Populations: Regulation Ruesink Lecture 5 Biology 356

Three basic forms of population dynamics Density independent –Continuous reproduction: Exponential equation –Discrete reproduction: Geometric equation Density dependent –Logistic equation

Figure 14.5 Exponential

Figure 14.6 Geometric and exponential equations are roughly interchangeable because r = ln( )

Exponential or geometric population growth Density-independent ( does not change with population size) Resources (light, prey, enemy-free space) not limiting Time Number

Figure 14.17

Logistic population growth Density-dependent (population growth depends on population size) Resources (light, prey, enemy-free space) are limiting, regulating population around K (carrying capacity) Time Number K

Logistic population growth dN/dt = r N (1 – N/K) Slow growth at low N Slow growth near K Time Number K

Simple dynamics of DI and DD populations Time series –Number of individuals (N) at each time t Population rate of change –dN/dt = N t+1 -N t Per capita rate of change –dN/dt/N = (N t+1 -N t )/N t

Geometric increase TimeNdN/dtdN/dt/N

Geometric increase TimeNdN/dtdN/dt/N = 33/20 = = 44/23=

Geometric increase TimeNdN/dtdN/dt/N = 33/20 = = 44/23= /27= /31= /66=

Geometric increase TimeNdN/dtdN/dt/N = 33/20 = = 44/23= /27= /31= /66= Accelerating population increase Constant per capita increase

Time Density (N) Population abundance (N) dN/dt dN/dt/N

Time Density (N) Population abundance (N) dN/dt dN/dt/N

Logistic TimeNdN/dtdN/dt/N

Logistic TimeNdN/dtdN/dt/N 058-5=33/5= =44/8=

Logistic TimeNdN/dtdN/dt/N 058-5=33/5= =44/8= /12= /18= /27= /38= /50=

Logistic TimeNdN/dtdN/dt/N 058-5=33/5= =44/8= /12= /18= /27= /38= /50= Highest population increase at intermediate densities Declining per capita contribution

Time Density (N) Population abundance (N) dN/dt dN/dt/N

How to recognize density dependence Manipulate density of an organism Record individual performance across a range of densities

Figure 14.19

Figure 14.20b, c Density dependence in sparrows

In class assignment Work in groups of ~4 Fill out separate workseets Use the definitions and equations on your handout Link demography, life tables, geometric and logistic population growth, population projection, and conservation

In class assignment r = exponential rate of population growth R0 = net reproductive rate ra = exponential rate of population growth estimated from life tables r0 = intrinsic rate, can be modified by DD