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II LABORATORY WORK
Variation and variability
Tasks – big picture; step by step
• Choose at least two populations of one type of species that you are going
to observe
– The populations must be located in different environments and potentially
isolated enough
– The number of individuas per observed population/loaclity must be minimum
• Chose the morphological characteristics you are going to observe
– Observe the variation of quantitative traits of the chosen species (at least
identify 3 quantitative traits)
– Observe the variation of qualitative traits of the chosen species (at least
identify two qualitative traits)
• Perform basic statistic analyses to see if there is any statistically significant
differences between the chosen traits in the two populations
– If there is, this tells us that that trait is different because of adaptation and
evoultion
• Discuss how and why could this be!
Morphological characteristics
• Quantitative
– Metric
– Meristic
• Qualitative
• The characteristics can be determined by
detailed observation of the chosen species
Quantitative traits
• Traits that show a certain amount of variation
and are registered in two ways:
• Metric
– You register them by counting
• Meristic
– You register them by measuring
• Quantitative (meristic) traits example:
• Number of flowers in the roseta–in one individuals
• Number of leaves in the roseta– indicates the number of leaves in the
roseta
• Number of sepale latice) – indicates the number of sepales of one flower
belonging to one individual
• Quantitative (metric) traits example:
• Lenght of the longest stem in the roseta
• Lenght of the longest leaf in the roseta
• Width of the largest leaf in the roseta
• Width of the largest flower in the roseta
Primula vulgaris
Salamandra atra
• Quantitative (meristic) traits example:
• Number of dots on the whole body in one individuals
• Number of dots on the parotid gland– blue circles on the right
picture
• Number of body ridges – only on the body not the tail
• Quantitative (metric) traits example:
• Lenght of the head (from nose till gular ridge)
• Lenght of the body (from nose tip till cloaca)
• Width of the head (between two mouth angles
• Width of the cloaca
QUALITATIVE TRAITS
QUANTITATIVE TRAITS
HABITAT DATA
Qualitative traits
• Can be only described
• Subjective
• ...Quality, How is it something?
• Variation in coloration
• Variation
• Qualitative traits example:
• Color of flowers
• Possibilities: Dark Yellow,Light yellow, Purple
• Color of leafes
• Possibilities: Dark green, Light green
• Heterostilia
• Possibilities: Yes/ No
• Hairs on the stem
• Possibilities: a lot/ small amount
Primula vulgaris
Assign numerical chategories
for each possibility of every
chosen qualitative trait!
Color of
flowers
Numerical category Possibility (variation)
1 Yellow
2 Light yellow
3 White
4 Purple
Color of leaf
Numerical
category
Possibility
(variation)
1 Dark green
2 Light green
Hairs on the stam
Numerical category Possibility (variation)
1 Very hairy
2 Slightly hairy
Heterostilia – mechanism to avoid self fertilization
Numerical category Possibility (variation)
1 Antheras are longer then stigma
2 Antheras are shorter than stigma
Picture the habitat of the chosen species
AIM of the research
• Comparative analyses of chosen morphological traits in order to see if
there is any statisticlly significance between each of them
– If there is, that can be a sgin of adaptation! Describe and discuss what kind of
adaptation!
– Find the link between the trait and adaptation
• Stems are more hairy where is colder
– It is colder on higher altitudes
• Determine the variation (variation of phenotype) of the species Primula
vulgaris according to the analysed quantitative and qualitative traits
Dependent/Indipendent variable
• Indipendent variable
– Type of habitat - Its characteristics and
environmental factors
• Sunlight, humidity, temperature, type of soil, exposition
• Dependent variable
– Chosen morphological traits that are observed
Structure of laboratory work
• parts:
1. Introduction
1. Definition of variation, variability, adaptation and evolution
2. General data regarding the chosen specie and its biology
2. Material and methods
1. Highlight the differences in habitats between the chosen
population you are observing
2. Present the types of chosen traits and their numerical
assignment (for qualitative data)
3. Pictures of measurments and habitat
4. List the needed material you used during field work
5. List statistical analysis you will perform in order to prove the
hypothesis
Structure of laboratory work
• parts:
– . Results
• .1 Present the statistical analyses in form of tables
with titles
– . Discussion
• .1 Discuss what could be the link between the
specifis trait that showed statistically significant
difference and its environment
• .2 Discuss why other triats did’t show statistically
significant variation
Structure of laboratory work
• parts:
– . Conclusion
• .1 Link all the traits that show statisticlly significanse
difference, with your conclusion why there is the
difference? Which environmental factor couses
difference and why in that particular trait?
– . Literature
• List all used resources: web-sites, books (writer, title,
year of publishing and editor)
Structure of laboratory work
• Maximum 18 pages with literature and
pictures
– Who has more, he will get minus points
– Pictures can be given in an “appendix”
• Aim: Short, clear, try to identify which data
are mandatory and which are not important
to mention!!!!!!
• Each table and every picture is numerated
and has a title
Comparative analyses of chosen morphological characteristics between
three populations of Primula vulgaris from the locality: mt IGMAN, mt
BJELAŠNICA and mt JAHORINA
Exampl e of f orm of l aborat ory work
Claim/Hypothesis: The variation in chosen
characteristics of three populations, is strictly
corelated with different strategy of adaptation
to the observed environments (3 mountains)
• Varijabilnost i varijacija (lat. varius –
različit) su termini koji se u našem
jeziku obično poistovjeduju i
međusobno i sa pojmom
promjenljivosti uopde.
• Varijabilnost (engl. variability) opisuje
sposobnost i pojavu vremenskog
(alohroničnog) mijenjanja istih živih
sistema, dok se varijacija (engl.
variation) primarno odnosi na
prostornu ili sinhroničnu nejednakost
različitih bioloških sistema
(Hadžiselimovid, 2005).
I NTRODUCTI ON
General characteristics of Primula
vulgaris
Imperium: Eukaryota Whittaker &
Margulis, 1978
Regnum: Plantae Haeckel, 1866
Subregnum: Tracheobionta
Phylum: Spermatophyta
(=Anthophyta)
Subphylum: Magnoliophytina
(=Angispermae)
Classis: Magnoliatae (=Dicotyledonae)
Subclassis: Dilleniidae
Nadred: Ericanae
Ordo: Primulales
Familia: Primulaceae Vent.
Genus: Primula L.
Species: Primula vulgaris Huds
Pri mul aceae Vent .
Familija obuhvata 18 rodova sa 255 registrovanih vrsta u
Germplasm Resources Information Network (GRIN) (United
States Department of Agriculture
Agricultural Research Service, Beltsville Area)
Pri mul a vul gari s Huds.
Kozmopolitska je biljka, rasprostranjena na
području zapadne i južne Evrope, sjeverne
Afrike i južne Azije. Spada među najranije
proljetnice o čemu govori i njeno ime - lat.
primus znači prvi, dok lat. vulgaris znači
običan, svakodnevan.
Biological
Classification
table
• Proljetni jaglac na dugačkoj čvrstoj
stabljici nosi mnogo sitnih žutih
cvjetova, sa 5 tamnih pjega u ždrijelu
vjenčida (cvijet pojedinačan, sraslih
latica i lapova).
• Ocvijede je dvostruko građeno od 5
latica i 5 lapova. Vršci latica su
rascijepani na 2 dijela. Cijev vjenčida je
produžena i valjkasta. Boja cvjeta varira,
može biti žuta, ljubičasta i bijela. Jaglac
naraste do 15 cm.
• Listovi su prizemni, cjeloviti, dužine
5 -10 cm sa kratkom lisnom drškom i
oblikuju rozetu, odozdo su gusto
dlakavi. Mladi listovi su natrag svinuti i
mrežasto naborani.
• Postoje brojni hortikulturni oblici koji se
upotrebljavaju u dekorativne svrhe.
• Jedna od karakteristika ove vrste je i
pojava heterostilije
MATERIAL AND METHODS
• Chosen localities: Bjelašnica,
Igman, Jahorina
• Number of individuals:
individua (po 35 iz svake populacije)
• Date of field work(s): .4. i 6.4.2009.
• Tools needed for field work: rooler,
scissors...par gumenih rukavica, lopata,
pinceta, linijar, papiridi za obilježavanje
individua, fotoaparat, sveska A4 formata
• Protocol for measurment and pictures:
se vrši dok su individue u svježem stanju,
tj. na licu mjesta uzorkovanja.
• Used softwares for statistical
analyses: PAST i Microsoft Office
Excel 2007
• Quantitative (meristic) traits example:
• Number of flowers in the roseta–in one individuals
• Number of leaves in the roseta– indicates the number of leaves in the
roseta
• Number of sepale latice) – indicates the number of sepales of one flower
belonging to one individual
• Quantitative (metric) traits example:
• Lenght of the longest stem in the roseta
• Lenght of the longest leaf in the roseta
• Width of the largest leaf in the roseta
• Width of the largest flower in the roseta
Primula vulgaris
• Qualitative traits example:
• Color of flowers
• Possibilities: Dark Yellow,Light yellow, Purple
• Color of leafes
• Possibilities: Dark green, Light green
• Heterostilia
• Possibilities: Yes/ No
• Hairs on the stem
• Possibilities: a lot/ small amount
Primula vulgaris
Assign numerical chategories
for each possibility of every
chosen qualitative trait!
Color of
flowers
Numerical category Possibility (variation)
1 Yellow
2 Light yellow
3 White
4 Purple
Color of leaf
Numerical
category
Possibility
(variation)
1 Dark green
2 Light green
Hairs on the stam
Numerical category Possibility (variation)
1 Very hairy
2 Slightly hairy
Heterostilia – mechanism to avoid self fertilization
Numerical category Possibility (variation)
1 Antheras are longer then stigma
2 Antheras are shorter than stigma
III. Results and discussion
• Quantitative traits
– Univariant statistics
– T test
• Qualitative traits
– Chi square analyses
• Download PAST software!
UNIVARIANTN STATISTIC ANALISES for
each quntitative trait separately of each
population
• Number of samples
• Max
• Min
• Median
• Mean
• Standard devation
– Variance
• Standard error of mean
• Mean = Aritmetička sredina
– Sum of all results divided with total number of
results
• Median
Vidiii
• Varianca (measure of variability)
– Odstupanja od aritmetičke sredine pojedinacnih
rezultata
• Primjer s prosjekom; stranica 62
– Square of variance = Standard deviation
• Standard for measuring variability
• Important for T test
Prikaz osnovnih statističkih podataka
za posmatranu osobinu : broj cvjetova
za populaciju Bjelašnice
Prikaz osnovnih statističkih podataka
za posmatranu osobinu : broj listova za
populaciju Bjelašnice
Prikaz osnovnih statističkih podataka
za posmatranu osobinu : broj latica
za populaciju Bjelašnice
% of samples results are
in the range between – to +
result (3.49 – 17.25 = big
range of variation!!! )
Add to mean
and
substract to
mean
• Standard error
– If a trait varies a lot within a population, the less samples you measure, there is higher
probability your final mean is not the actual one (as if you had measured for example 2 times
more samples
– The error is less if we increase the number of samples, but it doesn’t lower in a propotional
trend
• It lowers proportionally if we square the total number of measurments
• STANDARD ERROR
• It is higher if the standard deviation is higher
• It tells you how much is truly possible that the calculated mean is truly the actual
one
• It showes us the odstupanja of calculated aritmetic means (of each trait) from the
real, true aritmetic mean of that trait for that population
• You need it for calculating T test
Prikaz osnovnih statističkih podataka
za posmatranu osobinu : broj cvjetova
za populaciju Bjelašnice
Prikaz osnovnih statističkih podataka
za posmatranu osobinu : broj listova za
populaciju Bjelašnice
Prikaz osnovnih statističkih podataka
za posmatranu osobinu : broj latica
za populaciju Bjelašnice
% of possibility that our
calculated mean for that
trait doesn’t diverge from
the true, actual means for
that population samples
from 9.21 - 11,53
Add to mean
and
substract to
mean
Prikaz osnovnih statističkih podataka
za posmatranu osobinu : broj cvjetova
za populaciju Bjelašnice
Prikaz osnovnih statističkih podataka
za posmatranu osobinu : broj listova za
populaciju Bjelašnice
Prikaz osnovnih statističkih podataka
za posmatranu osobinu : broj latica
za populaciju Bjelašnice
Prikaz osnovnih statističkih podataka za
posmatranu osobinu : broj listova za
populaciju Igmana
Prikaz osnovnih statističkih podataka za
posmatranu osobinu : broj lapova za
populaciju Igmana
Prikaz osnovnih statističkih
podataka za posmatranu
osobinu : broj cvjetova za
populaciju Igmana
Prikaz osnovnih statističkih podataka za
posmatranu osobinu : broj cvjetova za
populaciju Jahorina
Prikaz osnovnih statističkih podataka za
posmatranu osobinu : broj listova za
populaciju Jahorina
Prikaz osnovnih statističkih
podat aka za posmat r anu osobi nu
: br oj l at i ca za popul aci j u
Jahor i na
T- TEST: TEST SLIČNOSTI I DISTANCE
(Euclidean model procjene distance i sličnosti
Matrix distance)
• The test is performed by using mean values (of all quantitative traits respectively: number of sepals,
number of leaves, number of flowers). This test is performed to see the distance between
populations (in terms of evolution). The conclusion is therefore, made by comparing means of each
trait per popualtion.
• You prove your null hypothesis in this way
– There are no statistifically significant differences between each population for the observed trait
– if p is smaller then 0.05 (meaning that the result you got could only just by chance happen in 5 cases out of 100) we
reject the null hypothesis concluding that the observed difference is statistically significant
• Degree of feedom is a korigiran number of results (confirmed) so you avoid an untrue result (N-1):
(N1-1)+(N2-2); N1 npr, number of samples in bjelasnica; N2 number of samples inIgman
• T tables: dobijeno t mora biti vece ili jednako od t vrijednosti ocitane sa tablice za vrijednost
p=0.05, da bi se razlika izmedju populacija smatrala statisticki znacajnom (showes in red using
statistical programs)
• % isto sto i 0,05 nivo statisticke znacajnosti : znaci ako postoji razlika izmedju populacija za
odredjenu kvantitativnu osobinu, t je vece ili jednako datoj vrijednosti sa tablice (pa je p manji od
.05); da ne postoji razlika, t bi bio manji od vrijednosti date u tablici (a p veci od 0,05 u tom
slucaju)...
• ako je nasa t vrijednost veca ili jednaka vrijednosti sa tablice za razinu znacajnosti 5%, onda znaci da
rezultate koje smo dobili, nismo slucajno dobili, odnosno postoji samo 5% slucajnosti da bi dobiveni
rezultati bili tek tako slucajno tu, e pa onda ne moze nikako biti da je slucajno nego fakat postoji
razlika!
Mat r i ks di st ance za posmat r anu osobi nu: br oj
l i st ova
Mat r i ks di st ance za posmat r anu osobi nu: br oj l at i ca
Komparativni prikaz distance na osnovu svih kvantitativnih osobina
KLASTER ANALIZA (Eulidean distance)
KVALITATIVNA ANALIZA – hi kvadrat test
Bjelašnica vs. Igman za boju cvjetova
Deg. Freedom: 34
• Chi^2: 18,583
• p(same): 0,98533
Bjelašnica v.s Jahorina za boju cvjetova
Deg. freedom: 33
• Chi^2: 18,083
• p(same): 0,98363
Igman v.s Jahorina za boju cvjetova
Deg. freedom: 34
• Chi^2: 18,833
• p(same): 0,98355
• p > 0,05 Odbacujemo nul hipotezu i zaključujemo da postoji razlika između
uočene i očekivane frekvencije za boju cvjetova kod Bjelašnice i Igmana,
Bjelašnice i Jahorine, Igmana i Jahorine.
Procjena frekvencija za kvalitativne osobine
Bjelašnica
Žuta
Svjetložuta
Bijela
Ljubičasta
Žuta – 48,56% (17 jedinki)
Svijetložuta – (45,71% (16 jedinki)
Bijela – nema ni jedna jedinka
Ljubičasta – 5,71% (2 jedinke)
Bjelašnica
Žuta
Svjetložuta
Bijela
Ljubičasta
Žuta – 11,43% (4 jedinke)
Svijetložuta – 80% (28 jedinki)
Bijela – 5,71% (2 jenike)
Ljubičasta – 2,86% (1 jedinka)
Igman
Jahorina
Žuta
Svjetložuta
Bijela
Ljubičasta
Žuta – 17,14% (6 jedinki)
Svijetložuta – 40% (14 jedinki)
Bijela – 34,3% (13 jedinki)
Ljubičasta – 5,71% (2 jedinke)
ANALIZA DIVERZITETA
• Indeksi raznovrsnosti (heterogenosti) objedinjuju indekse zastupljenosti
i indekse ravnomjernosti u jednu brojčanu vrijednost.
• Razvijen je veliki broj indeksa raznovrsnosti, a u radu su korišteni sljededi
indeksi:
 Simpsonov indeks raznovrsnosti
(varira između 0 i 1)
 Shannonov indeks raznovrsnosti:
zasnovan je na informacionoj teoriji i predstavlja mjeru srednjeg stepena
nesigurnosti u predviđanju kojoj vrsti slučajno odabrane individue iz
populacije pripadaju.
A – Bjelašnica, B - Igman, C - Jahorina
A B C
Taxa_S 1 1 1
Individuals 353535
Dominance_D 1 1 1
Shannon_H0 0 0
Simpson_1-D 0 0 0
Analiza Shannonov-og indeksa i Simpsonov-og indeksa
Conclusion
• Conclude accoridng to each measure and statistics the
results and link it with environment characteristics!
• Each statistic analyses has to be discussed and
interpretated!
• Which trait show the more variation?
– Why? Could it be an adaptation if you assume that that
particular population lives in a slightley different environment?
• Is it statistically significant and what does that mean?
Literatura
• Petz, B. 1997: «Osnovne statističke metode za nematematičare», naklada
IV izdanje
• Past software manual
• Izvod iz magistarskog rada: „KOMPLEKSNA ANALIZA RAZLIČITIH MODELA
• PROUČAVANJA GENETIČKE DISTANCE I NJENIH MOGUDIH FAKTORA U
STANOVNIŠTVU BIH” (Naris Pojskid, 2003)
• Izvod iz doktorske disertacije: “POLIMORFIZAM MIKROSATELITNIH
MARKERA NUKLEARNOG GENOMA U BH. POPULACIJAMA
SALMONIDA“, (Pojskid Naris, 2005)
• Izvod iz magistarskog rada: “DISTRIBUCIJA HAPLOTIPOVA
MITOHONDRIJALNE DNK I GENETIČKE OSOBENOSTI LJUDKIH POPULACIJA
U BOSNI I HERCEGOVINI” (Lejla Kapur, 2004)
• Hadžiselimovid Rifat, 2005: “Bioantropologija, diverzitet recentnog
čovjeka”. Institut za genetičko inženjerstvo i biotehnologiju, Sarajevo

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Unit 4 revision notes
 

Lab report instrukcije

  • 2. Tasks – big picture; step by step • Choose at least two populations of one type of species that you are going to observe – The populations must be located in different environments and potentially isolated enough – The number of individuas per observed population/loaclity must be minimum • Chose the morphological characteristics you are going to observe – Observe the variation of quantitative traits of the chosen species (at least identify 3 quantitative traits) – Observe the variation of qualitative traits of the chosen species (at least identify two qualitative traits) • Perform basic statistic analyses to see if there is any statistically significant differences between the chosen traits in the two populations – If there is, this tells us that that trait is different because of adaptation and evoultion • Discuss how and why could this be!
  • 3. Morphological characteristics • Quantitative – Metric – Meristic • Qualitative • The characteristics can be determined by detailed observation of the chosen species
  • 4. Quantitative traits • Traits that show a certain amount of variation and are registered in two ways: • Metric – You register them by counting • Meristic – You register them by measuring
  • 5. • Quantitative (meristic) traits example: • Number of flowers in the roseta–in one individuals • Number of leaves in the roseta– indicates the number of leaves in the roseta • Number of sepale latice) – indicates the number of sepales of one flower belonging to one individual • Quantitative (metric) traits example: • Lenght of the longest stem in the roseta • Lenght of the longest leaf in the roseta • Width of the largest leaf in the roseta • Width of the largest flower in the roseta Primula vulgaris
  • 6. Salamandra atra • Quantitative (meristic) traits example: • Number of dots on the whole body in one individuals • Number of dots on the parotid gland– blue circles on the right picture • Number of body ridges – only on the body not the tail • Quantitative (metric) traits example: • Lenght of the head (from nose till gular ridge) • Lenght of the body (from nose tip till cloaca) • Width of the head (between two mouth angles • Width of the cloaca
  • 7.
  • 9. Qualitative traits • Can be only described • Subjective • ...Quality, How is it something? • Variation in coloration • Variation
  • 10. • Qualitative traits example: • Color of flowers • Possibilities: Dark Yellow,Light yellow, Purple • Color of leafes • Possibilities: Dark green, Light green • Heterostilia • Possibilities: Yes/ No • Hairs on the stem • Possibilities: a lot/ small amount Primula vulgaris Assign numerical chategories for each possibility of every chosen qualitative trait!
  • 11. Color of flowers Numerical category Possibility (variation) 1 Yellow 2 Light yellow 3 White 4 Purple
  • 13. Hairs on the stam Numerical category Possibility (variation) 1 Very hairy 2 Slightly hairy
  • 14. Heterostilia – mechanism to avoid self fertilization Numerical category Possibility (variation) 1 Antheras are longer then stigma 2 Antheras are shorter than stigma
  • 15. Picture the habitat of the chosen species
  • 16. AIM of the research • Comparative analyses of chosen morphological traits in order to see if there is any statisticlly significance between each of them – If there is, that can be a sgin of adaptation! Describe and discuss what kind of adaptation! – Find the link between the trait and adaptation • Stems are more hairy where is colder – It is colder on higher altitudes • Determine the variation (variation of phenotype) of the species Primula vulgaris according to the analysed quantitative and qualitative traits
  • 17. Dependent/Indipendent variable • Indipendent variable – Type of habitat - Its characteristics and environmental factors • Sunlight, humidity, temperature, type of soil, exposition • Dependent variable – Chosen morphological traits that are observed
  • 18. Structure of laboratory work • parts: 1. Introduction 1. Definition of variation, variability, adaptation and evolution 2. General data regarding the chosen specie and its biology 2. Material and methods 1. Highlight the differences in habitats between the chosen population you are observing 2. Present the types of chosen traits and their numerical assignment (for qualitative data) 3. Pictures of measurments and habitat 4. List the needed material you used during field work 5. List statistical analysis you will perform in order to prove the hypothesis
  • 19. Structure of laboratory work • parts: – . Results • .1 Present the statistical analyses in form of tables with titles – . Discussion • .1 Discuss what could be the link between the specifis trait that showed statistically significant difference and its environment • .2 Discuss why other triats did’t show statistically significant variation
  • 20. Structure of laboratory work • parts: – . Conclusion • .1 Link all the traits that show statisticlly significanse difference, with your conclusion why there is the difference? Which environmental factor couses difference and why in that particular trait? – . Literature • List all used resources: web-sites, books (writer, title, year of publishing and editor)
  • 21. Structure of laboratory work • Maximum 18 pages with literature and pictures – Who has more, he will get minus points – Pictures can be given in an “appendix” • Aim: Short, clear, try to identify which data are mandatory and which are not important to mention!!!!!! • Each table and every picture is numerated and has a title
  • 22. Comparative analyses of chosen morphological characteristics between three populations of Primula vulgaris from the locality: mt IGMAN, mt BJELAŠNICA and mt JAHORINA Exampl e of f orm of l aborat ory work Claim/Hypothesis: The variation in chosen characteristics of three populations, is strictly corelated with different strategy of adaptation to the observed environments (3 mountains)
  • 23. • Varijabilnost i varijacija (lat. varius – različit) su termini koji se u našem jeziku obično poistovjeduju i međusobno i sa pojmom promjenljivosti uopde. • Varijabilnost (engl. variability) opisuje sposobnost i pojavu vremenskog (alohroničnog) mijenjanja istih živih sistema, dok se varijacija (engl. variation) primarno odnosi na prostornu ili sinhroničnu nejednakost različitih bioloških sistema (Hadžiselimovid, 2005). I NTRODUCTI ON
  • 24. General characteristics of Primula vulgaris Imperium: Eukaryota Whittaker & Margulis, 1978 Regnum: Plantae Haeckel, 1866 Subregnum: Tracheobionta Phylum: Spermatophyta (=Anthophyta) Subphylum: Magnoliophytina (=Angispermae) Classis: Magnoliatae (=Dicotyledonae) Subclassis: Dilleniidae Nadred: Ericanae Ordo: Primulales Familia: Primulaceae Vent. Genus: Primula L. Species: Primula vulgaris Huds Pri mul aceae Vent . Familija obuhvata 18 rodova sa 255 registrovanih vrsta u Germplasm Resources Information Network (GRIN) (United States Department of Agriculture Agricultural Research Service, Beltsville Area) Pri mul a vul gari s Huds. Kozmopolitska je biljka, rasprostranjena na području zapadne i južne Evrope, sjeverne Afrike i južne Azije. Spada među najranije proljetnice o čemu govori i njeno ime - lat. primus znači prvi, dok lat. vulgaris znači običan, svakodnevan. Biological Classification table
  • 25. • Proljetni jaglac na dugačkoj čvrstoj stabljici nosi mnogo sitnih žutih cvjetova, sa 5 tamnih pjega u ždrijelu vjenčida (cvijet pojedinačan, sraslih latica i lapova). • Ocvijede je dvostruko građeno od 5 latica i 5 lapova. Vršci latica su rascijepani na 2 dijela. Cijev vjenčida je produžena i valjkasta. Boja cvjeta varira, može biti žuta, ljubičasta i bijela. Jaglac naraste do 15 cm. • Listovi su prizemni, cjeloviti, dužine 5 -10 cm sa kratkom lisnom drškom i oblikuju rozetu, odozdo su gusto dlakavi. Mladi listovi su natrag svinuti i mrežasto naborani. • Postoje brojni hortikulturni oblici koji se upotrebljavaju u dekorativne svrhe. • Jedna od karakteristika ove vrste je i pojava heterostilije
  • 26. MATERIAL AND METHODS • Chosen localities: Bjelašnica, Igman, Jahorina • Number of individuals: individua (po 35 iz svake populacije) • Date of field work(s): .4. i 6.4.2009. • Tools needed for field work: rooler, scissors...par gumenih rukavica, lopata, pinceta, linijar, papiridi za obilježavanje individua, fotoaparat, sveska A4 formata • Protocol for measurment and pictures: se vrši dok su individue u svježem stanju, tj. na licu mjesta uzorkovanja. • Used softwares for statistical analyses: PAST i Microsoft Office Excel 2007
  • 27. • Quantitative (meristic) traits example: • Number of flowers in the roseta–in one individuals • Number of leaves in the roseta– indicates the number of leaves in the roseta • Number of sepale latice) – indicates the number of sepales of one flower belonging to one individual • Quantitative (metric) traits example: • Lenght of the longest stem in the roseta • Lenght of the longest leaf in the roseta • Width of the largest leaf in the roseta • Width of the largest flower in the roseta Primula vulgaris
  • 28. • Qualitative traits example: • Color of flowers • Possibilities: Dark Yellow,Light yellow, Purple • Color of leafes • Possibilities: Dark green, Light green • Heterostilia • Possibilities: Yes/ No • Hairs on the stem • Possibilities: a lot/ small amount Primula vulgaris Assign numerical chategories for each possibility of every chosen qualitative trait!
  • 29. Color of flowers Numerical category Possibility (variation) 1 Yellow 2 Light yellow 3 White 4 Purple
  • 31. Hairs on the stam Numerical category Possibility (variation) 1 Very hairy 2 Slightly hairy
  • 32. Heterostilia – mechanism to avoid self fertilization Numerical category Possibility (variation) 1 Antheras are longer then stigma 2 Antheras are shorter than stigma
  • 33. III. Results and discussion • Quantitative traits – Univariant statistics – T test • Qualitative traits – Chi square analyses • Download PAST software!
  • 34. UNIVARIANTN STATISTIC ANALISES for each quntitative trait separately of each population • Number of samples • Max • Min • Median • Mean • Standard devation – Variance • Standard error of mean
  • 35. • Mean = Aritmetička sredina – Sum of all results divided with total number of results • Median Vidiii • Varianca (measure of variability) – Odstupanja od aritmetičke sredine pojedinacnih rezultata • Primjer s prosjekom; stranica 62 – Square of variance = Standard deviation • Standard for measuring variability • Important for T test
  • 36. Prikaz osnovnih statističkih podataka za posmatranu osobinu : broj cvjetova za populaciju Bjelašnice Prikaz osnovnih statističkih podataka za posmatranu osobinu : broj listova za populaciju Bjelašnice Prikaz osnovnih statističkih podataka za posmatranu osobinu : broj latica za populaciju Bjelašnice % of samples results are in the range between – to + result (3.49 – 17.25 = big range of variation!!! ) Add to mean and substract to mean
  • 37. • Standard error – If a trait varies a lot within a population, the less samples you measure, there is higher probability your final mean is not the actual one (as if you had measured for example 2 times more samples – The error is less if we increase the number of samples, but it doesn’t lower in a propotional trend • It lowers proportionally if we square the total number of measurments • STANDARD ERROR • It is higher if the standard deviation is higher • It tells you how much is truly possible that the calculated mean is truly the actual one • It showes us the odstupanja of calculated aritmetic means (of each trait) from the real, true aritmetic mean of that trait for that population • You need it for calculating T test
  • 38. Prikaz osnovnih statističkih podataka za posmatranu osobinu : broj cvjetova za populaciju Bjelašnice Prikaz osnovnih statističkih podataka za posmatranu osobinu : broj listova za populaciju Bjelašnice Prikaz osnovnih statističkih podataka za posmatranu osobinu : broj latica za populaciju Bjelašnice % of possibility that our calculated mean for that trait doesn’t diverge from the true, actual means for that population samples from 9.21 - 11,53 Add to mean and substract to mean
  • 39. Prikaz osnovnih statističkih podataka za posmatranu osobinu : broj cvjetova za populaciju Bjelašnice Prikaz osnovnih statističkih podataka za posmatranu osobinu : broj listova za populaciju Bjelašnice Prikaz osnovnih statističkih podataka za posmatranu osobinu : broj latica za populaciju Bjelašnice
  • 40. Prikaz osnovnih statističkih podataka za posmatranu osobinu : broj listova za populaciju Igmana Prikaz osnovnih statističkih podataka za posmatranu osobinu : broj lapova za populaciju Igmana Prikaz osnovnih statističkih podataka za posmatranu osobinu : broj cvjetova za populaciju Igmana
  • 41. Prikaz osnovnih statističkih podataka za posmatranu osobinu : broj cvjetova za populaciju Jahorina Prikaz osnovnih statističkih podataka za posmatranu osobinu : broj listova za populaciju Jahorina Prikaz osnovnih statističkih podat aka za posmat r anu osobi nu : br oj l at i ca za popul aci j u Jahor i na
  • 42. T- TEST: TEST SLIČNOSTI I DISTANCE (Euclidean model procjene distance i sličnosti Matrix distance) • The test is performed by using mean values (of all quantitative traits respectively: number of sepals, number of leaves, number of flowers). This test is performed to see the distance between populations (in terms of evolution). The conclusion is therefore, made by comparing means of each trait per popualtion. • You prove your null hypothesis in this way – There are no statistifically significant differences between each population for the observed trait – if p is smaller then 0.05 (meaning that the result you got could only just by chance happen in 5 cases out of 100) we reject the null hypothesis concluding that the observed difference is statistically significant • Degree of feedom is a korigiran number of results (confirmed) so you avoid an untrue result (N-1): (N1-1)+(N2-2); N1 npr, number of samples in bjelasnica; N2 number of samples inIgman • T tables: dobijeno t mora biti vece ili jednako od t vrijednosti ocitane sa tablice za vrijednost p=0.05, da bi se razlika izmedju populacija smatrala statisticki znacajnom (showes in red using statistical programs) • % isto sto i 0,05 nivo statisticke znacajnosti : znaci ako postoji razlika izmedju populacija za odredjenu kvantitativnu osobinu, t je vece ili jednako datoj vrijednosti sa tablice (pa je p manji od .05); da ne postoji razlika, t bi bio manji od vrijednosti date u tablici (a p veci od 0,05 u tom slucaju)... • ako je nasa t vrijednost veca ili jednaka vrijednosti sa tablice za razinu znacajnosti 5%, onda znaci da rezultate koje smo dobili, nismo slucajno dobili, odnosno postoji samo 5% slucajnosti da bi dobiveni rezultati bili tek tako slucajno tu, e pa onda ne moze nikako biti da je slucajno nego fakat postoji razlika!
  • 43. Mat r i ks di st ance za posmat r anu osobi nu: br oj l i st ova Mat r i ks di st ance za posmat r anu osobi nu: br oj l at i ca
  • 44. Komparativni prikaz distance na osnovu svih kvantitativnih osobina
  • 46. KVALITATIVNA ANALIZA – hi kvadrat test Bjelašnica vs. Igman za boju cvjetova Deg. Freedom: 34 • Chi^2: 18,583 • p(same): 0,98533 Bjelašnica v.s Jahorina za boju cvjetova Deg. freedom: 33 • Chi^2: 18,083 • p(same): 0,98363
  • 47. Igman v.s Jahorina za boju cvjetova Deg. freedom: 34 • Chi^2: 18,833 • p(same): 0,98355 • p > 0,05 Odbacujemo nul hipotezu i zaključujemo da postoji razlika između uočene i očekivane frekvencije za boju cvjetova kod Bjelašnice i Igmana, Bjelašnice i Jahorine, Igmana i Jahorine.
  • 48. Procjena frekvencija za kvalitativne osobine Bjelašnica Žuta Svjetložuta Bijela Ljubičasta Žuta – 48,56% (17 jedinki) Svijetložuta – (45,71% (16 jedinki) Bijela – nema ni jedna jedinka Ljubičasta – 5,71% (2 jedinke)
  • 49. Bjelašnica Žuta Svjetložuta Bijela Ljubičasta Žuta – 11,43% (4 jedinke) Svijetložuta – 80% (28 jedinki) Bijela – 5,71% (2 jenike) Ljubičasta – 2,86% (1 jedinka) Igman
  • 50. Jahorina Žuta Svjetložuta Bijela Ljubičasta Žuta – 17,14% (6 jedinki) Svijetložuta – 40% (14 jedinki) Bijela – 34,3% (13 jedinki) Ljubičasta – 5,71% (2 jedinke)
  • 51. ANALIZA DIVERZITETA • Indeksi raznovrsnosti (heterogenosti) objedinjuju indekse zastupljenosti i indekse ravnomjernosti u jednu brojčanu vrijednost. • Razvijen je veliki broj indeksa raznovrsnosti, a u radu su korišteni sljededi indeksi:  Simpsonov indeks raznovrsnosti (varira između 0 i 1)  Shannonov indeks raznovrsnosti: zasnovan je na informacionoj teoriji i predstavlja mjeru srednjeg stepena nesigurnosti u predviđanju kojoj vrsti slučajno odabrane individue iz populacije pripadaju.
  • 52. A – Bjelašnica, B - Igman, C - Jahorina A B C Taxa_S 1 1 1 Individuals 353535 Dominance_D 1 1 1 Shannon_H0 0 0 Simpson_1-D 0 0 0 Analiza Shannonov-og indeksa i Simpsonov-og indeksa
  • 53. Conclusion • Conclude accoridng to each measure and statistics the results and link it with environment characteristics! • Each statistic analyses has to be discussed and interpretated! • Which trait show the more variation? – Why? Could it be an adaptation if you assume that that particular population lives in a slightley different environment? • Is it statistically significant and what does that mean?
  • 54. Literatura • Petz, B. 1997: «Osnovne statističke metode za nematematičare», naklada IV izdanje • Past software manual • Izvod iz magistarskog rada: „KOMPLEKSNA ANALIZA RAZLIČITIH MODELA • PROUČAVANJA GENETIČKE DISTANCE I NJENIH MOGUDIH FAKTORA U STANOVNIŠTVU BIH” (Naris Pojskid, 2003) • Izvod iz doktorske disertacije: “POLIMORFIZAM MIKROSATELITNIH MARKERA NUKLEARNOG GENOMA U BH. POPULACIJAMA SALMONIDA“, (Pojskid Naris, 2005) • Izvod iz magistarskog rada: “DISTRIBUCIJA HAPLOTIPOVA MITOHONDRIJALNE DNK I GENETIČKE OSOBENOSTI LJUDKIH POPULACIJA U BOSNI I HERCEGOVINI” (Lejla Kapur, 2004) • Hadžiselimovid Rifat, 2005: “Bioantropologija, diverzitet recentnog čovjeka”. Institut za genetičko inženjerstvo i biotehnologiju, Sarajevo

Editor's Notes

  1. Tab. 22. Prikaz osnovnih statističkih podataka za posmatranu osobinu : broj latica za populaciju Jahorina
  2. Matriks distance za posmatranu osobinu:broj listova