Estimation of population size history in four cattle breeds using ABC.

<p>Angus (<i>n</i> = 25 animals), Fleckvieh (<i>n</i> = 25), Holstein (<i>n</i> = 25) and Jersey (<i>n</i> = 15). Estimations were obtained independently in each breed, based on whole genome NGS data from sampled animals. Summary statistics considered in the ABC analysis were (i) the AFS and (ii) the average zygotic LD for several distance bins. These statistics were computed using SNPs with a MAF above 20%. Other parameter settings are the same as in <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1005877#pgen.1005877.g005" target="_blank">Fig 5</a>.</p

Accuracy of ABC estimation and relative importance of the summary statistics.

<p>Prediction error for the estimated population size in each time window (left) and standard deviation of this error (right), evaluated from 2,000 random population size histories. Summary statistics considered in the ABC analysis included different combinations of (i) the AFS (possibly without the overall proportion of SNPs) and (ii) the average zygotic LD for several distance bins. These statistics were computed from <i>n</i> = 25 diploid individuals, using all SNPs for AFS statistics and only those with a MAF above 20% for LD statistics. The posterior distribution of each parameter was obtained by neural network regression [<a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1005877#pgen.1005877.ref032" target="_blank">32</a>], with a tolerance rate of 0.005. Population size point estimates correspond to the median of the posterior distribution. The prediction errors were scaled in order that point estimates obtained from the prior distribution would result in a prediction error of 1.</p

Estimation of population size history using MSMC with two haplotypes in five different simulated scenarios.

<p>For each scenario, the five PODs considered for MSMC estimation were the same as in <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1005877#pgen.1005877.g003" target="_blank">Fig 3</a>. The expected TMRCA shown here is also the same as in <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1005877#pgen.1005877.g003" target="_blank">Fig 3</a>, it corresponds to samples of 50 haploid sequences.</p

Influence of phasing and sequencing errors on ABC estimation.

<p>Estimation of population size history in the Holstein cattle breed using ABC, based on whole genome NGS data from <i>n</i> = 25 animals. Summary statistics considered in the ABC analysis were (i) the AFS and (ii) the average LD for several distance bins. LD statistics were computed either from haplotypes or from genotypes, using SNPs with a MAF above 20%. AFS statistics were computed using either all SNPs or SNPs with a MAF above 10 or 20%. The posterior distribution of each parameter was obtained by neural network regression [<a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1005877#pgen.1005877.ref032" target="_blank">32</a>], with a tolerance rate of 0.005. Population size point estimates were obtained from the median of the posterior distribution. Generation time was assumed to be five years.</p

<b>Parameter values.</b>

<p>Interval boundaries of the uniform distributions used to sample the 14 uncertain input factors included in the sensitivity analyses (i.e., ecological and epidemiological factors) are given between parentheses: default value (min - max).</p><p>*Incubation period. The range was set using data for EBLV-1 reported in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0095610#pone.0095610-Banyard1" target="_blank">[2]</a>. The default value was set to the mean reported in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0095610#pone.0095610-Jackson1" target="_blank">[26]</a> for RABV infection in <i>Eptesicus fuscus</i>.</p><p>**Infectious period. Observed <i>Lyssavirus</i> infectious periods in mammals have not exceeded 1 month <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0095610#pone.0095610-Aubert1" target="_blank">[23]</a> and thus it is probably measured in days. Amengual et al., Plos One (2007) estimated the infectious period of <i>M. myotis</i> at 5.1 days <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0095610#pone.0095610-Amengual2" target="_blank">[13]</a>. A later reevaluation with longer time-series data gave an estimate of approximately 7 days. The uncertainty intervals were set around that value.</p><p>***Immune period. Individual data from <i>M. myotis</i> recaptured bats in the Balearic Islands suggest that the presence of antibodies might be measured in years <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0095610#pone.0095610-Amengual5" target="_blank">[19]</a>.</p><p>Because no data exist for <i>M. schreibersii</i> and <i>M. capaccinii</i>, we used the same values that we used for <i>M. myotis</i>. Furthermore, for the infectious and the immune periods, the differences between <i>R. ferrumequinum</i> and the other three species were set according to population-level observations. In the Balearic Islands it has been observed that <i>R. ferrumequinum</i> populations have lower levels of antibodies, but higher levels of viral RNA positive blood clots, than <i>M. myotis</i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0095610#pone.0095610-Amengual5" target="_blank">[19]</a>.</p

Ecological factors effect in EBLV-1 persistence on both islands.

<p>The persistence index is represented as a function of the seasonal interisland exchanges (<i>Y</i>-axes) and reduction of contacts during low-transmission periods (<i>X</i>-axes), for three different intraspecies <i>R</i>₀ values (2, 4 and 6). Persistence index shades of gray from white to black correspond, respectively, to low and high probabilities of virus persistence.</p

EBLV-1 seroprevalence by subpopulation.

<p>Observed EBLV-1 seroprevalences with 95% CI in two <i>Myotis myotis</i> colonies (A, B) and one <i>Rhinolophus ferrumequinum</i> colony (C). Null rates of seroprevalence at some times might not be indicative of local virus extinctions, but just virus extinctions in that subpopulation or a consequence of under-reporting.</p

Individual bat species effect in EBLV-1 persistence.

<p>The persistence index is represented as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0095610#pone-0095610-g006" target="_blank">Figure 6</a>. The first column corresponds to the reference scenario (Ref), in which none of the species is removed from the transmission process. The remaining columns correspond to the tested scenarios in which one after the other the indicated species is excluded from the transmission process. Abbreviations are as given in the legend to <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0095610#pone-0095610-g003" target="_blank">Figure 3</a>.</p

Estimated sensitivities of EBLV-1 persistence-index to the parameters in the model.

<p>The persistence index is highly sensitive to the reduction of contacts in the low-transmission period, and three <i>M. schreibersii</i> and <i>M. capaccinii</i> related parameters (<i>R</i>₀, and incubation- and immune-period durations). Virus persistence is also slightly sensitive to the <i>R. ferrumequinum R</i>₀ and the infectious period duration. The remaining parameters have total-order Sobol' indexes <0.1. Abbreviations are as given in the legend to <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0095610#pone-0095610-g003" target="_blank">Figure 3</a>.</p

One model simulation run.

<p>Gray lines correspond to anti-EBLV-1 antibody seroprevalence in each subpopulation over 50 years. Black lines correspond to seroprevalence measured at the end of May. The parameter values used are: <i>R</i>₀ = 3, <i>r</i> = 0.6, interisland exchange  = 3 individuals, immune-period duration  = 6 months, and the default values reported in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0095610#pone-0095610-t002" target="_blank">Table 2</a> for the incubation- and immune-period durations. Abbreviations are as given in the legend to <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0095610#pone-0095610-g003" target="_blank">Figure 3</a>.</p