Comments to Bruford report
The most important part of the report supports the currently decided lowest wolf number 270 (FRP=270), but the report has shortcomings making in unsuitable for cherry-picking support for a high FRP.
Sammandrag av mina kommentarer på svenska: Rapporten har brister. Rapporten ger stöd för att behålla varggolvet
vid 270 (den genetiska diversiteten minskar mindre än fem procent på hundra
år). Men bristerna är för stora för att stödja sig på rapportens resultat för
en ökning av golvet över beslutat 270.
Rapporten negligerar att immigranterna troligen har mer än dubbelt så stort inflytande som beräknat. Immigranterna har högre fertilitet, vilket möjligen ibland beaktas. Men framförallt är immigranterna och deras avkomma skyddade från jakt, vilket fördubblar effekten av immigration när vargantal hålls konstant. Rapporten sätter en ogenomtränglig mur för invandring från resten av världen till Fennoskandia, helt orealistiskt. Rapporten beaktar inte ens invandring från Karelen, fast läsaren måste vara uppmärksam för att märka det. De negativa effekterna av släktskap avklingar med tiden, detta har för inavel konstaterats, men inte tillfullo beaktats. För diversitet har det inte beaktats alls. Simuleringarna kan inte återge den historiska utvecklingen av vargen, skall man tro på simuleringarna borde varg inte finnas i Sverige. Resultaten om invandrarna antas vara obesläktade negligeras, eftersom resultaten blir konstiga. Då ter det sig logiskt att inte tro på simuleringarna för huvudresultaten heller, eftersom den låga effekten av immigration inte stämmer med erfarenhet eller intuition och eftersom simulatorn inte givit trovärdiga resultat för de mer transparanta alternativen. Rapportens låga effekt av immigration kan bero på rapportens val av loci, den förklaringen avfärdas för lättsinnigt. Det finns alltså fyra goda skäl att hävda att rapportens prognoser underskattar effekten av immigration! Rapporten är svårläst, jag har svårigheter att förstå centrala avsnitt och det beror delvis på att förklaringar saknas. Vid sidan av det vetenskapliga är det tveksamt om Naturvårdsverket skulle argumentera för fler vargar med stöd av en rapport, som är så svårtillgänglig även för ”experter”. Med rapporten i hand går det inte att upprepa studien - vilket borde varit möjligt för en simuleringsstudie - upprepbarhet brukar vara ett krav i vetenskapliga sammanhang.
The Bruford report titled “Additional Population Viability Analysis of the Scandinavian Wolf Population” is available at: http://www.naturvardsverket.se/Documents/publikationer6400/978-91-620-6639-0.pdf?pid=14226 and can be reached via http://www.naturvardsverket.se/978-91-620-6639-0/ Main purpose of the report was to respond to five questions. The focus of this document is if this report is acceptable as a scientific ground for a FRP (FRP=the lowest acceptable number of wolves in Sweden) above 270, as decided by SEPA (Naturvårdsverket) in compliance with decisions of the Swedish parliament.
The comments to the report are placed on two websites, one which is better formatted and updated at http://daglindgren.upsc.se/VargGYBS/BrufordReportComment.html and another at https://vargweb.wordpress.com/ . The last web accept comments, I try to respond to comments and questions if justified.
# The report and simulations should be interpreted as support to current FRP=270. Already in the Swedish summary, the response to the first question says that FRP= 270 seems satisfactory (p 8): ”Med en skandinavisk vargstam på 300 individer (varav 270 i Sverige) och 1 ny reproducerande immigrant varje 6-årsintervall…Simuleringarna indikerade att då förloras totalt sett mindre än 5 % av gendiversiteten på 100 år”
In the English response to questions (p 46-47); Table
9 (p 45,titled “key outcome”) was mentioned 6 out of 8 table references. Table
9 for 300 wolves and 1 effective immigrant/six years retain more than 95 % of
the Gene Diversity for hundred years. Thus FRP=270 for Swedish wolf seems
sufficient to maintain diversity. Increase in inbreeding is in the long run
almost the same thing as loss in gene diversity, so if loss in diversity is
acceptable, so is increase in inbreeding.
# Bruford´s summary (p 10) does not support FRP>270. A calculation indicating FRP=370 is mentioned, but discarded after improved calculations resulting in that FRP=270 is sufficient to keep decrease in diversity within 5 percent in hundred years. Inbreeding is raising is said to raise in hundred years but not dramatically much.
# No clear support from Bruford for FRP>270 in responding SEPAs
questions. Five questions were asked which Bruford respond to (p 46-47). §1
Reasonable scenarios keep gene diversity and inbreeding in reasonable limits.
Effective migration is the key parameter, not numbers. §2 The SEPA proposal
FRP=417 given immigration 3.5 effective wolves per generation seem to overshoot
the needs for inbreeding and gene diversity. §3 insufficient information. §4 The
simulation suggests a loss of rare alleles. However, there are no citations to
guidelines what is acceptable and I do not think such exists. Allele loss is an
issue on higher levels of population hierarchy rather than regional Swedish. §5
Like question, 3 there is insufficient information.
Above the focus was that the most significant results seem to support that FRP=270 is enough, while no results strongly contradict FRP=270. Below comments are made weakening the value of results as support for FRP>270.
# Ten percent retained ought to be enough for genetic viability. Bruford does not know but asks for advice (p 55): “It would be good to know if the retention of at least (or more than) 90% of the gene diversity (Balmford et al. 1996, Frankham et al. 2013) or of at least (or more than) 95% (Allendorf & Ryman 2002) in a subpopulation is a recommendation or demand from conservation geneticists”, Two of three references suggest 10%, the latest reference suggest 10%, all references which are not reviewers of Brufords report suggest 10%. SEPA consider 10% when Bruford was mentioned in its wolf management plan early 2015. When Bruford uses 5% it seems an instruction and not his independent decision (p 63:“applying SEPA’s goal for short-term conservation, i.e. retention of 95% of heterozygosity over 100 years”). Ten percent probability of extinction is often regarded as a limit for demographic viability, it seems extremely illogic the border for genetic diversity should be smaller, extinction is certainly worse than a loss of a minor part of the gene diversity.
# Reproducibility. The first demand is that a document should be reproducible, thus the actual input in Vortex given to allow someone like me to reproduce the results. This is not possible. E.g. *The allele frequencies of the few loci used for the study are not given and a test with another set is not shown (p34). The option used for capping is not given. The vital statistics when the population is capped is not given. All the inputs in Vortex are not well understood or given. Thus the simulations are not reproducible.
# Insufficient explanation, too hard or impossible to fully understand. The text and explanations are not always understandable to me, besides that it is hard to follow. In particular I do not understand how number of effective immigrants can be exactly given. “Effective immigrant”/(year or generation) should, as far as I understand, be a result of the simulation, not an input (like for k). I do not understand how capping functions, thus what happens when carrying capacity is reached. Can an immigrant vanish before it get progeny? That would explain some of the “missing” immigrants. The structure of the presentation is hard to understand. I note that some of the peer-rewiews seem to base their evaluation on misunderunderstandings of the key results of the information last added to the report, because premature information is still in the report.
# Many input values irrelevant. The input viable statistic is not relevant when the rules for removing wolves when “carrying capacity” is reached, which is during most of the simulated time, different for different tested alternatives. What I can see the values after carrying capacity is reached are not mentioned or discussed.
# The Finnish and FennoScandia wolf populations are dealt with as no immigration ever occurs. (p 34). The real word wolf “populations” are not closed in that sense. There are more than ten thousand wolves in Europe except Russia and twenty thousand in European Russia. Wolf move long distances, wolf genes will pass through any geographic borders drawn in continental Europe. Wolve genes outside FennoScandia will come to Finland and Scandinavia. The rate and geographic distance of immigration is highly uncertain and future immigration and population movements is still more uncertain. Any limit in the terrain impassible by wolf genes will be arbitrary. But not to include that wolves can move large distances is no solution to the problem.
# Neglected that effects of
high inbreeding and low diversity decays over time
At Ne at least 500 many scientists consider the negative effects of increase in inbreeding and loss of gene diversity balanced by forces compensating for these negative effects (adaptation, selection, decrease of the frequency of alleles causing inbreeding depression, mutation, release of “hidden” genetic variation” (e.g. in short term alleles on a chromosome segment are inherited together as a single allele, but in long term this association is broken by crossing-over or that a genetic block is circumvented by selection). In a FennoScandian population with maybe a thousand wolves near the size when the effect of low population size is compensated by other mechanisms, these forces will be important and should be considered. This important effect reducing needed wolf number and immigration are neglected. I guess the effect of decay of inbreeding depression is faster and more important in a 10-20 generation perspective than the decay of effect of low diversity
## The effect of high inbreeding decays over time. Inbreeding using pedigree is not the essential, but inbreeding depression. Formal inbreeding depend on how many generations back pedigree is considered, the more generations back the pedigree is considered, the higher will the relatedness of the parents be and thus the inbreeding of their progeny. Inbreeding depression decreases by adaptation to the particular conditions. If homozygosity of an allele is negative it will be selected against. Even many alleles causing less drastic form of inbreeding depression are selected against, but at a slower pace. Inbreeding itself responds, but only rather little to the release of the genetic load (figure 6b). The coefficient of inbreeding maybe what is shown in simulations, but inbreeding depression raises slower and may sink even when inbreeding raises, and that is what matter. One may express it that inbreeding caused by relatedness long back in the pedigree has less effects than late relatedness. The study shows that decrease in inbreeding depression by release of the genetic load is likely to be important (figure 5, figure 6a). p:19 “As expected, when the percentage load due to lethal equivalents was high, the population recovered more rapidly due to the effects of purging (removal of genetic load due to the death of homozygous individuals)”. The wolves increase their vitality measured as population growth (in absence of the “carrying capacity” limit) by near to a factor two, thus inbreeding depression will be reduced to near half, thus equivalent to reducing “the effective inbreeding” to somewhat more than half of the inbreeding figures mentioned. It has been argued that dog breeders usually do not recommend matings resulting in higher inbreeding than F=0.0625 (first cousin mating), but dog breeders usually do not consider inbreeding by relatedness which tracks more than five generations back. If Scandinavian wolves were treated as a race of dogs (as wolves actually are), the inbreeding considered would now start to sink down to say F=0.05, as old relatedness would be neglected. I do not suggest such a drastic effect but my point is that it is recognized that relatedness of mates is less important if the relatedness is many generation old.
## The effect of low diversity decays over time. Vortex has a function for considering that the effects of low diversity decays by mutations creating new genetic variation. But this was neither used nor the effect discussed. As the populations discussed are not very small compared to those which can be considered sustainable forever, it must be considered in some way.
# Neglected that migrants get large offspring. That migrants
offspring is not inbred and wherefore contribute more than other parents is
neglected. This is acknowledged by the author (p10: “it is predicated on the
assumption that immigrants have similar reproductive success to residents
(there is circumstantial evidence that immigrant can outperform residents)). I
have guessed the effects of migration is 25% higher than results indicate for
that reason. But some effect of inbreeding on reproduction may be considered
# Improper way of culling when “carrying capacity” is reached. Hunting doubles the impact of immigrants! Circumstances change drastically when a population grows up to the artificial ceiling input into Vortex (the population growth is constrained to the “carrying capacity” as the author calls it with a misleading terminology). No information seems to be given about the population control which keeps population at carrying capacity “by environment” (p14: “total number of individuals that the environment can allow”). The “environment” capping Scandinavian wolf to a non-growing population is hunting. It is not understandable to me that the mortality of wolf in the input is independent of if 15% of the population is shot or not, as the author seems to suggest (Table 3 p 19). The key is that immigrants and their progeny are intentionally more seldom shot than other wolves (that is easy as immigrants and their offspring keeps geographically known territories where quota hunting is not done). This results in less inbreeding and more gene diversity than if culling is done at random as I think it is when carrying capacity is reached. Quantitatively it seemed reasonable to me that to protect immigrants and their offspring from shooting results in a doubling of the impact of immigration. I explained that e.g. Lindgren D 2011. Licensjakt minskar inaveln. Svensk jakt 2011(8): 34-35. When I estimated that shooting wolves according to the rules, which have been applied till now in Sweden, doubles the effect of immigration compared to the random culling. My estimation of the influence of hunting and immigrant superiority at https://vargdag.wordpress.com/2012/07/23/inavel_om_ett_sekel/ The inbreeding values will be higher as I have disregarded relatedness among immigrants, but still the relations of alternatives are informative. I believe Vortex does consider this selection and superiority of immigrants and their progeny when reaching the carrying capacity. I have considered the practical difficulties involved and that the wolf population was kept constant by shooting (culling), not growing as has been practiced till now. Liberg O, and Sand H. 2012. Effects of migration and selective harvest for the genetic status of the Scandinavian wolf population. A report to the Swedish Environment Protection Agency SEPA (Naturvårdsverket). Grimsö Wildlife research Station, Swedish University of Agricultural Sciences. 19 s. has made computations mainly in agreement with my predictions. These have been tested in court which did not object to the calculations but thought the intended application had too small effect (shooting a quarter of the population growth a single year long after the last migration event does not give a big effect if shooting all growth forever doubles the effect of migration). Olof Liberg has told me he works on a scientific publication on that, I hope he submits the draft to this investigation. I directly condemn the unwillingness of Naturvårdsverket to take actions involve this effect of hunting in the evaluation of FRP and see that it is not considered in the Bruford report.
# The low effect of high immigration is contra-intuitive We Swedes have been trained that immigrants bring new blood to the wolf population. Of course we understood that there is some relatedness both between immigrants and between immigrants and the Scandinavian population, but Swedes have seen from reports supported by genetic data and statements that two immigrants in two decades was enough to keep inbreeding, gene diversity and number of alleles about constant. I think it needs more than a report with doubtful results to change that view or act as it was radically changed. The report makes a verifiable prediction about loss of alleles since 2012. I would like to see the predicted decrease in number of alleles some decades, rather than just trusting in the prediction.
# Only immigration from Finland assumed, not Finland/Karelia (p 34) “I therefore chose to use the Finland population allele frequencies for the second population” A reviewer was misled to believe that the Karelian population was a possible immigrant source, P65: “the Finnish and Karelian populations are genetically diverged (FST ~ 0.1) and can currently not be considered to represent one panmictic population.” Also evidently Naturvårdsverket has misunderstood what they asked for; p3: “de invandrande vargarna då har
genetiska egenskaper likt de finsk-karelska.” I am sure many other
readers make the same mistake.
The first two immigrant males Y-chromosome haplotypes were special. These haplotypes could not be found outside Scandinavia in a sample of 86 males where 15 other haplotypes were found (Sundqvist et al 2001). Finland had four of these other haplotypes. That indicates that the origins of the males is distant, probably beyond Finland. The first immigrant female haplotype (mtDNA) Lu-3 of the first female immigrant was not found in Finland and the somatic chromosome DNA was highly differentiated from the Finnish wolves. Thus it seems that immigrating wolves often carry genes from larger distance than Finland (may be in some generation steps so the fathers father or mothers mother originated in Russia). Immigrants to Finland (refreshing the wolves of the assumed source population) and Sweden from Russia (Russian Karelia) are not considered. This means that the allele frequencies reflect a source population which is more related to Scandinavia and to itself than is the case for the source. There will be some other rare alleles in the source population and wherefore the drop in alleles will be overestimated. The impact of immigration on heterozygosity, inbreeding and rare alleles are somewhat underestimated.
# No information about allele frequencies or selection grounds of used loci (P 64): “The allele frequencies + dispersal model is said to use empirical estimates on allele frequencies in Finland, Karelia, and Scandinavia. However, information is missing on the frequencies that were used, the number of individuals from which they were estimated, pairwise FST values between populations, diversity indices at different loci, and information on from where in Finland and Karelia samples originated (as we have pointed out in previous reviews).” No information about how the loci utilized were chosen, where may be a bias in selection, it is impossible to evaluate as the information is not given.
# Statistical sampling error of loci neglected. (p 34): “Allele frequencies for the first five markers were selected” (p 34): “although parallel simulations using the second five markers were carried out as a control for a small number of scenarios and the results were similar (data not shown).” The effect of immigration on heterozygosity and allele occurrence is highly depending on the allele frequencies of the recipient and donor population in the actual specific locus. As I understand it: if common alleles are more common and rare allele less common in the source than the recipient population, the effect of immigration will be less heterozygosity and fewer alleles!! This contra-intuitive response can happen for an individual locus because of statistical variation, but not on average for a sufficient large sample of loci. If the loci used behave in this odd way cannot be seen without inspection, and I have no idea if five is a generally sufficient sample size. That the author claims that similar results are obtained with a small number of - not shown - simulated scenarios with five other loci increases the probability that results are not severely affected by statistical sampling error. But the unwillingness of the author to neither discuss the possible magnitude of the statistical error; or show the results of validation runs done; or show the allele frequencies of the actual loci - weakens the trust in the surprising results of the low migration impact. I suggest ascribing part of this observed low migration impact to this statistical error rather than reflecting real relatedness.
# Vortex fails and the application of the report is thus generally not
very trustworthy. According to the author Vortex fails in two of three
models (predict the past and PS). Many think the third model (allele and
dispersal) applied suggests too small effect of immigration. Thus, the rapport
application of Vortex simulations generally is not very trustworthy and results
should not be regarded as safe.
## The more understandable and established simulation of two simulation models was disregarded partly because of the odd results. The simpler, more established and more transparent model till now used as main model (PS), was discarded arguing its results seemed unreasonable. In the Swedish summary (p 9): ”PS-modellen visade även orealistiskt låg populationstillväxt; (p 30) “The mean final population size was 550 ± 237 (carrying capacity 700)”; …(p 60): “this indicates the model has a problem.” (p 39) “Of concern is the observation that the predicted inbreeding coefficient using this model did not vary as a function of population size for a given supplementation rate. These two parameters are expected to covary under standard population genetic models, suggesting that this model may not be responding in a predictable manner.” P 69: a reviewer (and the author) “As the author points out, there is reason to be concerned about the fact that when pedigree data were linked to Vortex, predicted inbreeding coefficient was completely unaffected by population size… This absence of covariation between population size and final inbreeding coefficient seems to contradict all previous theory and modeling experience within the field. Since there is no plausible biological explanation for this result.” P 64: “inbreeding appears to increase independently of population size under the pedigree +supplementation model… which is not expected under traditional population genetics theory.” I make the same reflection myself, population size ought to influence the speed inbreeding change as a result of migration before equilibrium is close. I had expected to see more of that in the figures showing the development of inbreeding over time, and equilibrium should not be that close after 50 years for many wolves. That was actually an important reason for me to believe in rather low wolf numbers to reduce inbreeding at the next decades, but if the Tiveden wolves do not get progeny that argument becomes weaker.
## The PS model does reduce inbreeding as much as expected! The inbreeding expected after “a large number of generations” is a function only of the number of immigrants per generation. Each generation the equilibrium comes closer. From Figure 10 it seems evident that the number of generations is enough to approach equilibrium. Shown in https://vargdag.wordpress.com/2012/11/12/framtida-inavel-funktion-av-migration/ The formula which is sufficient for good for wolf is F=1/(4M+1) where M is immigrants per generation. I use the values from Supplement Table 3 for the small population size (there the equilibrium should occur faster). Immigrants assuming 5 years generation interval
Immigrants per generation
Inbreeding at equilibrium
Vortex result after 50 years
Suppl Table 3
Start value around F=0.27
The deviation from
expected are huge and puzzling. Low immigration leads to considerable lower
inbreeding than expected and a high migration to a much higher level of
inbreeding than expected. I cannot see an acceptable explanation. This large
deviations from the “Island model” has also focused attention of reviewers P59:
“why these values deviate so much from the values expected from the so called Island
model. For example, the model result for 4 migrants/3 years is F =0.147. The
theoretical equilibrium value for this scenario is F = 0.036 with a generation
time of 5 years, and F = 0.045 with generation time of 4 years.” That the
response of the PS model seems weird does not give trust in that weird results
with other models are more trustworthy.
## Vortex predicts that the Swedish wolf would have gone extinct but it did not! The author tries to apply Vortex to the past history of the Scandinavian wolf, with the result that Vortex simulations predicts it would have gone extinct (p 16 ): “The implication of this result, given the parameters used here, is that the persistence of the Swedish wolf population was a statistically unlikely event” … “even under the least severe inbreeding model, the projected population size at 2008 was only 57% of the actual value”. Thus Vortex cannot predict the past, how could it when be trusted to predict the future? Possible explanations are that the genes of the founders are resistant to inbreeding depression, or the hybrid vigor observed for immigrants has not been fully considered. But no effort to use this information in the real runs were done, leading to too low estimates of FRP.
# The statistical precision of differences among alternatives tend to be low and thus many results statistically insignificant. Look at standard deviations of the results when presented in Tables and figures! Remember that a 95% confidence interval is double as large!
# The predictions of the fate of a real single wolf population is highly uncertain. Example look at Figure 12a (or any of the figures for no immigration and variation shown). Remark: an individual population may come considerable longer from the mean than a standard deviation. It looks like good chance that the “inbreeding” of “the Scandinavian wolf” will sink during the following fifty years even if there is no immigration at all.
# Too detailed control over the report by Naturvårdsverket. The study is governed in detail by instructions from SEPA, which seems too narrow, shadow some relevant and highlight some less relevant considerations. Too little room for own initiatives seems left to this qualified expert. The instructions seem partly governed by irrelevant motives.
# Where is much positive to say about the report and positive critics, which I do not spend much space, effort and time to express here. The allele and dispersal method offer many potential advantages in theory and should be possible to develop to more trustworthy application. The report give a better understanding even if it does not reach to trustworthy practical application. My critical remarks should not be interpreted as against the competence, abilities, cooperation or scientific ambition of Prof Bruford. I do not think the task could have been better done by anyone else given the rather narrow task specified by SEPA and the limited budget and time frame. But it was not enough to make a trustworthy sufficiently good foundation to give sufficient accurate replies to the questions or to support a possible increase of FRP.
# My scientifically founded opinion: I claim as professor of genetics that it is beyond reasonable doubt that increasing FRP now will have a very small effect on the probability that wolf remains in Sweden in a sustainable condition 2115.
# I am personally frustrated that a qualified analyses using Vortex did not produce more trustworthy results, I predicted it should perform better than it did, and regard the shortcoming of the report as a personal shortcoming.
# Wolf management is more about psychology than Science. Probably it does not help psychologically to base so called scientific decisions on a report by a foreign expert which is so difficult to understand, comprehend and accept as the Bruford report. It helps if wolf can come off the agenda, so thinking how to do that can be a good idea. But the likelihood wolf leaves the agenda is not helped by reports which opens more questions than they answer. It helps with a material the most concerned parties can discuss about, but this report will leave them out of the discussion.
I place this article on the net and it is allowed to make articles based on this material och use the text without citation or link to it. I change the text if I find it in need of modification. Last edit 150815
Dag Lindgren, Umeå
Retired Professor of Forest Genetics