Midterm review

BSC 417

Outline

• Major points• Question formats• Study tips

Major topics

• Theory and purpose of environmental modeling• Systems thinking & why it is important• Basic STELLA nomenclature & structures• Mathematical relationships– All types covered in detail

• Feedback loops, synergy• Sensitivity analysis • Case analysis

Concepts/things you should know

• Dimensional analysis and how it relates to environmental modeling – Working with units

• The basic layout (STELLA) of each behavior pattern

• Difference equations• Rate equations• Key features of examples from

homework/class discussions• Vocabulary from text

Behavior patterns• Linear growth/decay• Exponential growth/decay• Logistic growth• Overshoot and collapse• Oscillation

• Know equations, recognize patterns, know how patterns are influenced by the inputs, know steady state conditions

• Be able to cite (and describe in detail) examples for each

Linear•Rate equation: dR(t)/dt = k•Solution: R(t) = R0 + kt•K is the slope•K = sum of inflows – sum of outflows

Exponential

•Rate equation: dR(t)/dt = kR(t)•Solution: R(t) = R0 x ekt

•K = inflow rate – outflow rate

Logistic

•Rate equation: dR(t)/dt = k(t) x R(t)•Solution: R(t) = cc/(1+Ae-unconst.gr.rt x t)•K(t) = unconstrained growth rate x (1-(R(t)/cc)•Cc = carrying capacity•A = (carrying capacity – R0)/R0

Overshoot and collapse

•Rate equation (population): dP(t)/dt = ((B-(1-R(t)/R0)) x P(t)•Rate equation (resource): dR(t)/dt = -C x P(t)•P(t) = population at time = t•R(t) = resource reservoir at time = t•B = per capita birth rate in population per unit time•C = per capita consumption rate of resource per unit time•R0 = initial value in reservoir

•Solution to rate equations: depends – system of differential equations

Oscillation

•Rate equation (consumer): dC(t)/dt = G x R(t) - D•Rate equation (resource): dR(t)/dt = W – Q x C(t)•G = consumer growth rate•D = consumer deaths per unit time•W = resource growth per unit time•Q = resource consumption rate•Equilibrium oscillation for the consumer: W/Q•Equilibrium oscillation for the resource: D/G

•Solution to rate equations: depends – system of differential equations

Problem types you should be prepared to face

• Short answer• Multiple choice• Simple calculations• 1-2 questions involving application of systems

thinking to a hypothetical problem– Basic model set up and analysis

Study tips

• Straightforward assessment of your understanding of the basics of modeling– No surprises, but comprehensive

• Application of those basics to hypothetical problems

• Everything in Chapters 1-3 in text• Class notes and homework

About the exam

• In room 229, Biology• Closed book/notes• Bring a calculator• One hour, 15 minutes to complete

Questions?