The post-glacial colonization of fish populations can be
dated with DNA in lake sediments.
Fredrik Olajos
Student
Thesis in Biology 60 ECTS
Master’s level
Report passed: 26/8 - 2016
Supervisor: Göran Englund
Abstract
The age of natural populations is crucial information when studying processes like extinction,
colonization, adaptation and evolutionary divergence. Here I evaluate if DNA in lake
sediments can be used to date the colonization by whitefish (Coregonus lavaretus) in lakes in
central Sweden. Three species-specific primer pairs were designed to detect the presence or
absence of whitefish DNA in sediments from lake Hotagen where I hypothesized that
whitefish colonized before 1790 but long after the ice-melt 10 000 years ago. By applying
Bayesian estimation on binary PCR results, the colonization of whitefish in lake Hotagen was
dated to 2098 – 2632 BP. To examine if DNA could be detected in 10 000 year old sediments
and if the detection probability declines over time I also analysed the presence of DNA in a
core from lake Stora Lögdasjön. DNA was successfully recovered and amplified throughout
the sediment core with no loss of detection probability from present time to 9535 – 9480 BP.
I conclude that species-specific PCR and lake sediment DNA can be used to reconstruct the
history of natural populations of aquatic organisms.
Keywords: Whitefish, Sediment DNA, Species specific, Holocene, Colonization, Method.
Table of Contents
1 Introduction ................................................................................................................... 1
2 Materials and methods ................................................................................................. 2
2.1 Study site and core sampling ......................................................................................... 2
2.2 Sediment core processing and DNA extraction ............................................................ 2
2.3 Primer design ................................................................................................................ 3
2.4 PCR analysis ................................................................................................................. 3
2.5 Dating of the cores ........................................................................................................ 4
2.6 A statistical model for colonization date ...................................................................... 4
3 Results ...........................................................................................................................5
4 Discussion...................................................................................................................... 7
5 References .................................................................................................................... 9
6 Supplementary information ........................................................................................ 11
1 Introduction
Knowing the age of natural populations is critical for our ability to study the rates of
fundamental ecological and evolutionary processes such as colonization, extinction,
adaptation and evolutionary divergence (Hugueny et al., 2011, Öhlund, 2012, McGee et al.,
2016). Analysis of colonization and extinction histories can provide information on
ecosystem dynamics, species interactions, and potential dispersal routes (Crawley, 2005).
However, our knowledge of colonization and extinction events are predominately based on
historical data which tend to be scarce or incomplete (Estoup and Guillemaud, 2010).
Modern methods, such as genetic modelling can provide information about colonization
routes and demographic histories (Cristescu et al., 2001) but struggle in determining a
precise time frame. In this study I therefore propose a method for determining the age of fish
populations using species-specific PCR to detect the presence/absence of DNA in lake
sediments.
DNA-based tools for taxonomic identification enables detection of one or more species
present in a single environmental sample (Taberlet et al., 2012, Valentini et al., 2009,
Ficetola et al., 2008, Jerde et al., 2011). As demonstrated by previous studies, extracellular
DNA from a wide variety of taxa has successfully been recovered from natural archives such
as lake sediments, peat, and soils (Anderson-Carpenter et al., 2011, Giguet-Covex et al., 2014,
Willerslev et al., 2003, Andersen et al., 2012, Epp et al., 2012, Haile et al., 2007, Hofreiter et
al., 2003, Jorgensen et al., 2012a, Jorgensen et al., 2012b, Lydolph et al., 2005, Parducci et
al., 2012, Yoccoz et al., 2012). However, when shed from an organism, DNA is prone to
decomposition (hydrolyzation, oxidation and defragmentation), the rate of which is
determined by both biotic and abiotic factors such as temperature, oxygen availability and
microbial activity (Hansen et al., 2006, Willerslev et al., 2004). In some environments (soils
and sediments) DNA binds to charged surfaces and particulate organic compounds which
drastically reduce the rate of decomposition (Pote et al., 2009, Pote et al., 2007,
Pietramellara et al., 2009). The effects of time on detection probability and to what degree
DNA is transported between sediment layers of different age are, however, still largely
unknown and potential obstacles when reconstructing past communities.
Here I investigate whether DNA-based species identification can provide a reliable method
for determining the age of European whitefish (Coregonus lavaretus) species-specific
mtDNA primers to detect the presence and absence of DNA in lake sediment cores. The
European whitefish is a model species for studying sympatric speciation, and dating
populations that differ in the degree of divergence can potentially allow us to elucidate the
processes that are critical under different stages of the speciation process. It is believed that
whitefish colonized many Scandinavian lakes after the last glaciation ca 9000-12000 years
ago (Svärdson, 1979, Svärdson, 1953). However, natural migration barriers prevented
colonization of many systems and extensive introductions by humans have been documented
since the late 18th century (Nordlander, 1894). These young introduced populations are
considerably less diverged in heritable traits than populations that presumably colonized
after the ice melt (Öhlund, 2016). To fill the gap in the evolutionary chronosequence I
therefore investigated when whitefish first colonized lake Hotagen in central Sweden.
Historical data show that whitefish were present in Hotagen at 1790, whereas the degree of
divergence suggests that the whitefish populations are considerably younger than 10 000
years (Nordlander, 1894, Svärdson, 1979). Moreover, there is a steep waterfall, Näsforsen,
downstream of the lake that likely has hindered natural colonization. As a control used to
examine if the detection probability change over time I analyzed a sediment core from lake
Stora Lögdasjön. This lake was well-connected to the Baltic sea when the Weichsel ice sheet
melted and it contains clearly diverged whitefish populations (Olofsson, 1919-38, Svärdson,
1979). Thus, I hypothesized that whitefish colonized Stora Lögdasjön immediately after the
ice melt, which should allow detection of whitefish DNA throughout the Holocene sediment
profile (ca 9500 years).
1
I found that whitefish DNA was present throughout the sediment profile in lake Stora
Lögdasjön, and there was no evidence that detection probability decreased with sediment
depth. Thus I conclude that whitefish colonized this lake soon after the icemelt ca 9500 years
ago and that the effects of DNA degradation on detection probability is negligible. In lake
Hotagen the occurrence of DNA suggest that whitefish colonized in the period 2098 – 2632
BP.
2 Materials and methods
2.1 Study site and core sampling
Lake Hotagen and Stora Lögdasjön are boreal lakes located in central Sweden (see
supplementary fig 5). Lake Hotagen (45.5 km2, 313m above sea level, maximum depth 71 m,
coordinates lat: 63,78905, long: 14,66803) is a tributary to Indalsälven river system. The
catchment (201.7 km2) is dominated by pine rich forest (65%). Lake Stora Lögdasjön (13,0
km2, 266 m above sea level, maximum depth 75m, coordinates lat: 64,08098, long:
18,60826) is a tributary to Lögdeälven river system. The catchment (59.8 km2) is dominated
by pine rich forest (63%).
Both lakes were cored in September 2015 at a depth of 20 meters avoiding areas where major
tributaries enter to obtain an undisturbed sediment chronology (see supplementary figure
3,4). From a stable anchored position, a composite plastic tube (86 mm inner diameter) was
entered vertically into the lake sediment until reaching the underlying moraine or clay. Both
cores were immediately sealed and taken to Umeå University where they were stored in 4°C
overnight. The lengths of the retrieved cores were: lake Hotagen – 196 cm, lake Stora
Lögdasjön – 251 cm.
2.2 Sediment core processing and DNA extraction
The two cores were processed in a paleolimnological laboratory at Umeå University where no
genetic or molecular level research had been performed prior to this study. Sterile disposable
equipment was used to remove the peripheral layer of sediment. Samples for DNA analysis
were then taken from the exposed centre of the core, placed in sealed containers and stored
in -40°C. Samples were laid out differently in the two lakes: In lake Stora Lögdasjön samples
were distributed evenly throughout the core (15 in total) (see results: fig 1), whereas in lake
Hotagen, sampling effort was higher in the top 25% of the core to increase resolution for the
time period when whitefish presumably were introduced (35 in total) (see results: fig 2). The
top 6 cm were avoided in both cores because high water content made the sediment
unstable. From each sediment sample, four DNA extractions were carried out using 0.25 mg
sediment wet weight per extraction. In both cores the upper 95% was dominated by gyttja,
whereas the lowest 5% consisted of post glacial clay.
Sediment DNA extraction was carried out with Power Soil DNA isolation kit (MoBio,
Carlsbad, CA, USA) using an alternative lysis method. Samples were incubated for 10
minutes at 70°C, spun in a vortex for 5 seconds and incubated another 10 minutes at 70°C.
Extraction proceeded by following the manufacturer’s instructions from protocol step 5. Final
elution volume was 100 µl per sample. To increase DNA concentrations all extractions were
concentrated in a speedvac to a final volume of 25 µl. The four DNA extractions
corresponding to one level within a core were pooled to a single sample with a final volume of
100 µl. To remove any excess PCR inhibitors, all final samples were purified using a OneStep
Inhibitor Removal Kit (Zymo Research, Irvine, CA, USA). DNA extraction was performed
using sterile equipment in a laboratory at the department of Ecology and Environmental
Science, Umeå University, where no genetic work on aquatic species had been performed
prior to this study.
2
2.3 Primer Design
Whitefish specific primers were designed using mitochondrial sequence data available in the
GenBank nucleotide database (accessed May 2015). A genome wide alignment of the most
prevalent Swedish salmonid taxa was rendered using BioEdit 7.2.5 . Complicit species were;
whitefish (Coregonu lavaretus NC_002646.1), atlantic salmon (Salmo salar NC_001960.1),
brown trout (Salmo trutta NC_024032.1), arctic char (Salvelinus alpinus NC_000861.1) and
grayling (Thymallus thymallus NC_012928.1). Contingent on this alignment, the software SPdesigner (Villard and Malausa, 2013) was used to find conserved regions in the whitefish
mitochondrial genome with suitable criteria for efficient PCR primers. Species-specific
primers were designed to be invariable within the target species yet sufficiently distinctive to
inhibit erroneous PCR amplifications and mispriming of nontarget taxa. Parameters related
to amplification efficiency (CG-content, secondary structures etc)(Dieffenbach et al., 1993)
were also taken into consideration. Due to potential defragmentation and degradation of
environmental DNA, shorter PCR product lengths of approximately 100 bps were deemed
necessary. Primer specificity was tested in vitro employing ncbi BLAST (May 2015) and in
silico using DNA extract from tissue of whitefish and closely related salmonids. DNA
extraction was performed using the E-Z 96® Tissue DNA Kit (Omega, USA) following the
manufacturer’s instructions. Three primer pairs were designed in total (table 1).
Table 1. Primer sets designed for PCR amplification of sediment DNA with expected product length, position in
the genome and annealing temperature.
Name
Target region of genome
Product
length (bp)
Annealing
temperature (°C)
NADH dehydrogenase subunit 5
90
62
NADH dehydrogenase subunit 2
122
63
Cytochrome C oxidase subunit 3
115
59,5
Sequence (5´- 3´)
wfNAD5F
CTGAGCCCTAACCCTTACCC
wfNAD5R
CGAGGGTGTCCCATAGATACG
wfNAD2F
CATGACAGCCCTTCTCAGC
wfNAD2R
GGGTGGTGTGGGTAAAGTCC
wfCOX3F
AAGTCCCGCTACTGAACACC
wfCOX3R
GTTAGGGTGAGAGATTGGATGG
2.4 PCR analysis
All amplifications were performed on a T100™ Thermal Cycler (Bio-Rad) with the following
PCR protocol: initial denaturation at 95°C for two minutes followed by 45 3-step cycles of
denaturation at 95°C, annealing at corresponding primers Tm° (63°C, 62°C or 59.5°C) and
extension at 72°C for 30 seconds each, ending with a final extension at 72°C for five minutes.
Final volume per reaction was 30 µl and contained the following concentrations: 5 µl of
environmental DNA extract, 1.3 mg/ml BSA (Thermo Fisher scientific), 0.8 U Taq DNA
polymerase (Thermo Fisher scientific), 1.0 X PCR buffer with (NH4)2SO4 (Thermo Fisher
scientific), 0.1 mM of each dNTP, 0.2 µM of each primer and 2.5 mM MgCl2. All samples were
loaded onto 1.7% agarose gel and separated at 90 volts for one hour. Pre and post PCR work
was carried out in different rooms (Cooper and Poinar, 2000).
One PCR per primer pair was run for each DNA extract. Each PCR included three different
negative controls and one positive control in duplicate. The negative controls consisted of
3
reverse osmosis autoclave water which had been prepared together with 1) sediment core
sampling and 2) DNA extraction, concentration and purification. The third negative control
was sealed up to PCR preparation. These controls allowed identification of potential sporadic
contaminants during different stages of the study. The positive control contained whitefish
DNA extracted from tissue using the E-Z 96® Tissue DNA Kit (Omega, USA) following the
manufacturer’s instructions. Analysis of the data was strictly binary and executed visually of
the gel electrophoresis photographs using precautionary principle. Amplification was
considered positive if a clear product matching the positive control was visible; all other cases
were considered negative.
2.5 Dating of the cores
The cores were dated with accelerator mass spectrometry 14C dating by the Beta Analytic
Radiocarbon Dating Laboratory Miami, Florida. All calendar dates were calibrated (2 sigma)
using a fitted spline curve (Thalma and Vogel, 1993) and the INCAL13 calibration database
(Reimer et al., 2013) (supplementary figure 1). Two bulk sediment samples from lake Stora
Lögdasjön and three terrestrial macrofossil remains from lake Hotagen were dated. The agedepth model in lake Hotagen was constructed with linear regression using sample depth and
the mid value of the 95% confidence interval of the calibrated age for each of the three 14C
samples. The age-depth model indicated that the top segment (~ 0 -1250 years cal. BP) was
missing from the lake Hotagen core (supplementary figure 2).
2.6 A statistical model for colonization date
When estimating the date of colonization it is necessary to consider two types of errors. False
negatives may occur when detection probability is low because DNA is present in low
concentrations in the sediment, and false positives may occur due to contamination of
sediment samples and controls where whitefish DNA is expected to be absent. The
probability of these errors are denoted Pfn (false negative) and Pfp (false positive). I assume
that whitefish colonized once and was present thereafter, hence the presence or absence of
whitefish can be described by a step function that switches from absent to present at time of
colonization, tc. Between the present and tc, each successful amplification has probability 1Pfn(t) and each unsuccessful amplification has probability Pfn(t) (table 2). For samples older
than tc, successful amplification has probability Pfp and unsuccessful amplification has
probability 1-Pfp (table 2). In other words, let ti be the age of the sediment in the i-th sample,
and let pi be the probability of the outcome (sucessful/unsuccessful amplification) of that
sample. Then pi equals Pfp,1-Pfp,Pfn or 1-Pfn as shown in table 2. The log likelihood (L) of the
results is the sum of all the logarithmic probabilities of the n individual samples:
 Pfp if t i  t c , successful amplificat ion
1  P if t  t , unsuccessf ul amplificat ion
n

fp
i
c
p

Eq.1: L   ln pi ,where i 
i 1
 Pfn if t i  t c , unsuccessf ul amplificat ion
 1  Pfn if t i  t c , successful amplificat ion
The three primer pairs could have different amplification probabilities. Let pij be the
probability of the outcome of the i-th sample using the j-th primer pair, and let Pfp,j and Pfn,j be
the probabilities of false positive and false negative amplification for that primer pair.
Equation 1 then can be rewritten:
4
Eq.2: L 
n
3
 ln p
i 1 j 1
ij
 Pfp, j if ti  tc , amplificat ion successful using primer j
1  P if t  t , amplificat ion unsuccessf ul using primer j

fp, j
i
c
Where pij  
 Pfn, j if ti  tc , amplificat ion unsuccessf ul using primer j
 1  Pfn, j if ti  tc , amplificat ion successful using primer j
By adjusting the values of Pfn, Pfp and tc to maximise this likelihood, the most likely value of tc
can be obtained. As no prior knowledge about the parameters were available I generated
initial values for parameters Pfn, Pfp and tc from uniform probability distributions (Pfn, Pfp: 0 –
1)( tc: 0-infinity) and used the Markov Chain Monte Carlo (MCMC) method to generate a
posterior probability distribution for the date of whitefish colonization time (tc). Every
iteration was rejected or accepted based on its likelihood ratio (Metropolis-Hastings
algorithm). The model was run with 11000 iterations and a burn-in of 1000 selecting every
10th sample (for R script and additional information see supplementary table 1 and 2).
Table 2. Possible amplificatin outcomes.
Whitefish present
Whitefish absent
Successful
1-Pfn
False positive: Pfp
Unsuccessful
False negative: Pfn
1-Pfp
3 Results
No negative control and all positive controls amplified the target sequences (table 3). In lake
Stora Lögdasjön, PCR amplified at least one target sequence in 11 out of 15 sediment samples
distributed throughout the entire sediment profile (fig. 1). The highest frequency of successful
amplifications were observed in the deepest part of the core and the oldest successful
amplification (241 cm) was located between the two 14C samples that were calibrated to 9535
– 9480 BP and 9347 – 9327 BP. Thus, I concluded that degradation had negligible effects on
detection probability and that whitefish colonized shortly after the ice melt. Primer pair
amplification distribution was the following: wfNAD5 – 8 out of 15 amplifications, wfNAD2 –
6 out of 15 amplifications and wfCOX3 – 7 out of 15 amplifications.
In lake Hotagen, PCR amplified the target sequence in 12 of 35 samples. These samples were
all younger than 2552 years BP (fig. 2). The MCMC analysis showed that the most likely
colonization date was 2125 BP (fig. 3). However, because the oldest successful amplification
was preceded by three negative samples there is a second peak in the probability distribution
at around 2400 BP. The estimated probability of false positives were low, whereas the
average probabilities of false negatives for each of the primers were rather high (Table 4).
5
Primer pair amplification distribution was the following: wfNAD5 – 3/35 amplifications,
wfNAD2 – 7/35 amplifications and wfCOX3 – 5/35 amplifications.
Table 3. Amplification of positive controls (Pos C) and negative controls (Neg C 1-3). Bracketed figures indicate
replicates.
Lake Stora
Lögdasjön
Pos C(1)
Pos C(2)
Neg C1(1)
Neg C1(2)
Neg C2(1)
Neg C2(2)
Neg C3(1)
Neg C3(2)
Primer wfNAD5
1
1
0
0
0
0
0
0
Primer wfNAD2
1
1
0
0
0
0
0
0
Primer wfCOX3
1
1
0
0
0
0
0
0
Lake Hotagen
Pos C(1)
Pos C(2)
Neg C1(1)
Neg C1(2)
Neg C2(1)
Neg C2(2)
Neg C3(1)
Neg C3(2)
Primer wfNAD5
1
1
0
0
0
0
0
0
Primer wfNAD2
1
1
0
0
0
0
0
0
Primer wfCOX3
1
1
0
0
0
0
0
0
Figure 1. Primer amplification in sediment from lake Stora Lögdasjön. Blue circles represent samples taken in the
sediment core. The size of the circles indicates how many of the three primer pairs that amplified the target
sequence. The arrows represent bulk sediment samples that were 14C dated. The mid values of the 95% confidence
intervals (9347-9327 and 9535-9480, respectively) are given in the figure.
Figure 2. Primer amplification in sediment from lake Hotagen. Blue circles represent samples taken in the
sediment core. The size of the circle indicate how many of the three primer pairs that amplified the target
sequence.
6
Figure 3. The posterior frequency distribution of colonization dates estimated from lake Hotagen PCR results. The
black circle is the median (2243 years Cal. BP), red circles show the 5th (2098 years Cal. BP) and 95th quantiles
(2632 years Cal. BP).
Table 4: Average values for Pfn and Pfp generated by the MCMC iterations in lake Hotagen.
Primer
Average Pfn
(95% CI)
Average Pfp
(95% CI)
wfNAD5
0,78 ( +/- 0,006)
0,027 ( +/- 0,0014)
wfNAD2
0,59 ( +/- 0,007)
0,027 ( +/- 0,0014)
wfCOX3
0,67 ( +/- 0,006)
0,027 ( +/- 0,0014)
4 Discussion
Overall my results demonstrate that ancient DNA in lake sediments can be used to estimate
the age of lacustrine fish populations that colonized after the melting of the Weichsel ice, ca
10 000 years ago. In lake Stora Lögdasjön whitefish DNA was successfully amplified
throughout the core with no indication of loss in detection probability in old samples (fig 1).
In lake Hotagen, no primer pair amplified below 2552 years cal. BP following a series of
successful reads (fig 2). Taken together these results suggests that the null amplicons in the
bottom part of lake Hotagen core is indeed indicative of whitefish absence and thus that
arrival of whitefish to this lake can be dated.
The reliability of environmental DNA in sediments is influenced by thermal and geochemical
processes that need to be favorable for long term DNA preservation (Hansen et al., 2006,
Willerslev et al., 2004, Pote et al., 2009, Pote et al., 2007, Pietramellara et al., 2009). Both
study systems experience seasonal winters and summertime stratification with temperatures
at the sediment surface around 4°C for most of the year. Sediment composition in both lakes
was dominated by gyttja (freshwater mud containing an abundance of organic matter) which
allow DNA adsorbance (Pote et al., 2007). These parameters are of great importance
preventing DNA degradation over time (Giguet-Covex et al., 2014). In lake Stora Lögdasjön
(control lake), two independent 14C datings located at the bottom of the core calibrated to
9535 – 9480 BP and 9347 – 9327 BP respectively (fig 1). This indicate that the entire
Holocene sediment profile was recovered. Interestingly I found a higher frequency of
successful amplifications towards the bottom of the core. A reasonable interpretation of this
7
finding is that the sedimentation rates were higher or initial degradation rates lower in the
first thousand years after whitefish colonization. This could for example be caused by
variation in whitefish densities or concentrations of fine organic and minerogenic particles
that DNA fragments could bind to.
In theory, the reliability of environmental DNA can be compromised by analytical and
sampling procedures (mainly contamination and PCR amplification) (Kowalchuk et al.,
2007). Stringent precautions were taken during laboratory work to avoid contamination.
Different stages (core processing, DNA extraction, pre PCR, PCR and post PCR) were all
carried out in different rooms dedicated to genetic research where no studies on aquatic
organisms had been conducted prior or in rooms where no molecular research had been
performed at all (as adviced by Cooper and Poinar, 2000). Sterilized disposable equipment
was used at all stages of laboratory work and no equipment was transferred between rooms.
Additionally, as the study organism was aquatic the overall contamination risk should be
considerably lower than for taxa prevalent in the terrestrial environment (such as humans,
plants and microbes). None of the three negative controls amplified the target sequences in
any of the six PCRs, suggesting that the precautionary measures taken were sufficient.
The presence of false negatives appears to be more of a problem. Sporadic negative
amplifications among successful amplifications may suggest either that the target species was
absent or that the concentration of DNA fragments were too low to be detected. Likewise,
outlying positive amplifications can be interpreted either as species presences or false
positives. This complication is partially visible in this study (fig 2), where a total of 6 null
amplicons are present between 1356 – 2552 years cal. BP in the Hotagen core. Furthermore,
the oldest positive amplification (2552 years cal. BP) is followed by three younger negative
samples. To deal with this uncertainty, I used the Markov Chain Monte Carlo method to
generate a posterior distribution of proposed introduction dates based on the prior inference
of lake Hotagen PCR results (fig 3). The results of this model indicates that whitefish most
likely colonized in the period 2098 – 2632 BP. The estimated probability of false positives
were as expected very low. However, the estimated probability false negatives for each primer
were rather high (0.59-0.78) and the estimated combined probability were 0.31 (table 4).
Thus it is motivated to take measures to reduce this uncertainty in future studies. This could
be done by using more primer pairs or increasing the number of samples from each level.
The DNA-based species identification method applied on lake sediments revealed novel data
on whitefish colonization dynamics in Scandinavian post glacial lakes. Previous theories
concerning whitefish colonization is based on current distribution patterns, as subfossils
from whitefish from early Holocene are lacking (Lepiksaar, 2005). It is hypothesized that
whitefish was present in the Ancylus lake and Yoldia sea and could colonize Scandinavian
freshwater bodies as the Weichsel ice sheets retracted 9000-12000 years ago (Lepiksaar,
2005, Svärdson, 1979).The results of this study support this hypothesis. It has also been
speculated that different whitefish ecotypes represent different invasion waves (Lepiksaar,
2005, Svärdson, 1979), but recent phyleogeographic studies indicate ecotypes have diverged
within lakes or sub-catchments (Ostbye et al., 2006, Ostbye et al., 2005, Siwertsson et al.,
2010, Öhlund, 2016). My findings suggests that ancient DNA in sediments can be used to
describe the colonization process in great detail and thus potentially could be used to test the
two competing hypotheses about the whitefish speciation process. More generally my results
suggests that DNA based species identification can be an important complement to
conventional paleoenvironmental methodology when reconstructing Holocene environments
and further increase our knowledge of colonization, extinction and speciation events for an
array of aquatic species.
8
5 References
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11
6 Supplementary information
Supplementary figure 1: Spline curves for all 14C samples. Black bars indicate 1-sigma calibration; white bars
indicate 2-sigma calibration.
12
Supplementary figure 2. Age-depth model for the sediment core taken in lake Hotagen based on 14C datings of 3
macrofossils
13
Supplementary figure 3. Map indicating sample location in lake Stora Lögdasjön.
Supplementary figure 4. Map Indicating sample location in lake Hotagen.
14
Stora Lögdasjön
Hotagen
Supplementary figure 5: Map Indicating sample locations (red triangles.
15
Supplementary table 1. R script for MCMC used to estimate introduction dates.
FindIntroTime<-function(niter=1000,samplefreq=1,burnin=0){
GetLik<-function(obs,t,ti,Pfn,Pfp){ #likelihood function
L<-matrix(nrow=length(t), ncol=length(Pfn))#empty matrix to store likelihoods
for (j in 1:length(Pfn)) {
ind<-(obs[,j]==0) & (t<=ti)#false negatives
L[ind,j]=Pfn[j]#[ind]
ind<-(obs[,j]==0) & (t>ti)#not false positives
L[ind,j]=1-Pfp[j]
ind<-(obs[,j]==1) & (t<=ti)#not false negatives
L[ind,j]=1-Pfn[j]#[ind]
ind<-(obs[,j]==1) & (t>ti)#false positives
L[ind,j]=Pfp[j]
}#end of for-loop
GetLik=sum(sum(log(L)))#sum the likelihood values
}#end of function GetLik
d<-read.table("Point to data directory eg.(C:/mydata.csv or .txt)", header=TRUE, sep=",")
#initial values
ti<-40 #time of introduction
Pfn<-numeric(3)#P(false negative) for each primer
Pfn[1:3]<-0.8
Pfp<-numeric(3)#P(false negative) for each primer
Pfp[1:3]<-0.05
L<-GetLik(d[,2:4],d$time,ti,Pfn,Pfp)#get initial likelihood
mcmclength<-floor((niter-burnin)/samplefreq)#determine length of mcmc output
mcmc <- data.frame(L=numeric(length=mcmclength),ti=numeric(length=mcmclength),
Pfp1=numeric(length=mcmclength),Pfp2=numeric(length=mcmclength),Pfp3=numeric(leng
th=mcmclength),
Pfn1=numeric(length=mcmclength),Pfn2=numeric(length=mcmclength),Pfn3=numeric(leng
th=mcmclength),
stringsAsFactors=FALSE)
for (iter in 1:niter){ #repeat the steps below niter times
#update ti
pti<-ti+rnorm(1, mean = 0, sd = 10)#propose new value for ti
while (pti<0) {pti<-ti+rnorm(1, mean = 0, sd = 10)}#sample again if time became negative
pL<-GetLik(d[,2:4],d$time,pti,Pfn,Pfp)#get likelihood of proposal
if (log(runif(1))<(pL-L)) { #with probability equal to likelihood ratio...
ti<-pti#... accept proposed time of introduction
L<-pL#...update value of likelihood accordingly
}
#update PfP
pPfp<-Pfp+rnorm(1,mean=0,sd=0.01)#propose new value for Pfp
while (any(pPfp<0 | pPfp>1)) {pPfp<-Pfp+rnorm(1,mean=0,sd=0.001)}#sample again if
P<0 or P>1
pL<-GetLik(d[,2:4],d$time,ti,Pfn,pPfp)#get likelihood of proposal
if (log(runif(1))<(pL-L)) { #with probability equal to likelihood ratio...
Pfp<-pPfp#accept proposed prbability of false positive
16
L<-pL#update value of likelihood accordingly
}
#update Pfn
pPfn<-Pfn+rnorm(3,mean=0,sd=0.01)#propose new value for Pfn
while (any(pPfn<0 | pPfn>1)) {pPfn<-Pfn+rnorm(3,mean=0,sd=0.001)}#sample again if
P<0 or P>1
pL<-GetLik(d[,2:4],d$time,ti,pPfn,Pfp)#get likelihood of proposal
if (log(runif(1))<(pL-L)) { #with probability equal to likelihood ratio...
Pfn<-pPfn#accept proposed prbability of false positive
L<-pL#update value of likelihood accordingly
}
if (iter>burnin & ((iter-burnin) %% samplefreq)==0){ #this is just to store the values in the
output variable
ind=(iter-burnin)/samplefreq
mcmc$L[ind]<-L
mcmc$ti[ind]<-ti
mcmc$Pfp1[ind]<-Pfp[1]
mcmc$Pfp2[ind]<-Pfp[2]
mcmc$Pfp3[ind]<-Pfp[3]
mcmc$Pfn1[ind]<-Pfn[1]
mcmc$Pfn2[ind]<-Pfn[2]
mcmc$Pfn3[ind]<-Pfn[3]
}#end if
}#end iter loop
FindIntroTime<-mcmc #assign output variable
}#end of main function
r<-FindIntroTime(11000,samplefreq=10,burnin=1000)
Supplementary table 2. Simplified explanation of MCMC algorithm.
0. Sample initial values for all unknown parameters Pfn, Pfp, ti, from their respective prior
distributions.
1. Evaluate the likelihood of the observed data
2. Propose new value for an unknown parameter from its respective prior distribution.
3. Evaluate the likelihood of the data given the proposed value
4. Accept with likelihood ratio
5. Repeat steps 2-4 for each parameters
6. Repeat steps 2-5 many times
17
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