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### ESPM-EEP%202010%20Lecture%2010

Course: EEP 115, Fall 2010
School: Berkeley
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104/EEP ESPM 115 Fall 2010: Lecture 10 1. Proportional harvesting of biomass growth model using effort variable v0: dx = f ( x ) qvx dt where catchability coefficient q&gt;0 is set to 1 through an appropriate choice of units for v. 2. Under proportional harvesting v = v results in corresponding equilibrium x solution f ( x ) vx = 0 . In this case the sustainable yield is T 1 Y =...

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104/EEP ESPM 115 Fall 2010: Lecture 10 1. Proportional harvesting of biomass growth model using effort variable v0: dx = f ( x ) qvx dt where catchability coefficient q>0 is set to 1 through an appropriate choice of units for v. 2. Under proportional harvesting v = v results in corresponding equilibrium x solution f ( x ) vx = 0 . In this case the sustainable yield is T 1 Y = lim vxdt = vx T T 0 3. Read: a. See Case 2000, p. 232242. b. See Part II Harvesting Theory Notes. c. Also see C.W. Clark 1976, 1985, and 2006 (The Worldwide Crisis in Fisheries, Cambridge University Press).
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Berkeley - EEP - 115
ESPM 104/EEP 115 Fall 2010: Lecture 11 1. GordonSchaefer Theory: exploitation of renewable resources contrasting maximum sustainable rent solutions (MSR) under sole ownership with bionomic solutions (Gordons principle: ( v , x
Berkeley - EEP - 115
1. 2.3.4.5.6.ESPM 104/EEP 115 Fall 2010: Lecture 12 Beverton and Holt Yield per recruit (cohort) analysis. a. See Case 2000, p. 232-242. b. See Part III Harvesting Theory Notes Biomass of cohort at time t is x(t)=n(t)w(t), x(0)=n0w(0) where
Berkeley - EEP - 115
ESPM 104/EEP 115 Fall 2010: Lecture 13 1. Population interactions: consider the pair of models in which the per-capita growth rate f of a species x is affected by the density of species y and the per-capita growth rate g of a species y is affecte
Berkeley - EEP - 115
ESPM 104/EEP 115 Fall 2010: Lecture 14 1. Lotka-Volterra original prey-predator model: http:/en.wikipedia.org/wiki/LotkaVolterra_equation See various texts including Case 2000. Also see http:/www.scholarpedia.org/article/Predator-prey_model x: de
Berkeley - EEP - 115
ESPM 104/EEP 115 Fall 2010: Lecture 15 1. Competition: Direct vs Indirect 2. Lotka-Volterra competion model:http:/www.utm.edu/departments/cens/biology/rirwin/441_442/LVComp.htm See various texts including Rockwood, 2006, Chapt 7 (download pages
Berkeley - EEP - 115
ESPM 104/EEP 115 Fall 2010: Lecture 16 1. SIR Models in Epidemiology: see Hastings 1996, Chapt 10 and EpiMaterial.pdf. S: susceptible E: exposed but note infectious I: infectious V: vaccinated D: dead (disease and other) R=D+V (removed individual
Berkeley - EEP - 115
ESPM 104/EEP 115 Fall 2010: Lecture 17 1. What does y = ax mean as a mapping of the real number line onto itself (also class notes)? y1 a b x1 2. What does y = Ax = mean as a mapping of y2 c d x2 the real plane onto itself (also class notes)? 3
Berkeley - EEP - 115
ESPM 104/EEP 115 Fall 2010: Lecture 20 1. Fisheries dynamics model xi(t): number of individuals aged i at time t i(t): natural mortality rate of individuals aged i at time t qi(t): catchability coefficient for individuals aged i at time t v: ef
Berkeley - EEP - 115
ESPM 104/EEP 115 Fall 2010: Lecture 21 1. Stochasticity (the influence of random processes and events). demographic: whether individuals live or die depends on the throw of a biased die, so does the size of a litter environmental: effects of th
Berkeley - EEP - 115
ESPM 104/EEP 115 Fall 2010: Lecture 22 1. Leslie matrix model with density-dependent survival of first age class x1 (t + 1) x2 (t + 1) x3 (t + 1) where s0 b1 s0 b2 = s1 ( N ) 0 0 s2 s0 b3 x1 (t ) 0 x2 (t ) s3 x3 (t ) s1 ( N , A) =1 + ( N /
Berkeley - EEP - 115
ESPM 104/EEP 115 Fall 2010: Lecture 23 1. Even-aged stand or plantation management: optimal rotation period: see Part I Harvesting Theory Notes for Faustmann Model. 2. SSG 4.4 for Marginal Value Theorem, pp. 5312, 3. SSG 4.4.,
Berkeley - EEP - 115
ESPM 104/EEP 115 Fall 2010: Lecture 24 Writing a report: Your report should contain the following elements 1. Front page: Name, date, affiliation (address, contact info) 2. Headers and footers (page numbers, running title, maybe date) 3. Summary
Berkeley - EEP - 115
ESPM 104/EEP 115 Fall 2010: Lecture 25 1. Life Cycle Graphs (A special case of state transition diagrams). These are from Caswell 20012. Lefkovitch stage-structured model (life cycle drawn on the board): bi(t): life table natality parameter for
Berkeley - EEP - 115
ESPM 104/EEP 115 Fall 2010: Lecture 26 1. Consider the model (we will focus on 2-dimension but this applies in general to n dimensions): x(t + 1) = Ax(t ) where x1 (t ) a11 a12 x(t ) = and A = x2 (t ) a21 a22 2. Suppose this has eigenvalue solu
Berkeley - EEP - 115
ESPM 104/EEP 115 Fall 2010: Lecture 27 1. Consider the 2-dimensional nonlinear system of differential equations dx1 = f1 ( x1 , x2 ) dt dx2 = f2 ( x1 , x2 ) dt f1 dx which can be written in vector notion as = fx where f = . f2 dt x1 Suppose it
Berkeley - EEP - 115
Harvesting ModelsWayne Marcus Getz Department of Environmental Science, Policy &amp; Management University of California at Berkeley, USA, wgetz@berkeley.edu Mathematical theories of harvesting biological resources can be traced back to Martin Faustmanns 184
Berkeley - EEP - 115
Berkeley - EEP - 115
Berkeley - EEP - 115
Berkeley - EEP - 115
Host-Parasite Models and Biological ControlSeptember 9, 2010IntroductionClassical biological control is the purposeful introduction and establishment of one or more natural enemies from the region of origin of an exotic pest, specically for the purpose
Berkeley - EEP - 115
LT*@|L? L_i*? Nt? |i wit*i @|h c @h| 2ki? vL!L)@4@ @| eD w?i@h *iMh@ Li4Mih .c bb.Mt|h@U| Ai wit*i L_i* t @ TLihu* |LL* ti_ |L _i|ih4?i |i hL| Lu @ TLT*@|L? @t i* @t |i @i _t|hM|L? |? @ TLT*@|L? Lih |4iW?|hL_U|L?Wklv lv wkh vhfrqg ode wkdw irfxvhv rq
Berkeley - EEP - 115
Mandelbrot SetInstructor: Wayne M. Getz Department of Environmental Science, Policy, and Management, University of California, Berkeley, CA 94720 September 7, 2010Bifurcation in discrete equationsWe have seen the bifurcation diagram for the quadratic m
Berkeley - EEP - 115
Matrix Algebra: Basic Introduction1. Matrix is a rectangular array of elements a 11 a 12 a 13 eg a 3x3 matrx A a 21 a 22 a 23 a 31 a 32 a 33 1 2. Distinguish column vector 2 from row vector 123 or 1, 2, 3 3 Often write row vector with a prime and column
Berkeley - EEP - 115
Berkeley - EEP - 115
Discussion Section Notes - Matrices Everything You Need to Know About Matrices Conceptually matrices are an extension of one-dimensional math values mapping effect(s) of multiplication multiplication condition to reduce dimension multiplication commutes m
Berkeley - EEP - 115
ARTICLE IN PRESSJournal of Theoretical Biology 264 (2010) 604612Contents lists available at ScienceDirectJournal of Theoretical Biologyjournal homepage: www.elsevier.com/locate/yjtbiHow to resolve the SLOSS debate: Lessons from species-diversity mode
Berkeley - EEP - 115
What is development about? Start from a broader view: What does it mean to say that a country develops? We might mean several things by the development process. For example, economic growth, increased capitalization, shifts away from agriculture and towar
Berkeley - EEP - 115
1Ed NotesWhat aects demand for education? How to model this? Ignore, for now, preferences. Demand for Schooling A simple model: Individuals live 2 years. In year 1, they decide whether they will go to school or work. In year 2, everyone works People wit
Berkeley - EEP - 115
School Quality Notes1School QualityReview of important elements from Du o:H If S0 6 denotes the mean schooling for 0-6 year olds in high program intensity regions,the we can measure the Program eect as beingH S = S0 6H S1217L S06L S1217This r
Berkeley - EEP - 115
1PROGRESASo far, we focused on supply-side innovations ve Who should be eected most by these? Recall our model kids go to school if (w1 w0 ) &gt; c + w0What if some people are poor and some people are rich? So, parents have income w1 or w0 ; i.e. we have
Berkeley - EEP - 115
1Population Growth &amp; the Demographic TransitionBroadly speaking, population growth rate = birth rate - death rate. Should we ex ante view high population growth rates as good or bad? Not really if, for example, birth rates are really,really high, this i
Berkeley - EEP - 115
1Migration and Rural/Urban TransitionsMuch of the developing world is characterized by a few situations: Most people live in rural areas; A large share of the labor force is employed in agriculture, often subsistence agriculture. Urban areas are charac
Berkeley - EEP - 115
1De Soto NotesChapter 3: Informal Trade: Recall Harris-Todaro: Informal sector is default outcome of unemployed urbanites. Informal businesses must operate outside the law, most are very small in scale. In particular, most have minimal capital stock. fo
Berkeley - EEP - 115
Credit 1: Overview &amp; TheoryNovember 9, 2010What do we know about Rural Credit (from Banerjee) 1): Sizeable gaps between lending rates and deposit rates within the same sub-economy lending interest rates in India 1950-1960 around 20%, deposit rate around
Berkeley - EEP - 115
Credit 2: Empirical Exercises1Do more banks mean less poverty?Can formal banks reduce poverty?Notes today are from Burgess, Robin and Rohini Pande (2004).&quot;Can Rural BanksReduce Poverty? Evidence from the Indian Social Banking Experiment&quot; The America
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Chapter 23 Weather and Climate: Notes 1. air mass a large horizontally uniform body of air with nearly the same temperature and moisture conditions. Forms when a large body of air, perhaps covering millions of square kilometers, remains over a large area
Daytona State College - PSC - 1121
Chapter 22 The Atmosphere of Earth: Notes 1. absolute humidity measurement of the amount of water vapor in the atmosphere at a particular time is called absolute humidity. 2. barometer used to measured atmospheric pressure. Invented in 1643 by Italian nam
Daytona State College - PSC - 1121
Chapter 18 Plate Tectonics: Notes 1. asthenosphere low velocity zone that is hot, elastic semiliquid layer that extends around the entire earth. Named after Greek word for weak shell. Seismic waves undergo a sharp decrease in velocity at this level. 2. co
Daytona State College - PSC - 1121
1. Achondrites Do not have the chondrules as their name implies, but have a homogeneous texture more like volcanic rocks such as basalt that cooled from molten rock. 2. asteroids Between the orbits of Mars and Jupiter is a belt or circular region of thous
Daytona State College - PSC - 1121
Chapter 14 The Universe: Notes 1. absolute magnitude Used to calculate the brightness that stats would appear to have if they were all at a defined, standard distance (32.6 light-years). The brightness of a star at this distance is called absolute magnitu
Daytona State College - PSC - 1121
waveChapter 8 Atoms and Periodic Properties Notes Key Terms: 1. atomic mass unit It is impossible to find the mass of a given atom. In order to compare the mass of one atom to another you compare the mass of any atom to the mass of an atom of a particular
Daytona State College - PSC - 1121
Chapter 3: Energy Work 3.1 Work done on the object is defined as the products of the applied force and the parallel distance through which the force acts: work = force * distance W = Fd Mechanical work is the products of a force and the distance an object
Daytona State College - PSC - 1121
Chapter 13 Nuclear Reactions: Notes 1. alpha particle Ernest rutherford studied the nature of radioactivity and found there are thee kinds, alpha, beta, and gamma radiation. known to be the nucleus of a helium atom. Two protons and two neutrons. 2. backgr
Daytona State College - PSC - 1121
Chapter 7 Light: Notes1. blackbody radiation Visible light emitted from incandescent sources at high temperatures produces electromagnetic radiation that is given off from matter at any temperature. Refers to an idealized material that prefectly absorbs
Daytona State College - PSC - 1121
Chapter 19 Building Earth's Surface: Notes1. anticline In general an arch-shaped folds is called an anticline. The most common region structures from deep plastic deformation are these arch-shaped and trough-shaped folds. Not always visible on earth's su
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Name: Enter the appropriate numbers/formulas in the shaded (gray) cells. An asterisk (*) will appear to the right of an incorrect answer. 3-1A Rite-Shop Employee No. Employee Name 711 512 624 325 422 210 111 Castro, Manny Corrales, Pat Guitar, Joseph Moor
Kaplan University - IT - 133
MonthsMonthly IncomeJanuary\$2,126February\$2,226March\$2,320April\$2,459May\$2,450June\$2,550ExpensesMortgage Car Note Electric Gas Water Cell Phone Car Insurance JC Penny Food \$825.00 \$415.00 \$56.00 \$110.00 \$32.00 \$126.00 \$198.00 \$50.00 \$125.00
Kaplan University - IT - 133
MonthsMonthly IncomeJanuary\$2,126February\$2,226March\$2,320April\$2,459May\$2,450June\$2,550ExpensesMortgage Car Note Electric Gas Water Cell Phone Car Insurance JC Penny Food Miscellaneous \$825.00 \$415.00 \$56.00 \$110.00 \$32.00 \$126.00 \$198.00
Kaplan University - AC - 122
Name: Enter the appropriate numbers/formulas in the shaded (gray) cells. An asterisk (*) will appear to the right of an incorrect answer. 2-2A Rate (a) x Hours = Minimum Weekly Wages(b)Minimum weekly wages Weekly wage regulary paid Additional weekly wag
Kaplan University - AC - 122
Name: Enter the appropriate numbers/formulas in the shaded (gray) cells. An asterisk (*) will appear to the right of an incorrect answer. 2-2A Rate (a) x Hours = Minimum Weekly Wages(b)Minimum weekly wages Weekly wage regulary paid Additional weekly wag
Kaplan University - AC - 122
Name: Enter the appropriate numbers/formulas in the shaded (gray) cells. An asterisk (*) will appear to the right of an incorrect answer.Continuing ProblemKIPLEY COMPAPAYROLL REGFOR PERIOD ENDINGJanuary 8, 20 - MARITAL STATUS NO. OF W/H ALLOW.REGULA
Kaplan University - AC - 122
Name: Enter the appropriate numbers/formulas in the shaded (gray) cells. An asterisk (*) will appear to the right of an incorrect answer. 4-8A COX SECURITY SYSTEMS PAYROLL REGISTERFOR PERIOD ENDINGDecember 24, 20 - MARITAL STATUS NO. OF W/H ALLOW.EMPLO
Kaplan University - AC - 122
Name: Enter the appropriate numbers/formulas in the shaded (gray) cells. An asterisk (*) will appear to the right of an incorrect answer.Continuing ProblemKIPLEY COMPAPAYROLL REGFOR PERIOD ENDINGJanuary 8, 20 - MARITAL STATUS NO. OF W/H ALLOW.REGULA
Kaplan University - AC - 122
Name: Enter the appropriate numbers/formulas in the shaded (gray) cells. An asterisk (*) will appear to the right of an incorrect answer. 5-2A Total payroll Less: Wages paid in excess of \$7,000 Earnings subject to FUTA and SUTA Taxable Earnings \$265,790 \$
Kaplan University - AC - 122
Name: Enter the appropriate numbers/formulas in the shaded (gray) cells. An asterisk (*) will appear to the right of an incorrect answer. 5-4A Taxable Earnings \$18,000 \$24,000 \$79,000 \$103,500 x Tax Rate 0.04 0.0265 0.029 0.008 = Tax \$720.00 \$636.00 \$2,29
Kaplan University - AC - 122
Name: Enter the appropriate numbers/formulas in the shaded (gray) cells, or select from the drop-down list. An asterisk (*) will appear to the right of an incorrect answer. 5-14A (a) M. Grady P. Monroe V. Hoffman A. Drugan G. Beiter S. Egan B. Lin Taxable