Populations

Population growth Nt + 1 = Nt + B – D + I – E

Population growth Nt + 1 = Nt + B – D + I – E Nt + 1 = Nt + B – D (assume no I and E)

Time: 0 Cells: 1

Time: 0 1 Cells: 1 2

Time: Cells: 1 2 4

Time: Cells:

Time: Cells:

Time: Cells:

Time: Cells:

Time: Cells:

“J” shaped or exponential growth

Exponential growth: # increase by constant factor (R or reproductive rate) each time interval

N t = N 0 R t R = 2, N 0 = 1, t = 5 N t = 1 * 2 5 = 32

Mathematical model for non- overlapping (discrete) populations

dN/dt = rN r = intrinsic rate of increase r = birth rate (b) – death rate (d) Mathematical model for overlapping populations

r > 0population will grow r = 0population won’t change r < 0population will shrink dN/dt = rN

Fig The exponential model for population growth

Fig 52.9

Fig 52.20

Fig 52.16

Cod in north Atlantic

Fig The patterns of exponential and logistic population growth

For: r=0.1K=100 if N = 10dN/dt =.1 (10) [( )/100] =.1 (10) (.9) =.9 if N = 99dN/dt =.1 (99) [( )/100] =.1 (99) (.01) =.099 dN/dt = r N [(K - N)/K]

What do I need to know about these models? ExponentialLogistic Pattern:J-shapedS-shaped Equation*:dN/dt = rN dN/dt = rN[(K-N)/K] Assumptions:-growth rate constantgrowth rate decreases with pop size -unlimited env.carrying capacity * Know what each term means and how changes in the terms affect the pattern of population growth.

Sometimes population growth is independent of density

Fig 52.18

Larch budmoth

Fig. 52.3

Fig

A Life Table Number Probability of#Offspring born Ageaged xsurvival to xto females aged x

Age group (x) NxNx bxbx lxlx lxbxlxbx Σ l x b x = Lifetime offspring per individual female