Quantitative thinking to understand complex ecological systems

Dr. Gaurav Kandlikar
Slides: https://talks-gklab.org/ecology-overview-26
Contact: gkandlikar@lsu.edu

Longleaf pine savannas

Historical range of the longleaf pine ecosystem

Code 
library(sf)
library(tidyverse)

little <- sf::st_read("../img/pinupalu.shp")
Reading layer `pinupalu' from data source 
  `/home/gkandlikar@lsu.edu/gklab/talks/img/pinupalu.shp' using driver `ESRI Shapefile'
Simple feature collection with 38 features and 5 fields
Geometry type: POLYGON
Dimension:     XY
Bounding box:  xmin: -95.21806 ymin: 26.61921 xmax: -75.79999 ymax: 36.84856
CRS:           NA
Code 
# States we want to show
llp_states <- c("texas", "louisiana","mississippi", "alabama", "florida", "georgia", "south carolina", "north carolina", "virginia", "tennessee")
states <- map_data("state") |> 
  filter(region %in% llp_states)

ggplot() +
  geom_polygon(data = states,
               aes(x = long, y = lat, group = group), fill = "transparent", color = 'darkgrey') + 
  geom_sf(data = little, fill = alpha('#228833', 0.5)) + 
  theme_void()

Image: AllAboutBirds

Image: Southern Science

Image: A Naturalist’s Journey blog

Image: Trees Atlanta

Fire is an important component of the system

Historic fire regime

  • Over evolutionary timescales, lightening-driven

  • Over the past several centuries, managed by indigenous groups

Prescribed burn at LSU Forestry Camp, 13 April 2026

Image: The Nature Conservancy

Problem

  • Historic range: nearly 100 million acres

  • Present day: less than 5 million acres

  • Fire is known to be important…

  • … but there was a long period of fire suppression

Still image from 1920s US Forest Service film “When Trees Talk”. Video available here.

Consequences of “woody encroachment”?

Causes of “woody encroachment”?

Current focus:

  • Interactions between plants and microbes in the soil
  • Fire suppression

Approach

  • Field studies

  • e.g. “How does variation in fire severity affect plants and soil microbes?”

LSU AgCenter’s Lee Memorial Forest, FranklintonLA

Low fuel

Mean fuel

High fuel

Approach

  • Field studies

  • e.g. “How does variation in fire severity affect plants and soil microbes?”

  • Greenhouse experiments

  • e.g. “How does fire disrupt plant–soil microbe interactions and can this affect the community as a whole?”

Experiment setup at LSU Ben Hur AgCenter

  • Field studies

  • e.g. “How does variation in fire severity affect plants and soil microbes?”

  • Greenhouse experiments

  • e.g. “How does fire disrupt plant–soil microbe interactions and can this affect the community as a whole?”

Other groups studying other aspects

But, there are limitations to what we can do in the field!

  • Lots of species in the system! How to generalize?

  • Fires happen every 2–3 years – how to make long-term predictions?

How to tackle this challenge?

How to use math for making sense of ecological systems?

An example from our work on plant–fire–soil relationships

Question: How fire impact woody encroachment?

How to use math for making sense of ecological systems?

How to use math for making sense of ecological systems?

Empty patches

\[\frac{dP_{00}}{dt} = \overbrace{\mu_g P_{g0} +\mu_s P_{s0}}^{\substack{\text{ plant mortality}}\\{\text{in unconditioned soil}}} + \overbrace{d_g P_{0g} + d_s P_{0s}}^{\substack{\text{microbial decay} \\ \text{in empty patches} }} - \\ \overbrace{r_gP_{00}(P_{{g0}+}P_{gg}+P_{gs})}^{\text{grass establishment}} - \\ \overbrace{r_sP_{00}(P_{{s0}+}P_{ss}+P_{sg})}^{\text{shrub establishment}} \]

Patches with plant present but soil not yet conditioned

\[\frac{dP_{g0}}{dt} = \overbrace{r_gP_{00}(P_{g0} + P_{gg} + P_{gs})}^{\substack{\text{grass establishment in} \\ \text{unconditioned soil}}} - \overbrace{c_g P_{g0}}^{\substack{\text{soil conditioning}\\\text{by grass}}} - \overbrace{\mu_g P_{g0}}^{\text{grass mortality}}\]

\[\frac{dP_{s0}}{dt} = \overbrace{r_sP_{00}(P_{s0} + P_{ss} + P_{sg})}^{\substack{\text{shrub establishment in } \\ \text{empty patch}}} - \overbrace{c_sP_{s0}}^{\substack{\text{soil conditioning}\\\text{by shrub}}} - \overbrace{\mu_sP_{s0}}^{\text{shrub mortality}}\]
Patches with plants and corresponding soil conditioning effects

\(\frac{dP_{gg}}{dt} = c_g (P_{g0} + P_{gs}) + r_g m_{gg} P_{0g}(P_{g0} + P_{gg} + P_{gs}) - \mu_g P_{gg}\)

\(\frac{dP_{ss}}{dt} = c_s (P_{s0} + P_{sg}) + r_s m_{ss} P_{0S}(P_{s0} + P_{ss} + P_{sg}) - \mu_s P_{ss}\)
Patches with no plant present but conditioned soil persists

\(\frac{dP_{0g}}{dt} = \mu_g P_{gg} + \mu_s P_{sg} - r_g m_{gg} P_{0g}(P_{g0}+P_{gg}+P_{gs}) - r_s m_{sg} P_{0g}(P_{s0}+P_{ss}+P_{sg})\)

\(\frac{dP_{0s}}{dt} = \mu_s P_{ss} + \mu_g P_{gs} - r_s m_{ss} P_{0s}(P_{s0}+P_{ss}+P_{sg}) - r_g m_{gs} P_{0s}(P_{s0}+P_{ss}+P_{sg})\)

Patches with plants growing in the other plant’s conditioned soil

\(\frac{dP_{sg}}{dt} = r_s m_{sg} P_{0g} (P_{s0} + P_{ss} + P_{sg})\)

\(\frac{dP_{gs}}{dt} = r_g m_{gs} P_{0s} (P_{g0} + P_{gg} + P_{gs})\)

How to use computer programming for making sense of ecological systems?

Code 
@M03569:457:000000000-L33K9:1:1101:15118:1548 1:N:0:TGCGAGAC+CATTGTTG
TTGCCAGCCGCCGCGGTAATACAGAGGGGGCAAGCGTTGTTCGGAATTACTGGGCGTAAAGGGCGCGTAGGCGGCCTTCTAAGTCGAACGTGAAATCCCTGGGCTCAACCCAGGAACTGCGTCCGATACTGAAAGGCTTGAATCCGGGAGAGGGATGCGGAATTCCAGGTGTAGCGGTGAGATGCGTAGATATCTGGAGGAACACCGGTGGCGAAGGCGGCATCCTGGACCGGTATTGACGCTGAGGCGCG
+
1>11>B1AADDDEEFGGGGGGGHHGHGGGGGGGGHGGGGGHGGGEEFHF@FFGHHGGGGGHHGEGEEGGGGHGGCCFHFGHGGHEGCFHCHHHGGG>>FGGEGHHGGHGHFEFGHHHHGGCEGCCGECAFFGGGGGFGGGGBFCCE@G@@ABFFAFEB@@@@FFBBFFFFFFFFB@@F@F-BFFF@FF@FFFFFFF/FFFBFAFB?@?@?FF@?@@FE@@@@@BBBFFFA-;@9@EFBB/-;ABBFFA?@=
@M03569:457:000000000-L33K9:1:1101:12725:1656 1:N:0:TGCGAGAC+CATTGTTG
GTGCCAGCCGCCGCGGTAAGACGGAGGATGCAAGTGTTATCCGGAATTATTGGGCGTAAAGCGTCTGTAGGTGGTTTAAAAAGTCCATGGTTAAAACTTGAAGCTTAACTTCAAAGATGCCATGGAAACTTTTAAACTTGAGTATGGTAGGGGTAAAGGGAATTTCCAGTGGAGCGGTGAAATGCGTAGATATTGGAAAGACCACCGACGGCGAAGGCACTTTACTGGGCCATTACTGACACTAAGAGACG
+
3AAABFFBBBBBGGGGGGGFGGGGGGG?GGHGHHHHHHFGGHEGEEFGFHHGGHHGGGGEH3EF1EFHHHHHHGGGHEGBGHEHHHFFFHHHHHHHHBFFG3FHGHHHGGHGDHDGHGGHGFFGHHFHHHHHHHCGHGHHGHHHHHHHHHGGGGGGHHHGHHHHHDGDGHHHEHFGGGGGHHGGGGGGGGGGGGGG0BFGEBCCEGGGAFFFFAFFFFFABFFFFFFFFAFFFFFFFFF99;;9BFFFFFD
@M03569:457:000000000-L33K9:1:1101:12734:1677 1:N:0:TTCGAGAC+CATTGTTG
TTGCCAGCCGCCGCGGTAATACGGAGGATGCAAGTGTTATCCGGAATTATTGGGCGTAAAGCGTCTGTAGGTGGTTTAAAAAGTCCATGGTTAAAACTTGAAGCTTAACTTCAAAGATGCCATGGAAACTTTTAAACTTGAGTATGGTAGGGGTAAAGGGAATTTCCAGTGGAGCGGTGAAATGCGTAGATATTGGTAAGACCACCGACGGCGAAGGCACTTTACTGGGCCATTACTGACACTAAGATACG
+
>11>AFBAAA1>AEEGGCF22FGECFG/FGHCDEDDGH2GEFG/AABGFHH1B/G@FEG/2FFG/B>FFHHHHEGGHB>1EFEHHE1G1BG1FGGE1F>>B1GHGHFG<GHG2B21<BB1C<FH0B1DFGHHFF11FGGDDFGFHG0FG1<.?>.0D=GCHGGGGGGBGHGB0C<@@GGGFHGCF.CC-AFBFGBB0;;B0C9FF??9----@;@@BAA-:F9//;/BA-E?FFBBFB://9;//:///9;
@M03569:457:000000000-L33K9:1:1101:17662:1753 1:N:0:TGCGAGAC+CATTGTTG
GTGCCAGCCGCCGCGGTAATACAGAGGGGGCAAGCGTTGTTCGGAATTACTGGGCGTAAAGGGCGCGTAGGCGGCCCGCTAAGTCGAACGTGAAATCCCCGAGCTCAACTCGGGAACTGCGTCCGATACTGGTGGGCTTGAATCCGGGAGAGGGATGCGGAATTCCAGGTGTAGCGGTGAAATGCGTAGATATCTGGAGGAACACCGGTGGCGAAGGCGGCATCCTGGACCGGCATTGACGCTGAGGCGCG
+
ABBABFFA>ADBEAEFFGGGGB3FFGCFGGFGGCFEFGGGHFEGEFFGFFGFGHFEFGGEHFGFE@EGGGGHGG@BDDGGGDGGFDGGGCHHHEGF1<<CDDCCC0CGGG<EGGGGGHHGGGGD-CED@FFGGGGGGGFFFBB;;ABFB@.9DDFFF9@DFFEF9:FFFFFF/B:-@ABFFEBF/;DDCEFFF/BF9/;DAB.B;9@AFCF.9-9DD?-99DFB/;FFFFBDD>;@FF;9A?;A9FE.;=D
@M03569:457:000000000-L33K9:1:1101:15966:1758 1:N:0:TGCGAGAC+CATTGTTG
GTGCCAGCCGCCGCGGTAATACGGAGGATCCAAGCGTTATCCGGAATCATTGGGTTTAAAGGGTCCGTAGGCGGTTTTGTAAGTCAGTGGTGAAAGCCCATCGCTCAACGGTGGAACGGCCATTGATACTGCAAGACTTGAATTATTGGGAAGTAACTAGAATATGTAGTGTAGCGGTGAAATGCTTAGAGATTACATGGAATACCAATTGCGAAGGCAGGTTACTACCAATATATTGACGCTGATGGACG
+
CCCCCFFCCBCCGGEGGGGGGGHGGGGGHGGHHHGGGGGHFGFGGGFFGGHHHHFFFGGGGGGHHHEHHGGHGGGGGGHHHGHHHHHHHHHGGHHHHGHFBBCEHFEHHGGGHGGHHGGFGGHG>>FFFGHHHHHGHGHHHHHHHHHGHHEHGHGHHGGGFHHCCGCGHHHGGGB?CGGGGGFFCFFGGFGFGGGGFCFGBBFB0BFFFFBBDBCFFFFDFFFFFFFBBFFFFFFFFFB;:DADDFFFFFC
@M03569:457:000000000-L33K9:1:1101:17648:1769 1:N:0:TGCGAGAC+CATTGTTG
GTGCCAGCCGCCGCGGTAATACAGAGGGGGCAAGCGTTGTTCGGAATTACTGGGCGTAAAGGGCGCGTAGGCGGCCCGCTAAGTCGAACGTGAAATCCCCGAGCTCAACTCGGGAACTGCGTCCGATACTGGTGGGCTTGAATCCGGGAGAGGGATGCGGAATTCCAGGTGTAGCGGTGAAATGCGTAGATATCTGGAGGAACACCGGTGGCGAAGGCGGCATCCTGGACCGGCATTGACGCTGAGGCGCG
+
AAAABFFBB@BBGGGGGGGGGGHHHGEGGGGGGGHGGGGGHHGGFGFHHEGBBGHGGGGHHBFGGGGGGGGHGGGGGGGGGDHHHGEFHGHHHGHHGGHGFGGGEGHHGGHGFGGGGHHGGGGG-ACBDGGGFGGGGGFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFF@CDFFFFFBFFFFFFFFFFFF9BFDFFFFFF;FFFFFFFAAFF-@ADFFFFFFFFF;FFF@FFFF:DAA.FFFFFF
@M03569:457:000000000-L33K9:1:1101:15954:1772 1:N:0:TGCGAGAC+CATTGTTG
GTGCCAGCCGCCGCGGTAATACGGAGGATCCAAGCGTTATCCGGAATCATTGGGTTTAAAGGGTCCGTAGGCGGTTTTGTAAGTCAGTGGTGAAAGCCCATCGCTCAACGGTGGAACGGCCATTTATACTGCAAGACTTGAATTATTGGGAAGTAACTAGAATATGTAGTGTAGCGGTGAAATGCTTAGAGATTACATGGAATACCAATTGCGAAGGCTGGTTACTACCAATATATTGACGCTGATGGACG
+
BBBBBFFBBBBBGGGGGGGGGGHGGGCFHGHHHHGGGFGHGGGGGGFGGGHFGHEBFGGHHFFHHHGHHGGHGGGGGGFHHHHHGHGHHHHGHHHEHHHGBB?CGGEHFDGGHGEHFGGGGGHH1FGGGGHGHHHGHHHHF0GHGHHBGHAGGHGHHC;CFHG;GGGHGHHHGGGBFGGGGGG0FFFGFFGGGGGGFC0FBBFFBFFFFF9;DFFFFE/;DFFFFFFBFFFFFFBBFB/;;AA:.FBFFB@
@M03569:457:000000000-L33K9:1:1101:18221:1790 1:N:0:TGCGAGAC+CATTGTTG
GTGCCAGCCGCCGCGGTAATACGTAGGTGGCAAGCGTTGTCCGGAATTATTGGGCGTAAAGCGCGCGCAGGTGGTTCCTTAAGTCTGATGTGAAAGCCCACGGCTCAACCGTGGAGGGTCATTGGAAACTGGGGAACTTGAGTGCAGAAGAGGAAAGTGGAATTCCAAGTGTAGCGGTGAAATGCGTAGAGATTTGGAGGAACACCAGTGGCGAAGGCGACTTTCTGGTCTGTAACTGACACTGAGGCGCG
+
BBAABFFBBBBBGGGGGGGGGGHHHHGHHGHHHGGGGEGGEGFGAEFGFHHGGHHGGGGHH3FEGCG?FGG?GGGGHFHHH?GHHHHHHHHHHHHFG0GHGGGGGDHHHHGGHGDHGGGHFGHHFFBGHGGFHGADGGHHGHHFHHHHHGGHFGFFGGGGGGFF;BFCBGGGGGF?BGGEFGFFFFFFFEFBFBFF/BFFDFFFFFFFFFF.DFFFFF-99BFFEFBFFFFFFFFFFFFF/BBBFFEFFFB
@M03569:457:000000000-L33K9:1:1101:17396:1805 1:N:0:TGCGAGAC+CATTGTTG
GTGCCAGCAGCCGCGGTAATACGAAGGGGGCTAGCGTTGCTCGGAATCACTGGGCGTAAAGCGCACGTAGGCGGCTTTTTAAGTCAGGGGTGAAATCCTGGAGCTCAACTCCAGAACTGCCTTTGATACTGAGAAGCTTGAGTCCGGGAGAGGTGAGTGGAACTGCGAGTGTAGAGGTGAAATTCGTAGATATTCGCAAGAACACCAGTGGCGAAGGCGGCTCACTGGCCCGGTACTGACGCTGAGGTGCG
+
ABBAAFFAFFCAEAEEGFGGGGGAEEGGGGGEFHFEGGGAGGFGEFGGHGFFCHHEGGEHH@EEEEEHHHGFEGEDGHHHGFHHFGHGHGGFGGHF?<GHHGGGG?FFFFFCGGGHHGFGGGGD0=DGDGFHHHGHHGGHGFHC;CDGCBDGGGFFGGGF;B9CFFGFGGGGGGB0;FFFFFFF/EFFEFFFFFBF...@BF;B;AEAFFFAB;CFFE-;-BFF/BFF.;;@C9BDBFF999;A.AEFEFC
@M03569:457:000000000-L33K9:1:1101:17390:1822 1:N:0:TGCGAGAC+CATTGTTT
GTGCCAGCAGCCGCGGTAATACGAAGGGGGCTAGCGTTGCTCGGAATCACTGGGCGTAAAGCGCACGTAGGCGGCTTTTTAAGTCAGGGGTGAAATCTTGGAGCTCAACTCCAGAACTGCCTTTGATACTGAGAAGCTTGAGTCCGGGAGAGGTGAGTGGAACTGCGAGTGTAGAGGTGAAATTCGTAGATATTCGCAAGAACACCAGTGGCGAAGGCGGCTCACTGGCCCGGTACTGACGCTGAGGTGCG
+
CCCCCFFCFFFCGGGGGGGGGGH2FFGAGGGEHHHGGGG?GHGGG1B3B3DFGHC>EEGHH3E//>EHHHGHGGGGGHHGHGHHHHH2FCGGHHHG11???GGHG1?FGG<<<<1<0>G1F<GD=DGGGGGGHGFHHHGHHHHHH?CA-ADGGGGFGGGGGG/;FBCBCGGGGG;;CFEFFFFFFAFFFFFFFB:/:AFFFFFFFF.9BBFEFFFFFF;CAFAFFFBFAF.@-;CFFFFB;DDDFFFFAFF
@M03569:457:000000000-L33K9:1:1101:16659:1829 1:N:0:TGCGAGAC+CATTTTTG
GTGCCAGCAGCCGCGGTAATACATGTGGGGCAAGCGTTGTTCGGAATTACTGGGCATAAAGGGTGCGTAGGTGGTTTGTTAAGTCAGGGGTGAAATCCCGCGGCCCAACCGTGGAACTGCCTTTGATACTGGCGAACTTGAGTGCGTGAGGGGTAGGGGGAACGAGCAGTGTAGCGGTGAAATGCGGAGATATTGGTCGGGAGGCCAGAGCCGAAGGTTCCCTACTGGTGCGTAACTGACTCTGAGGCACG
+
A>>AA@CAFF4>2EEEAACGGGGD5BDG2EEAAFGEGGGFHGEGA1BFE5FFHHE2BB5FG3EGG?EFEEGBFCEGHGHG@4BGDBBBCEGEGGBGBBBEECCD//?GA/<?GG/DGCDBBFHF11FFFGBHHC<-@<GH0GGHFGEA.CGGGE..;.DBG.9A.A--BFFFFFB=@DBABFBB/A-;=BFFFFB/;;;9-99-...;../9;-;BD/99//9BAFBFFF;BAA.9;F/9/;BFEFEE??.
@M03569:457:000000000-L33K9:1:1101:17930:1830 1:N:0:TGCGAGAC+CATTGTTG
GTGCCAGCCGCCGCGGTAATACGTAGGGTCCGAGCGTTGTCCGGAATTATTGGGCGTAAAGGGCTCGTAGGCGGTTTGTCGCGTCGGGAGTGAAAACTTGGGGCTTAACCCCATTCGTGCTTCCGATACGGGCAGACTAGAGGCAGGCAGGGGAGAACGGAATTCCTGGTGTAGCGGTGGAATGCGCAGATATCAGGAGGAACACCGGTGGCGAAGGCGGTTCTCTGGGCCTGTTCTGACGCTGAGGAGCG
+
BABBAFFBBBBBF?EGGGGGGGHHHHGGHHHEEGEEGFGGFHEGEEFHFGHGGHHGGGGHH3EFGHGGGGGHGGGGGGHGGHGGGGGGGDGHGHHHFGHHHHGGFHHG=GHFDCGGFHGGGHHGFGCAAEGGGGGGGGGGFGGGEGGGGGGFFFFFFFDFFFFFFFFFFFFFFFB9@DFFEFFFFFBFFFFBB9/B/;AF9FFFFDFFFFFFFAAFFF--BFEFFFFFFEFFF9F/FFB99AADDFFFFED
@M03569:457:000000000-L33K9:1:1101:16638:1830 1:N:0:TGCGAGAC+CATTGTTG
GTGCCAGCAGCCGCGGTAATACATGTGGGGCAAGCGTTGTTCGGAATTACTGGGCATAAAGGGTGCGTAGGTGGTTTGTTAAGTCAGGGGTGAAATCCCGCGGCCCAACCGTGGAACTGCCTTTGATACTGGCGAACTTGAGTGCGTGAGGGGTAGGGGGAACGAGCAGTGTAGCGGTGAAATGCGTAGATATTGCTCGGAAGGCCAGAGCCGAAGGGTCCCTACTGGTGCGTAACTGACACTGAGGCACG
+
BBCCCFFCFFFBGGGGGGGGGGHGFFHHGGGGGGHGGGGGHHGGEFFHGEGGHHHHGHHHHFGHGEEFGGGHHGGGHGHHGFGHHHHHHGGGHHHHB?GFEFGGCCDHGGGGHCDGGGH1FHHG<GGG=GHHGG-CCGHHFHFGHGGGGGHGGGGGGFGGGD?EFGFFFFFFFFB@CFCFFFFFFFFFFFFFFFFB;:;;9:ADAA?EFFF:@@>FFD./;AFFFFFFFFFFEFFFFB090;BBFFE:EAA
@M03569:457:000000000-L33K9:1:1101:12813:1846 1:N:0:TGCGCGAC+CATTGTTG
GTGCCAGCAGCCGCGGTGATACGTAGGGTCCGAGCGTTGTTCGGAATTATTGGGCGTAAAGGGTTTGTAGGTGGTTTGTTTTGTCGGGAGTGAAAACTTAGGGCTTAACTCTGAGACTGCTTCCGATACGGGCGGACTAGAGGATTGGAGGGGAGCATGGAATTCCTGGTGGAGCGGTGGAATGCGTAGATATCAGGAGGAACACCAGTGGCGAAGGCGGTTATCTGGGCATTTACTGACGCTGAGATACG
+
AAAAAFFA1FFAGGGGGEGGGGGAGHGGH0BAEEGGGFGFAFFEBFFGFHHHGHHGGGGHHFG0BEEHHHH1FFF/0/0>0BFHHEE//>EHHHH1FF11B<GHHHHHG2F111>11@FGB1F1?EACGGG?---;AAGHHHB./=C.9C.AG.9..;CFFGFGB90;FFF-EFF@@F@-EFBB9B-A@FBFFF/;9BEFFFFFFF-AFFFF@?@@FF@@;--/;;FF-9F-/BBFFFF/-;;-;;///:;
@M03569:457:000000000-L33K9:1:1101:15290:1856 1:N:0:TGCGAGAC+AATTGTTG
GTGCCAGCAGCCGCGGTAATACGTAGGTGGCAAGCGTTGTCCGGAATTATTGGGCGTAAAGCGCGCGCAGGCGGTCCTTTAAGTCTGATGTGAAAGCCCACGGCTCAACCGTGGAGGGTCATTGGAAACTGGGGGATTGGAGTGAGGAGGAGGAAAGGGGATTTCAAGGTGTGGCGGTGAAAGGCGTAGAGAGGGGGAGGAACACCATGGGGGAAGGGGTTTTTTTGGTTGGAAACTGAGGCTGAGGGGGG
+
>3A>ADFA>CB>AAEGGGGGGGFGCHFHHGGFGFFEGFGGGFBEAAFGFGHFGHFEGEEGH@?>EEE>EEGECGG>DHHFFBDF2FFGGGGGFFFF0??GFCDCD/FF0<<<.<.FGGE/CGGGFBDD/GHHGGC:.=/.0;/.00.9.9.;.99/9.;-..9F;9////9/...99999///9.-;-;.9/.9.9--;9....9..//;..--.;..-.-9;A9---A..-/99//9/;.....9..---
@M03569:457:000000000-L33K9:1:1101:15281:1876 1:N:0:TGCGAGAC+CATTGTTG
GTGCCAGCAGCCGCGGTAATACGTAGGTGGCAAGCGTTGTCCGGAATTATTGGGCGTAAAGCGCGCGCAGGCGGTCCTTTAAGTCTGATGTGAAAGCCCACGGCTCAACCGTGGAGGGTCATTGGAAACTGGGGGACTTGAGTGCAGAAGAGGAAAGCGGAATTCCACGTGTAGCGGTGAAATGCGTAGAGATGTGGAGGAACACCAGTGGCGAAGGCGGCTTTCTGGTCTGTAACTGATGCTGAGGCGCG
+
BBCBBFFCFFFCGGGGGGGGGGGHHHGHHGHHHGHGGGGGHHFGEGFHGHHGHHHGGGGHHGGGGGGGGGGGGGGGGHHHGGHHHHHHHHHHHHHHGGHHGGGGGFHHGHDGHGDHGGGHHGGGHFHHHGHHHGGA@CGFEGGGFFGGFGFFFGFGFBEGGFEGF0CFFFFFFFBDFDBEFFFFBDDFFFFBFFFF00EFDF.BFDEFFFFFDDFFFFFFFFFFFFFFFBFFFFFBFFF0::BFFFFABAA
@M03569:457:000000000-L33K9:1:1101:15299:1876 1:N:0:TGCGAGAC+CATTGTTG
GTGCCAGCAGCCGCGGTAATACGTAGGTGGCAAGCGTTGTCCGGAATTATTGGGCGTAAAGCGCGCGCAGGCGGTCCTTTAAGTCTGATGTGAAAGCCCACGGCTCAACCGTGGAGGGTCATTGGAAACTGGGGGACTTGAGTGCAGAAGAGGAAAGCGGAATTCCACGTGTAGCGGTGAAATGCGTAGAGATGTGGAGGAACACCAGTGGCGAAGGCGGCTTTCTGGTCTGTAACTGATGCTGAGGCGCG
+
AABBBFFBFFFBFGEFGGGGGGHHHHGHGDFFFFGGGGGGHHEGEEFGFGHGGGHGGGGHHBEEE@EEEGGGGGGGCHHHFBGGHHHHHHHHHGGH<FAGGFGFGDHHFGDDGDAFFGGGHFHHFGHFGHHHGGGCCHFHGGGGGGGGGGBFGGGGGFEGGAGG0;F/AEEFFF/@BFFFFFFEB9DDFAFBFBFFFFEF.F.BFFFAFFFEFFAFFABFFFAF/BB/;/BFFFFFBFB//9;B/AE9B-@
@M03569:457:000000000-L33K9:1:1101:13969:1890 1:N:0:TGCGAGAC+CATTGTTG
GTGCCAGCCGCCGCGGTAATACGAAGGGGGCTAGCGTTGCTCGGAATCACTGGGCGTAAAGCGCACGTAGGCGGACTCTTAAGTCGGTGGTGAAATCCTGGAGCTCAACTCCAGAACTGCCTTCGATACTGGGAGTCTCGAGTTCGGGAGAGGTGAGTGGAACTGCGAGTGTAGAGGTGAAATTCGTAGATATTCGCAAGAACACCAGTGGCGAAGGCGGCTCACTGGCCCGATACTGACGCTGAGGTGCG
+
BBBBBFFB3ADDEEFGGGGGGGHAFFGGGGGEHHHGGGG1FHFGEGF3BEGHHHHGGGGHH3EEEGFHHHGEGGC<B?GGGFGHHDGCGGGGHHFGFFHHHBGHGFGHHG<<<GHHFGHHGHG<GHGG<GHHFHGGHH0GFGHGHGGFGGGGGF?FGGGGGG/CB0A9BFFFFF/BFFFFFFFFFFFFFFFFFB9B999BFFBFFDFFFFFFFFBFFEFFFF.BFBFF.;99;BDCBB//.;;ADFFF.BB
@M03569:457:000000000-L33K9:1:1101:15281:1894 1:N:0:TGCGAGAC+CATTGTTG
GTGCCAGCAGCCGCGGTAATACGTAGGTGGCAAGCGTTGTCCGGAATTATTGGGCGTAAAGCGCGCGCAGGCGGTCCTTTAAGTCTGATGTGAAAGCCCACGGCTCAACCGTGGAGGGTCATTGGAAACTGGGGGACTTGAGTGCAGAAGAGGAAAGCGGAATTCCACGTGTAGCGGTGAAATGCGTAGAGATGTGGAGGAACACCAGTGGCGAAGGCGGCTTTCTGGTCTGTAACTGACGCTGAGGCGCG
+
CCBCCFFBFFFCGGGGGGGGGGHHHHGHHDHHHGHDGGGGHHGGG?FGGHHGBGHGGGGHHBEGGGGGGGGGGGGGCHHHHGHHGGHGHHHHHHHHGHHGGGGGGGHHGCDGGGDHGGGHHHHGHHFHHGHBEGGFGHHHGEBFGGGGGGFGGGGGGFGGGGFGFFGFFEFFFFBC;FFFFFFBFFFDBEFFFFFFFFFFBFAFFFFFFFFFADCFDEFFFFAFFFFFFFFFFFFBFFF/.;;A.FFEFFF
@M03569:457:000000000-L33K9:1:1101:13960:1907 1:N:0:TGCGAGAC+CATTGTTG
GTGCCAGCCGCCGCGGTAATACGAAGGGGGCTAGCGTTGCTCGGAATCACTGGGCGTAAAGCGCACGTAGGCGGACTCTTAAGTCGGTGGTGAAATCCTGGAGCTCAACTCCAGAACTGCCTTCGATACTGGGAGTCTCGAGTTCGGGAGAGGTGAGTGGAACTGCGAGTGTAGAGGTGAAATTCGTAGATATTCGCAAGAACACCAGTGGCGAAGGCGGCTCACTGGCCCGATACTGACGCTGAGGTGCG
+
BBBCCFFCBBCCGGGGGGGGGGHGHGGGGGGFHHHGGGGGHHGGEGFFGFGFCGHGGGGHHHGGGGGHHHGGGGGCGHHGG@GHHGGGGGGGHHHGFGHHHHHHHGHHHGGGHHHHHHHGHHGGHFG<AGHHHHGGHHHHHGHGFGGBFGGGGGGGGGGGGGGFFGGGFFFFFFFF/FFFFFBFFFFFFFFFFFFF.AAFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00;;;ADFFFFFF
@M03569:457:000000000-L33K9:1:1101:13982:1908 1:N:0:TGCGAGAC+CATTGTTG
GTGCCAGCCGCCGCGGTAATACGAAGGGGGCTAGCGTTGCTCGGAATCACTGGGCGTAAAGCGCACGTAGGCGGACTCTTAAGTCGGTGGTGAAATCCTGGAGCTCAACTCCAGAACTGCCTTCGATACTGGGAGTCTCGAGTTCGGGAGAGGTAAGTGGAACTGCGAGTGTAGAGGTGAAATTCGTAGATATTCGCAAGAACACCAGTGGCGAAGGCGGCTCACTGGCCCGATACTGACGCTGAGGTGCG
+
BBBBBFFBBDDBGGFGGGGGGGHGFFGGGGGFGHHGGGGGHHGGGGFFGGGHHHHGGGGHHFGGGGGHHHGGGGGGGHHHHFHHHGGGGGGGHHHG?FHHHHHHHFGGHFFFGHHFHGHHHHHHHHGGDHHHHHGGGHHHGGHGHGGGAFDCFGGGGGGGGGFGGGGGGFFFFFFFFFFFBFFFFFFFFFFFFFFFADDFFFFFFFFFFFFFFFFFFFFFACFFFFFFFFFFFFFFFFF/..;;;FFFFFF
@M03569:457:000000000-L33K9:1:1101:16940:1919 1:N:0:TGCGAGAC+CATTGTTG
GTGCCAGCAGCCGCGGTAATACGAAGGGGGCTAGCGTTGTTCGGAATTACTGGGCGTAAAGCGCACGTAGGCGGACATTTAAGTCAGGGGTGAAATCCCAGAGCTCAACTCTGGAACTGCCTTTGATACTGGGTGTCTTGAGTATGGAAGAGGTGAGTGGAATTCCGAGTGTAGAGGTGAAATTCGTAGATATTCGGAGGAACACCAGTGGCGAAGGCGGCTCACTGGTCCATTACTGACGCTGAGGTGCG
+
ABBAAFFBFFFBFEEGGGGGGGGAFFGGGGGGHHEEGGGGHHGGEFFHFFGFHHHGGGGHHBEEGGEHHHGHGFGGGHHHHFGHHHHHHGDGHHHHFFGHHHHHG?FGGFFHHHHHHGHGHHHHFGGD=GHHHHGGGHHHHHHGHHHCCHHGHHHHHHHGGGFGCFFECEEGGGB0;FGGFFFGGGGGGGGGFFFF.A>FDFFFFDEFFFFFFBDFFFADBFFFFFFFFBFFFFFFFB/9:.AA.AEFFFF
@M03569:457:000000000-L33K9:1:1101:13971:1923 1:N:0:TGCGAGAC+CATTGTTG
GTGCCAGCCGCCGCGGTAATACGAAGGGTGCTAGCGTTGCTCGGAATCACTGGGCGTAAAGCGCACGTAGGCGGACTCTTAAGTCGGTGGTGAAATGCTGGAGCTCAACTCCAGATCTGCCTTCGATACTGGGAGTCTCGAGTTCGGGAGAGGTGAGTGGAACTGCGAGTGTAGAGGTGAAATTCGTAGATATTCGCAAGAACACCAGTGGCGAAGGCGGCTCACTGGCCCGATACTGAGTCTGAGGTGCG
+
BBABBFFBBBBBGGGGGGGGGGH2BFGG2FEFHHHGGGG1BGEGGGFFGGFFFGHGGGGHH3EE/EGHHHGHGG//>222BFGF2<>DGGGGHHHF2?FGH0GHHGHHHHHHBHF1FDHHH1>1..<FGGD/.<.<CD=GB.:C0.;.-;.;E:CF?BFEGFBBFBEACGGFFGBFGGFBBB:BBAFFEEFFFFFE.;ABEF9B9DEFFFFFF;BFFFAFFF.BFFFFEAEC-B>@BF///:;BBBEFF/;
@M03569:457:000000000-L33K9:1:1101:12164:1927 1:N:0:TGCGAGAC+CATTGTTG
GTGCCAGCCGCCGCGGTAAGACGGAGGATGCAAGTGTTATCCGGAATTATTGGGCGTAAAGCGTCTGTAGGTGGTTTGAAAAGTCCATGGTTAAAACTTGAAGCTTAACTTCAAAGATGCCATGGAAACTTTTAAACTTGAGTATGGTAGGGGTAAAGGGAATTTCCAGTGGAGCGGTGAAATGCGTAGATATTGGAAAGACCACCGACGGCGAAGGCACTTTACTGGGCCATTACTGTCACTACGAGACG
+
AA11>F11AA?>E00EEAFGGGE/EEGEGHFBDFGGHHGHD1AEBABGDFGGHGGGGGGHF1EE/EGHBEFHHGGGHGEFFFFHDFGGFHHHFBBFGBFF<CGFGHFFFFGFFFBGHGGGCHFHHC1FFFHHGGCFFGHG1?GGHHHGHHGGGGF0>FGGF.<CG<==GGHFGHG@CEGA:;<CBEECGGGFC00F909FBB9;EGGA--9-;9;>----;;B/BFBFE?--;FB/;F//9/:B/9:9A-;
@M03569:457:000000000-L33K9:1:1101:12185:1930 1:N:0:TGCGAGCC+GATTGTTG
GTGCCAGCAGCCGCGGTAAGACGGAGGATGCAAGTGTTATCCGGAATTATTGGGCGTAAAGAGTCTGTAGGTGGTTTGATTAGTCCATGGTTAAAACTTGAAGCTTAACTTCAAAGATGCCATGGAAACTTTTAAACTTGAGTATGGTAGGGGTAAAGGGAATTTCCAGTGGAGCGGTGAAATGCGTAGATATTGGAAAGACCACCGACGGCGAAGGCACTTTACTGGGCCATTACTGACACTAAGAGACG
+
AAAAAFFABFFAGGGGGGF11B0EE0//B101FGAADA2D2D/EEEFG1DBG1/0/>/B/D1>D1BFG2F1@@F?>GE1222@BF21BBBFEHHHHBBFGGFGHGHHHGFGFGHGHHHHFGHGHHCGHHGHHHHHHHGHHHHHHHHGHHGGGGGGHHHHGHHGHHFFGHHHHGHHCGGGEHHDDDFGGGGHHHHHHBCHGGC/;;.C@@AG@G@@@FFFF;BFFFBBFFEEFFFFFBF//;9;9/BBFFFB

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