Short description of the problem:
Hi, I was going over the demographic parameters for the EarlyWolfAdmixture_6F14 model from Freedman et al. (2014), and after spending a couple of hours wrapping my head around what G-PhoCS is actually reporting, I believe the per-generation continuous migration rate parameters in the current implementation may be incorrect, or my understanding of G-PhoCS is completely wrong.
How to reproduce the problem:
After reading Gronau et al. (2011), it is my understanding that in G-PhoCS, each migration band from source population $S$ to target population $T$ has a scaled migration rate $m_{ST} = M_{ST} \div \mu$, where $M_{ST}$ represents the per-generation instantaneous migration rate, and backward-in-time migration along the band $\tau_{ST}$ (i.e., the time interval where both populations $S$ and $T$ exists) is modeled as a constant-rate Poisson process with rate $m_{ST}$ (see “The migration model” in section S4.2). The total (cumulative) migration rate corresponds to the product of the estimated scaled migration rate and the duration of the band $m_{ST}^{tot} = m_{ST} \times \tau_{ST}$, which can be used as an approximation for the probability a lineage in the target population $T$ will migrate (backward-in-time) into the source population $S$ and I believe this can be computed as $1 - e^{-m_{ST}^{tot}}$ (see the second paragraph in section S5.2 and section S6.4). Note that I got the migration probability equation for the approximation not directly from the original G-PhoCS paper, but from the methods section of vonHoldt et al (2016).
Moving to Freedman et al. (2014), I will use the gene flow event from the Israeli wolf population (ISW) to Basenji population (BSJ), i.e., ISW $\rightarrow$ BSJ as a motivating example, but I believe the same logic would apply to all of the current migration rates in EarlyWolfAdmixture_6F14. From the Figure 5 caption, we are told:
“Migration bands are shown in green with associated values indicating estimates of total migration rates, which equal the probability that a lineage will migrate through the band during the time period when the two populations co-occur.”
This is further elaborated in the first paragraph from supplemental section S9.2.3:
“The probablistic model of G-PhoCS also uses a scaled version of migration rate, $M = m / \mu$, where $m$ is the probability of migration across a given band in a single generation. The level of gene flow across a given migration band is measured by the total migration rate, which is the migration rate scaled by the time span of the migration band ($\tau_{m}$): $m^{tot} = M \tau_{m}$. If $m^{tot}$ is sufficiently small ($m^{tot} < 0.5$), then it approximately equals the probability that a given lineage will migrate through the band. By scaling the rate $M$ with the time span $\tau_{m}$, we obtain a measure that is independent of our assumptions on mutation rate. The time span of a migration band is defined using the start and end times of the two populations that define it. For example, the time span of the migration band from BSJ to ISW is $\min(\tau_{ancWLF1}, \tau_{ancDOG1})$...”
In Table S12, the total migration rate is $m_{ISW \to BSJ} = 0.18$ (95% Bayesian credible intervals: 0.12–0.24) which aligns with what is reported in Figure 5A, but I don’t understand why this is the continuous per-generation migration rate used in the EarlyWolfAdmixture_6F14 demographic model (or am I totally misunderstanding something). Naively, since the two populations exist starting from generation $\tau_{ancDOG1} = 12102$ until the present, shouldn’t the per-generation continuous migration rate be $m_{ISW \to BSJ} \div \tau_{ancDOG1} = 0.18 \div 12102 \approx 1.487 \times 10^{-5}$ or $(1 - e^{-m_{ISW \to BSJ}}) \div \tau_{ancDOG1} = 1.361 \times 10^{-5}$?
Suggested fixes:
If the migration rates in EarlyWolfAdmixture_6F14 are indeed misspecified, I would be more than happy to change them and submit a PR following either of the two approaches outlined above; I would need clarification on whether $m^{tot} \div \tau$ or $(1 - e^{-m^{tot}}) \div \tau$ is more correct. However, given that I have never actually used G-PhoCS, I am likely misunderstanding the nuances behind interpreting the estimated migration rates. If the current implementation of EarlyWolfAdmixture_6F14 is correct, I would greatly appreciate a brief explanation of the intuition for why using $m_{ISW \to BSJ} = 0.18$ as the per-generation migration rate is correct.
Short description of the problem:
Hi, I was going over the demographic parameters for the
EarlyWolfAdmixture_6F14model from Freedman et al. (2014), and after spending a couple of hours wrapping my head around whatG-PhoCSis actually reporting, I believe the per-generation continuous migration rate parameters in the current implementation may be incorrect, or my understanding ofG-PhoCSis completely wrong.How to reproduce the problem:$S$ to target population $T$ has a scaled migration rate $m_{ST} = M_{ST} \div \mu$ , where $M_{ST}$ represents the per-generation instantaneous migration rate, and backward-in-time migration along the band $\tau_{ST}$ (i.e., the time interval where both populations $S$ and $T$ exists) is modeled as a constant-rate Poisson process with rate $m_{ST}$ (see “The migration model” in section S4.2). The total (cumulative) migration rate corresponds to the product of the estimated scaled migration rate and the duration of the band $m_{ST}^{tot} = m_{ST} \times \tau_{ST}$ , which can be used as an approximation for the probability a lineage in the target population $T$ will migrate (backward-in-time) into the source population $S$ and I believe this can be computed as $1 - e^{-m_{ST}^{tot}}$ (see the second paragraph in section S5.2 and section S6.4). Note that I got the migration probability equation for the approximation not directly from the original
After reading Gronau et al. (2011), it is my understanding that in
G-PhoCS, each migration band from source populationG-PhoCSpaper, but from the methods section of vonHoldt et al (2016).Moving to Freedman et al. (2014), I will use the gene flow event from the Israeli wolf population (ISW) to Basenji population (BSJ), i.e., ISW$\rightarrow$ BSJ as a motivating example, but I believe the same logic would apply to all of the current migration rates in
EarlyWolfAdmixture_6F14. From the Figure 5 caption, we are told:This is further elaborated in the first paragraph from supplemental section S9.2.3:
In Table S12, the total migration rate is$m_{ISW \to BSJ} = 0.18$ (95% Bayesian credible intervals: 0.12–0.24) which aligns with what is reported in Figure 5A, but I don’t understand why this is the continuous per-generation migration rate used in the $\tau_{ancDOG1} = 12102$ until the present, shouldn’t the per-generation continuous migration rate be $m_{ISW \to BSJ} \div \tau_{ancDOG1} = 0.18 \div 12102 \approx 1.487 \times 10^{-5}$ or $(1 - e^{-m_{ISW \to BSJ}}) \div \tau_{ancDOG1} = 1.361 \times 10^{-5}$ ?
EarlyWolfAdmixture_6F14demographic model (or am I totally misunderstanding something). Naively, since the two populations exist starting from generationSuggested fixes:$m^{tot} \div \tau$ or $(1 - e^{-m^{tot}}) \div \tau$ is more correct. However, given that I have never actually used $m_{ISW \to BSJ} = 0.18$ as the per-generation migration rate is correct.
If the migration rates in
EarlyWolfAdmixture_6F14are indeed misspecified, I would be more than happy to change them and submit a PR following either of the two approaches outlined above; I would need clarification on whetherG-PhoCS, I am likely misunderstanding the nuances behind interpreting the estimated migration rates. If the current implementation ofEarlyWolfAdmixture_6F14is correct, I would greatly appreciate a brief explanation of the intuition for why using