CONSERVATION BIOLOGY BSC 3052
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Additional material BSCBOS2 About averages On means averages their calculation and interdependence Several summary statistics exist for the description of samples from a distribution Most commonly known is the average or arithmetic mean Less well known are the geometric mean and the harmonic mean History Pythagoras described the different means Cantrell 20037 but they were obviously well known before by the Babylonians Calculation Pythagoras showed a geometric representation Fig 17 and the algebraic representation for two numbers 071 is a b A 7 2 G ab 1 H 7 t The relationship among the 3 means is always H g G g A which can be seen rather clearly with geometric representation With more than two values we get a set of values a1 a2 Maj an A G a b Figure 1 Phytagorean means with two values a and b one can construct the arithmetic mean A7 the geometic mean7 and the harmonic mean geometrically Page 1 Additional material BSC3052 About averages 71 A l a n i1 71 G H L i 1 H 7 221 5 The 3 means are closely related and Havil 2003 showed that G12 H 1 Examples Calculate the means from a data set that has 6 numbers drawn from a Normal distribution with mean 100 and standard deviation 10 The expectation of this distribution is the same as the arithmetric mean data 103 86 98 11186 111 a H 980606 G 986168A 991667 With many data points the difference between the means gets smaller and smaller because the distribution is symmetric Data drawn from a Gamma distribution with parameters 04 2 B 50 would look like this data 78 19 255 150 9680 a H 606324 G 870576A 113 The Gamma distribution with the parameters speci ed above has expected value of 100 But with 6 sample points we can not expect lots of accuracy The Gamma distribution is skewed and has a heavy right tail whereas the Normal distribution is symmetric Data drawn from a distribution with a very heav right tail will make the difference between the mean more amd more obvious Six points from a Gamma distribution with 04 01 and B 1000 expected value is 100 824 2 5 411 163 17 give these values H780635 G459269 A237 Reference Cantrell David W 2003 Pythagorean Means From MathWorldiA Wolfram Web Resource created by Eric W Weisstein httpmathworldwolframcomPythagoreanMeanshtml Visited 2006 last update 2003 Havil J 2003 Gamma Exploring Euler s Constant Princeton NJ Princeton University Press pp 119121 Page 2 Orchid PVA Computer lab W Western Prairie Fringed Orchid Plantanthera praeclara Family Orchidaceae Status On September 28 1989 the Western prairie fringed orchid was designated as Threat ened in the entire range Within the area covered by this listing this species is known to occur in Iowa Kansas Minnesota Mis souri North Dakota Nebraska Oklahoma Manitoba Canada Photo by George Nelson Fiysgaard pollinated probably by sphinx moths In a given year seeds can either germinate to produce a seedling stay a seed or die Seedlings either become vegetative or flowering in the next year or die New plants may grow for many years before producing flowers Background information Western prairie fringed orchid WPFO is a wetland species once locally common west of the Mississippi River in tallgrass prairie gt80 of the original prairie has been converted to agriculture or devel oped and many wetlands have been drained The WPFO is gone from 75 of counties in which it was originally docu mented A few areas are managed for WPFO protection but in most places or chids grow where there are multiple uses hay meadow nearby row crops burning draining Life history The Western prairie fringed orchid is a perennial surviving from one year to an other as an underground stem In any given year a living plant can be dormant stay underground as a stem vegetative nonflowering lt150m tall or flowering up to 12 m tall Plants can go back and forth between these three states eg flowering one year dormant the next etc or remain in a given state for several years To produce seed a flower must be Your task Take the information provided above and carry out a population viability analysis for the WPFO You should use this analy sis to 1 Describe the current state of the population growing or shrinking 2 Predict the future trend in popula tion size and time to extinction 3 Determine which stages of the or chid s life history should be tar geted for management interven tion 4 Recommend one of several man agement options based on your analysis Orchid PVA Computer lab Instructions DUE DATE IS FRIDAY MARCH 18th We use the program populus version 53 it works on macintosh linux and win dows computers and can be down loaded from httpwwwcbsumnedubooulus Draw a lifecycle diagram for the WPFO Start by listing the stages to be included in your model Draw the diagram includ ing arrows for the possible transitions between stages Now enter your diagram into Populus don t worry about transition values yet Include a drawing by hand or from Populus of your life cycle diagram in your report Briefly describe how you might collect the data you need to build your model Calculating transition values You have data available in the Table be low Use the data to determine the average probability that a vegeta tive plant observed in one year will flower in the next year Calculate the number of viable seeds produced per flowering plant etc Fill in all the transition values on your life cycle diagram in Populus and assign ini tial numbers of plants in each stage These numbers can be arbitrary Examine your projection matrix and initial stage distribution vector to make sure they include the right numbers Include the projection matrix and ini tial stage distribution vector in your report Determine current status Is the population growing or shrink ing To support your conclusion pro vide the lambda for the first year cur rent lambda ls the population at its sta ble stage distribution How can you tell Choose and provide an appropriate graph to support your answer Can you always infer the longterm behavior of a population based on only a few years of calculating lambda as N1Nt1 Why or why not Determine future status What will this population do in the future To support your conclusion provide the longterm average lambda Choose a quasiextinction threshold minimum population size you will toler ate If the population will go quasi extinct roughly how long will that take Provide a graph of total number in the population over time long enough to show extinction if it is expected to sup port your conclusion Hint you can over lay a grid on your graphs using the op tions menu at the top of the graph page Determine which lifestages should be targeted for management Calculate and report the elasticity for each stage ie for each stage in turn change all elements by 5 and calculate the elasticity Recall that elasticity is cal culated as Anew original E i Aoriginal Ti TimeW Tipriginal Tioriginal Orchid PVA Computer lab were ri is a the transition rate to stage i If there are more transitions into a state we can calculate the denominator of the elasticity value as the average For ex ample if the transition rate from stage 1 to 2 is 03 and the transition rate from stage 2 to stage 2 is 05 and we increase both values by 5 we would calculate the denominator as the average of the two transition rate ratios 105 X 03 0303 105 x 05 05052 Which stages should be the focus of management Management options There is pressure from local citizens to make use of the areas where the WPFO grows For example 1 Use the field as a hay field which means mowing each year This results in cutting leaves off of plants which decreases flowering and vegetative plant survival Allow spraying of nearby crops with insecticides to reduce agricultural pests knowing that these sprays will reduce the number of pollinating moths moths are killed by the insec ticide Drain the field which will dry out the soil and reduce seed viability and the chances of seed germination N 0 Which of the above management op tions seems least harmful to the WPFO Provide data from your analysis to back up your recommendation How might you deal with conflicts that could arise with citizens whose activi ties might have to be curtailed eg if you chose to allow spraying but not hay ing What are some possible weaknesses of the model you used for this PVA and how might they affect your con clusions What additional data or analyses might allow you to make a better rec ommendation for management of this species If you have problems with parts of this assignment please see me or email me at beerlicsitfsuedu I will stop answering questions concerning this assignment Wednesday March 17th 5pm so plan ahead Spring 2004 Nora Underwood changed in Fall 2004 and in Spring 2005 Peter Beerli Orchid PVA Computer lab Data for orchid lab The following data are from a study conducted over 5 years at 16 sites in North Dakota Sieg and King 1995 Vegetative and flowering plants were marked in 1990 and each year the status flowering vegetative dormant of each plant was recorded newly germinated plants were marked and fruits were counted In this species an average fruit produces 21618 seeds of which 53 are viable and each plant produces an av erage of 12 fruits Roughly 50 of seeds do not germinate but remain viable alive in the soil from year to year Year 1 year 2 vegetative vegetative plants plants flowering in year flowering in year 19901991 74 0 1 991 1 992 54 1 0 19921993 154 53 19931994 361 12 From the data in the study the following transition rates have been calculated Seeds to seedlings 00015 Dormant to dormant 01015 Seedlings to vegetative 00301 Dormant to flowering 00299 Seedlings to flowering 00099 Flowering to vegetative 02106 Vegetative to vegetative 02806 Flowering to dormant 06968 Vegetative to dormant 05783 Flowering to flowering 01025 Dormant to vegetative 00815 Reference Sieg CH and RM King 1995 Influence of environmental factors and preliminary demographic analysis of threatened orchid Platanthera praeclara American Midland Naturalist 1346177 What explains total diversity in a community I Keystone species can influence diversity I Equilibrium theory of island biogeography I Disturbance Productivity am iii WE into momma Wm3 my mm iii Grimm riae Many empirical studies have found a humpshaped relationship between the productivity of a system and the number of species in that system I Productivity ProductIVIty richness m 2 U OPEN a a HALFSHRUB m A SHRUE V KVFKAT MOUND o g ANT MOUND 3 A re a 25 1 E 3 Z 39G a n m Biomass I u 20 4o 50 an ion Biomass Productivity and Productivity and Biodiversity Biodiversity Habi a he erogeneiy he Habi a he erogeneiy he crease 5 competition rela ion 1ip be ween species K AWWD 39 W 39 rela ion 1ip be ween species WOdUCIWiW E begins richness and bioma varies it 3 7 richness and bioma var39es g allOWSlO E remove iess among microhabi a s among microhabi a s 39G Coa er ce E competitive 0 species 3 Species I ICompe I Ion 5 5 L l d l g motin m E E 17 Z Biomass What explains total diversity in a Habitat heterogeneity and community Biodiversity with more quot more potential niches allowing the coexistence of more I Keystone species can influence diversity SPECIES I Equilibrium theory of island biogeography In a I Disturbance g 3 I Productivity 3 I Habitat heterogeneity 3 1 E Z Habitat heterogeneity What explains total diversity in a Habitat heterogeneity and Biodiversity community hr and MacArthurmgsi I Keystone species can influence diversity I 39 foui id that the bird diversity of a g habitat increage Wit 9 I Equilibrium theory of island biogeography o gt complexity ofthe habitats 37 E I I Disturbance a E 2 039 a3 3 I Productivity rSirnilai39 relationships have been demonstrated in other taxa I Habitat heterogeneity Foliage height diversty lS biodiversity rtant for No relationship More diversity is more stable ecosystem structure and function Ec osystem function Ec osystem functio lggteecgsystems With high species diversity function Species richness Species richness Are ecosystems with high species diversity more Redundancy Idiosyncratic stable Ecosystem function Ecosystem function Species richness Species richness Do ecosystems with more species function better Empirical evidence shows that in many ecosystems there is a positive relationship between productivity and species richness But some studies show that there is either no correlation or a negative correlation Are ecosystems with more species more stable Productivity Time Are ecosystems with more species more stable Productivity Time Are ecosystems with more species more stable Productivity Time Are ecosystems with more species more stable Hypothetical relationship between productivity and species richness Ecosystems with more species should be more resistant to disturbances and will recover faster than species poor communities Variance of Prod uctivity Species richness Are ecosystems with more species more stable Hypothetical relationship between speaes richness and invasion resistance Species rich communities are less susceptible to invasion because they use more of the available resources Resource availability Resistance to invasions Species richness Species richness Du Ecusysiemswiih high species diVEYSi y mndmn beiiey 7 a um m a e 57 Du Ecusysiemswiih high SpEEiESdNEYSi y WM p 3 VunciiquE Ey7 i Expemerns in Me vaan What dame empwimi data iaii us7 5 a E mmdwmmunmeswm veisaiaiaaiveanmw medium mm quota examinedme aiaiiansnia aeween biadimrs and mm mainquot imese amiaaisammumaes m amquot isasiiiyaesivnem esiaaiis smaiiiea expenmenui Are ecosystems with more Du aaasysiamswii high saaaias aiiaisiy species more stable Vunciiun beney 7 What an the empwimi aaiaiaii 57 NW N Wm mm iaaiimiaw iaaiiiiy a mam xpaiiiiams in We Emimn NM 67 XL iai rNgihhauenMw a L iaaawaaaaax am aim mamas max 55 am a anwiiamwaxm E a mam u a g We m i a magmas was an Manamaaaaysassi maimmaaiam Mammy Are ecosystems with more Are ecosystems with more species more stable species more stable Minnesola grassiand pioi experiment Minnesola grassiand pioi experiment 2 so Bamass vaiiasiassiiaii i1 nshivhexweendmugm g u aaa yam aas iiiquot a am aiaaaaian f high species richness E 88 and viaquot a m a spaciasiiannassyiaimma g m 7 i Dmu m is as was m g maasuaaasfiaiaa Mama w i imha sssanheheigmm v I m 2 is amugmm Ham hamsss i i may Datame Shawn as means SE redvawn m Tiimansnd Dawning i994 Are ecosystems with more species more stable Minnesota grassland plot experiment resource usage ity Tilman et al I996 I997 examined the effect of species diversity on productivity and soil nutrients Resource availa Species richness Are ecosystems with more species more stable E i Minnesota grassland 1 es plot experiment 1 resource usage E 1quot r e a w 15 an s v D 0 J E Desi Plots with more species g use less nitrogen in their soil 3 ms i 3 02 1 lower resource availability g m 7 e 5 z 5 K 15 20 5 new i Dependenmufkmwulshb il wufmh almanexuev imnully immasuees numbevtrmment z noeemmwmebmym mildew m hymn masmmma m hum We ona x olio sptms Jammy on 10mm numb i s e nwowm Tilman et al 2006 nature Are ecosystems with more species more resistant to invaders 5 Species Diversity and Inwsion Resistance in a Marine Ecosystem 2 John J Smehowia Robert B Whiuamh Richard w Osman 1999 Science 2355771579 Theory pxeeieis heisysuems Lhatare mme diverse should be more resistantlo exotic species but expenme s an y decreased inmsionsuccess 2p aren y because speciesrnch mmumues more eempieueiy andef ciendy used amiable space the Limiting resource in this sysuem Declining biodiversity thus femineues mvesmh in this sysuem penenueiiy accelemung the loss ofbiodivemty and the homogenization enhe umrlds biota umuumru snh ls biodiversity important for ecosystem function I Some studies show that species rich communities are more productive but some other studies show alternative interpretation I Some studies show that species rich communities are more stable and recover from disturbances faster and are less vulnerable to invasive species I More studies are needed to allow generalizations beyond some model systems