were found, both of which were responsible for different disease syndromes. Duffus et al. [34] found that while the major capsid protein sequences for these two isolates were similar to FV3, the partial sequence of open reading frame 57r (an eIF-2α homologue) was similar to that found in an isolate of Chinese giant salamander virus (a common midwife toad-like virus). These differences could be indicative of larger scale molecular differences between the RUK isolates that result in the different ranaviral syndromes seen in common frogs in the UK. Our models were greatly limited by a lack of robust parameter estimates. The contact rates were unknown for common frogs and the transmission coefficients were based on experiments with small sample sizes and unrealistic viral titres. Better parameter estimation (e.g., contact rates, individual susceptibility to ranavirosis, and disease-induced mortality in adults) would be key to improving the predictive values of all presented models.

Author Contributions: A.L.J.D. conceived the models. T.W.J.G. and R.A.N. provided valuable guidance to A.L.J.D. on model development. J.P.S. ran and modiﬁed the original models, as necessary. A.L.J.D., J.E.E., and T.W.J.G. wrote the manuscript. All authors edited the manuscript and approved it. Funding: Support for this work from 2006 to 2010 was provided by a Queen Mary, University of London Studentship to A.J.L.D., an Overseas Research Scholarship to A.L.J.D., and a Natural Science and Engineering Council (NSERC) of Canada PGS-D3 Grant to A.L.J.D. T.W.J.G. was supported by a RCUK fellowship and R.A.N. and T.W.J.G. were supported by NERC (NE/M00080X/1 and NE/M000338/1, respectively). Acknowledgments: We would like to thank Robert Knell for the helpful discussions about model development and two anonymous reviewers who’s comments and suggestions greatly improved the quality of the manuscript. Viruses 2019, 11, 556 12 of 13

Conﬂicts of Interest: The authors declare no conﬂict of interest. The funders had no role in the design of the study, in the collection, analyses, or interpretation of data; in the writing of the manuscript or in the decision to publish the results.

References

1. Gray, M.J.; Chinchar, V.G. Introduction: History and future of ranaviruses. In Ranaviruses: Lethal Pathogens of Ectothermic Vertebrates; Gray, M.J., Chinchar, V.G., Eds.; Springer: New York, NY, USA, 2015; pp. 1–7. 2. Duffus, A.L.J.; Waltzek, T.B.; Stöhr, A.C.; Allender, M.C.; Gotesman, M.; Whittington, R.J.; Hick, P.; Hines, M.K.; Marschang, R.E. Distribution and host range of ranviruses. In Ranaviruses: Lethal Pathogens of Ectothermic Vertebrates; Gray, M.J., Chinchar, V.G., Eds.; Springer: Secaucus, NJ, USA, 2015. 3. Miller, D.L.; Pessier, A.P.; Hick, P.; Whittington, R.J. Comparative pathology of ranaviruses and diagnostic techniques. In Ranaviruses: Lethal Pathogens of Ectothermic Vertebrates; Gray, M.J., Chinchar, V.G., Eds.; Springer: Secaucus, NJ, USA, 2015. 4. Hoverman, J.T.; Gray, M.J.; Haislip, N.A.; Miller, D.L. Phylogeny, life history, and ecology contribute to differences in amphibian susceptibility to ranaviruses. EcoHealth 2011, 8, 301–319. [CrossRef][PubMed] 5. North, A.C.; Hodgson, D.J.; Price, S.J.; Griffiths, A.G.F. Anthropogenic and ecological drivers of amphibian disease (ranavirosis). PLoS ONE 2015, 10, e0127037. [CrossRef][PubMed] 6. Balseiro, A.; Dalton, K.P.; del Cerro, A.; Marquez, I.; Cunningham, A.A.; Parra, F.; Prieto, J.M.; Casais, R. Pathology, isolation and molecular characterisation of a ranavirus from the common midwife toad Alytes obstetricans on the iberian peninsula. Dis. Aquat. Org. 2009, 84, 95–104. [CrossRef][PubMed] 7. Green, D.E.; Converse, K.A.; Schrader, A.K. Epizootiology of sixty-four amphibian morbidity and mortality events in the USA, 1996–2001. Ann. N. Y. Acad. Sci. 2002, 969, 323–339. [CrossRef][PubMed] 8. Muths, E.; Gallant, A.L.; Grant, E.H.C.; Battaglin, W.A.; Green, D.E.; Staiger, J.S.; Walls, S.C.; Gunzburger, M.S.; Kearney, R.F. The Amphibian Research and Monitoring Iniative (ARMI): 5-Year Report; US Geological Survey Scientific Investigations Report 2006-5224; USDOI, USGS, Eds.; US Geological Survey: Reston, VA, USA, 2006; p. 77. 9. Teacher, A.G.F.; Cunningham, A.A.; Garner, T.W.J. Assessing the long-term impact of ranavirus infection in wild common frog populations. Anim. Conserv. 2010, 13, 514–522. [CrossRef] 10. Price, S.J.; Garner, T.W.J.; Nichols, R.A.; Balloux, F.; Ayres, C.; Mora-Cabello de Alba, A.; Bosch, J. Collapse of amphibian communities due to an introduced ranavirus. Curr. Biol. 2014, 24, 1–6. [CrossRef][PubMed] 11. Earl, J.E.; Gray, M.J. Introduction of ranavirus to isolated wood frog populations could cause local extinction. EcoHealth 2014, 11, 581–592. [CrossRef] 12. Earl, J.E.; Chaney, J.C.; Sutton, W.B.; Lillard, C.E.; Kouba, A.J.; Langhorne, C.; Krebs, J.; Wilkes, R.P.; Hill, R.D.; Miller, D.L.; et al. Ranavirus could facilitate local extinction of rare amphibian species. Oecologia 2016, 182, 611–623. [CrossRef] 13. Farrell, A.P.; Collins, J.P.; Greer, A.L.; Thieme, H.R. Times from infection to disease-induced death and their influence on final population sizes after epidemic outbreaks. Bull. Math. Biol. 2018, 80, 1937–1961. [CrossRef] 14. Anderson, R.M.; May, R.M. Population biology of infectious disease. Nature 1979, 280, 361–461. [CrossRef] 15. May, R.M.; Anderson, R.M. Population biology of infectious diseases: Part II. Nature 1979, 280, 455–461. [CrossRef][PubMed] 16. Brunner, J.L.; Yarber, C.M. Evaluating the importance of environmental persistence for Ranavirus transmission and epidemiology. Adv. Virus Res. 2018, 101, 129–148. [PubMed] 17. Brunner, J.L.; Schock, D.M.; Davidson, E.W.; Collins, J.P. Intraspecific reservoirs: Complex life history and the persistence of a lethal ranavirus. Ecology 2004, 85, 560–566. [CrossRef] 18. Duffus, A.L.J.; Pauli, B.D.; Wozney, K.; Brunetti, C.R.; Berrill, M. Frog virus 3-like infections in aquatic amphibian communities. J. Wildl. Dis. 2008, 44, 109–120. [CrossRef][PubMed] 19. Duffus, A.L.J.; Nichols, R.A.; Garner, T.W.J. Experimental evidence in support of single host maintenance of a multihost pathogen. Ecosphere 2014, 5, 1–11. [CrossRef] 20. Duffus, A.L.J.; Nichols, R.A.; Garner, T.W.J. Investigations into the life history stages of the common frog (Rana temporaria) affected by an amphibian ranavirus in the United Kingdom. Herpetol. Rev. 2013, 44, 260–263. Viruses 2019, 11, 556 13 of 13

21. Cunningham, A.A.; Langton, T.E.S.; Bennett, P.M.; Lewin, J.F.; Drury, S.E.N.; Gough, R.E.; MacGregor, S.K. Pathological and microbiological findings from incidents of unusual mortality of the common frog (Rana temporaria). Philos. Trans. R. Soc. Lond. B Biol. Sci. 1996, 351, 1539–1557. 22. Otto, S.P.; Day, T. A Biologist’s Guide to Mathematical Modeling in Ecology and Evolution; Princeton University Press: Princeton, NJ, USA, 2007; p. 732. 23. Miaud, C.; Guyetant, R.; Elmberg, J. Variations in life-history traits in the common frog Rana temporaria (Amphibia: Anura): A literature review and new data from the French Alps. J. Zool. 1999, 249, 61–73. [CrossRef] 24. Gibbons, M.M.; McCarthy, T.K. Growth, maturation and survival of frogs Rana temporaria L. Holarct. Ecol. 1984, 7, 419–427. [CrossRef] 25. Cunningham, A.A.; Hyatt, A.D.; Russell, P.; Bennett, P.M. Emerging epidemic diseases of frogs in britain are dependant on the source of ranavirus agent and the route of exposure. Epidemiol. Infect. 2007, 135, 1200–1212. [CrossRef][PubMed] 26. Vieites, D.R.; Nieto-Román, S.; Barluenga, M.; Palanca, A.; Vences, M.; Meyer, A. Post-mating clutch piracy in an amphibian. Nature 2004, 431, 305–308. [CrossRef][PubMed] 27. Price, S.J.; Wadia, A.; Wright, O.N.; Leung, W.T.; Cunningham, A.A.; Lawson, B. Screening of a long-term sample set reveals two ranavirus lineages in british herpetofauna. PLoS ONE 2017, 12, e0184768. [CrossRef] [PubMed] 28. Price, S.J.; Leung, W.T.M.; Owen, C.; Puschendorf, R.; Sergeant, C.; Cunningham, A.A.; Balloux, F.; Garner, T.W.J.; Nichols, R.A. Effects of historic and projected climate change on the range and impacts of an emerging wildlife disease. Glob. Chang. Biol. 2019, in press. [CrossRef][PubMed] 29. Teacher, A.G.F.; Garner, T.W.J.; Nichols, R.A. Evidence for directional selection at a novel major histocompatability class i marker in wild common frogs (Rana temporaria) exposed to a viral pathogen (Ranavirus). PLoS ONE 2009, 4, e4616. [CrossRef] 30. Campbell, L.J.; Garner, T.W.J.; Tessa, G.; Scheele, B.C.; Griffiths, A.G.F.; Harrison, X.A. An emerging viral pathogen truncates population age structure in a european amphibian and may reduce population viability. PeerJ 2018, 6, e5949. [CrossRef][PubMed] 31. Kik, M.; Martel, A.; Spitzen-van der Sluijs, A.; Pasmans, F.; Wohlsein, P.; Gröne, A.; Rijks, J.M. Ranavirus-associated mass mortality in wild amphibians, the netherlands, 2010: A first report. Vet. J. 2011, 190, 284–286. [CrossRef] 32. Duffus, A.L.J.; Nichols, R.A.; Garner, T.W.J. Detection of a frog virus 3-like ranavirus in native and introduced amphibians in the United Kingdom in 2007 and 2008. Herpetol. Rev. 2014, 45, 608–610. 33. Mihaljevic, J.R.; Hoverman, J.T.; Johnson, P.T.J. Co-exposure to multiple ranavirus types enhances viral infectivity and replication in a larval amphibian system. Dis. Aquat. Org. 2018, 132, 23–35. [CrossRef] 34. Duffus, A.L.J.; Garner, T.W.J.; Davis, A.R.; Dean, A.W.; Nichols, R.A. Phylogentic analysis of 24 ranavirus isolates from English amphibians using 2 partial loci. J. Emerg. Dis. Virol. 2017, 3.[CrossRef]

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).