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# exam study guide WFS 446

Penn State

GPA 3.3

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## Popular in Population Dynamics

## Popular in Wildlife Studies

This 9 page Study Guide was uploaded by Dani on Monday March 2, 2015. The Study Guide belongs to WFS 446 at Pennsylvania State University taught by David Miller in Spring2015. Since its upload, it has received 99 views. For similar materials see Population Dynamics in Wildlife Studies at Pennsylvania State University.

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Date Created: 03/02/15

Population Dynamics 11215 Population Dynamics 0 Concerned with understanding and quantifying how populations change in number and composition and the factors that influence these changes Why study population dynamics OOO Often we want to manage population abundance for a species Understanding individual populations first step towards community management Tools to make smart decisions about wildlife populations Types of applications I Harvestexploitation I Pestinvasive species management I Species conservation I Management of rareendangered species Population models 0 O O O A representation of reality that we can learn from Mathematical models I Equations to describe how population abundance and structure change across time and space Step beyond conceptual models I Quantify predictions Why do we use models I Explain how things became the way they are retrospective o What was the effect of road construction on the abundance of interior forest birds past I Predict the future and the effect of potential actions prospective o What will be the effect of increasing fishing access on the number of trout in a stream future Predicting effects of harvest 0 O O 0 How does harvest effect survival How does survival effect abundance What other factors affect abundance How does abundance effect reproduction of new individuals Harvest management model 000 N Nlt SAt SJt Pt SAt harvest rate and environment SM harvest rate and environment Pt environment 11415 I Decision making 0 Objective maintain and increase populations of arroyo toads 0 Actions protect habitat change waterflow regimes remove nonnatives I Nonnative examples fish crayfish bullfrogs I Why a population model 0 Determine the impact of nonnatives on toads 0 Determine how water affects interactions nonnatives are reliant on water I Basic steps to build a population model 0 Determine the problem 0 Determine the decision context I Objectives I Actions I Potential models 0 Collect and analyze data 0 Build a mathematical model 0 Make predictions I This class will focus on the tools to complete these five steps I Basics of population dynamics 0 Models for populations I Unstructured simplest way to describe a population 0 Description of how abundance total of individuals changes across time 0 Ex time series on lynx and hare populations changes shows lynx populations will increase at a slight lag with hare population increase I Structured add more complexityrealism 0 Age or size classes 0 Males vs females FEMALES ARE MOST IMPORTANT FOR PREDICTIONS 0 Demographic parameters included 0 Spatial distribution of populations 0 Basics of unstructured models I Exponentialgeometricgrowth o The rate of change stays constant 0 A 10 annual increase is bigger when we have 10000 individuals than when we have only 10 o No effect of density no density dependence 0 Reproduction and survival not affected by the current abundance I Density dependent growth 0 Negative effect of density 0 Logistic types growth curve Scurve o Difficult to determine carrying capacity 0 BIDE Model I Management focused on changing B I D E rates depending on needs of population I Births and immigration 0 Introducing new animals into population I Deaths and emigration 0 Number of animals leaving the population I Nt1NtBID E 0 Open population 0 Increasing abundance o BI gt DE o Decreasing abundance o BI lt DE o If movement does not occur in a population or if negligible I Nt1NtB D 0 Closed population 0 Structured models I Not all individuals are equal I Age and size dependent demography 0 Survival 0 Age of first reproduction o Fecundity I Sex specific models 0 Males often ignored I Continuous versus discrete 0 Continuous population abundance measured on a continual basis 0 Insects and invertebrates with short lifespans o Longlife span species with lots of generational overlap 0 Discrete abundance measured at intervals 0 Often annual 0 Seasonal reproduction or little overlap in generations I Stochastic versus deterministic o Deterministic variables stay constant across time o Often sufficient to ignore variation 0 Stochastic variability across time 0 Lots of sources I Environment I Small populations I Sampling error 12115 0 Measuring change in abundance o Arithmetic change y mx b I Absolute change is constant 0 Eg abundance increases by 10 individuals per year I Does not make sense for populations 0 Geometric growth discrete I Rate change is constant 0 Eg 10 increase in population size per year I Abundance measured at discrete intervals 0 Exponential growth continuous I Instantaneous rate of change continuous measurement I New individual immediately contribute to growth 0 Compound interest 0 Basic exponentialgeometric growth model 0 Density dependent I Growth rate is constant I Longterm unrealistic I Shortterm may be a good predictor o Unstructuredexponential I All individuals are the same I Age size and other characters not considered 0 Per capita growth rate I Lambda 1 population stable I Lambda gt 1 population increasing I Lambda lt 1 population decreasing o Geometric growth 0 If population continues to grow for quotTquot years 0 NT No1 A2 A3 AT NT No AT 39 A NTNo1T 0 Exponential growth 0 Instantaneous rate of change given by r I r 0 stable I r gt 0 increasing I r lt 0 decreasing o Shrink interval between observations until it approaches 0 o rN dNdt rate of change in N with respect to change int I depends on r growth rate and N abundance 0 growth period over time period T given by NT NoerT I A er I lnA r Average rate of increase 0 LnNTNo1 r Ex NT 500 N0 100 T 34 o r 0473 O Tdouble ExponentialGeometric Equations 0 Other applications I Banks and finance interest calculated using exponential equation I Physics halflife of a radioactive isotope Plotting abundance O Exponential curves on a natural scale I Linear on a log scale 0 Stable flat line 0 Decline negative slope 0 Increase positive slope I LnNT lnNo rT 0 r constant 0 lnNo intercept Plotting GeometricExponential Growth 0 O O O Abundance versus time Lnabundance versus time Change in abundance versus abundance Per capita growth rate versus abundance BIDE and Geometric growth 0 O 0 Delta N BD For geometric or exponential growth B and D are proportional to N Bt bNt and Dt dNt I b and d are constants per capita birth and death rates Nt1 N bNt dNt 9 1bdNt I R bd 39 Nt NtR Nt1 I A 1bd 1R I deltaN NtR Nt1 If birth rate greater than death rate increasing population 12615 12815 Negative Density Dependence 0 Population growth rate decreases as abundance increases 0 Carrying capacity abundance where we expect population growth to be stable 0 Denoted using K o K is I Abundance where birth rate equals death rate I Abundance where A1 or r0 o Equilibrium value population abundance will tend to move towards the carrying capacity I If NgtK the population will decrease I If NltK the population will increase 0 Logistic equations continuous o dNdt roN 1 NK 0 NT K1IltNo No er T When does population size increase fastest 0 Max population change when NK2 2215 0 Allee Effects 0 Positivedensity dependence at small population size depressed growth rates 0 Why I Predator swamping I Ability to find mates 0 When will an Allee effect lead to extinction I Small population with a negative growth rate 0 Weak allee effect I Per capita growth rate lambda does not go below 0 0 Strong allee effect I Per capita growth rate below 0 at small population sizes 2915 0 Age structured models 0 Variation in vital rates with age I Survival I Growth I Reproduction I Movement 0 Agestructure models capture this variation when making predictions 0 Survival o Conditional I Survival of individuals from age x1 to age x o Agedependentsurvival o 3 reasons why survival might vary with age 0 What do you think mortality versus age looks like for I Humans I Salmon I Sea turtle I Deer mouse 0 What are the ways these species might differ Why should they 21115 0 Age Structured Models 0 Survival I Conditional 0 Survival of individuals from age x1 to age x o Denote as SX 0 Age specific mortality mX 1Sx I Unconditional 0 Survival of individuals from age 0 to age x o Denote as lX lx 160 Si 0 Agedependent reproduction I Age at first reproduction 0 Many species do not mature in the first year 0 Reproduction is 0 until age of first reproduction I Reasons for decline with age 0 Reproductive senescence I Reasons for increase with age 0 Learning 0 Dominance better territory 0 Growth 0 Timing of measurements I Birthpulse models 0 Assumes reproduction for all animals occurs around the same time I Prebreeding or prebirthpulse model 0 Population sizes in each age class measured just before breeding I Postbreeding or postbirthpulse model 0 Population sizes in each age class measured just after breeding o Representingabundance I Total number of animals no longer sufficient O I Need to keep track of number in each age class at each time period nxt o x age 0 t timeyear o n population size I usually to only keep track of females I Usually group all individuals greater than some age together We want to predict population structure in time t1 based on the population structure in time t I If we know the agespecific survival rate we could multiply survival rate by previous age group ex age 1 to get the approximate population structure for the next year ex age 2 22515 0 Lab Review 0 0 Reproductive value how likely is an individual at any given age to contribute young to a population and how many young on average are they to contribute over their lifespan I Central idea each individual replaces itself I Percentages in matrix mean age based percentage of young contributed to the population compared with that of a one year old 0 Le 07 means this age class contributes 70 as many young as one year olds Relative value the value of having one agestage class over another I Ie an adult may be much more valuable than a new born in a species with high infant mortality Sensitivity derivative of rate of change in lambda as we change an element of the matrix model by a small amount Elasticity how changing survival changes reproduction 0 Measuring abundance O O 0 Census complete count of all individuals I Obstacles o Incomplete coverage moneytimepeople limited 0 Incomplete detection missed individuals 0 Canonical estimator of abundance 0 Population size 1proportion sampled Countprobability detected 1 C o N Probability detected Proportion sampled Index proxy for abundance Estimate statistical approach to abundance I Estimates best guess of the true value based on collected data and statistical approaches I Estimator an equation or set of equations used to generate the estimate 0 Sampling nonrandom dangerous because we introduce biases Systematic sample 0 Sample every 5th wetland 0 May work if animals random with respect to system Convenience sample 0 Sampling near roads volunteer database 0 Generally not representative of population as a whole 0 Sampling Random sampling representatives of a population as a whole unbiased LAB NOTES Simple random sample randomly choose from whole population Stratified random sample weight sample based on categories 0 Works when low variability within strata high variability among strata Cluster sampling clumps of sample units Adaptive sampling adjust based on what you are finding Many other types 0 N Abundance o N Population at Time years 0 N1938 in year 0 NM Next year 2 Nt1Nt 0 per capita growth rate Nt139Nt o absolute change in population size

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