1. INTRASPECIFIC COMPETITION Individuals in a population have same resource needs Combined demand for a resource influences its supply – leads to competition Competition affects population processes 1 : 20 5 : 20 FITNESS

2. 8 : 20 12 : 20 17 : 20

3. Characteristics of Competition Increases in density – decrease in individual fitness (growth, survivorship or fecundity) Resource/s in limiting supply All individuals inherently equal Effects of competition on an individual’s fitness density dependent Population size / density Numbers dying Numbers dying per individual Which line shows density independent mortality? If N = 100, and number dying = 15: q = 15 / 100 = 0.15 If N = 300, and number dying = 45: q = 45 / 300 = 0.15 If N = 300 and number dying = 90: q = 90 / 300 = 0.30

4. Population size / density Mortality rate I II III Numbers Dying I II III Population size / density I II III I = Independent II and III - Dependent II = under-compensating III = over-compensating Population size / density Exactly compensating

5. Population size / density Rate Birth Death K Define K Born Population size / density Numbers Dying Difference = NET Recruitment S-Shaped Growth Curves Characteristic of intra- specific competition N - Shaped K

6. Palmblad Data – Is Competition Occurring? Is there any evidence that an increase in density results in a reduction in fitness? Is there any evidence that the reduction in fitness is density dependent? Germination Mortality Reproducing

7. Competition affects QUALITY of individuals Is there any evidence that the population reaches a carrying capacity? Law of Constant Yield – Plants

8. If competition is occurring – is density dependence over-, under- or exactly compensating? How do you tell? Plot k values against (log 10 ) sowing density – if slope of the line unity, over- compensating; if = 1, exactly compensating What are k-values? k killing power – reflects stage specific mortality and can be summed K Calculated with reference to sowing density

9. Exactly - Under - Over -

10. 70 40 01200 125 50 Density (no. m -2 ) Biomass (g. m -2 ) Mean Shell Length Scutellastra cochlear Log Density K gamete output

11. 1225 m 2 365 m 2 125 m 2 Reproductive Asymmetry

12. N t = N 0.R t Exponential Growth Models built to date, constant R Not realistic, because R varies with population size due to competition How do we build a model where R varies?

13. Populations showing discrete breeding (pulse) When N t =A (very small), R = R, A = 1/R A N t+1 = N t.R t NtNt N t+1 = 1/R NtNt N t+1 NtNt 1/R Equation for a straight line: Y = mx + c Equation for a straight line: y = c + mx NtNt N t+1 = 1/R +.N t (1 – 1/R) K [] K 1 When N t = B, R = 1 B

14. Equation for a straight line: y = c + mx NtNt N t+1 = 1/R +.N t (1 – 1/R) K [] Therefore: N t+1 = N t / {(1/R) + [N t (1/R)(R-1)(1/K)]} Simplify Denominator on RHS (1/R) + [N t (1/R)(R-1)(1/K)] = (1/R) {1 + [N t (R-1)/K]} Therefore: N t+1 = N t / {(1/R)[1 + (N t.(R-1)/K)]} N t+1 = (N t R) / {1 + [N t.(R-1)/K]} N t+1 / Nt = R = R / {1 + [N t.(R-1)/K]} Simplify [1 – (1/R)] = [(R/R) – (1/R)] = (1/R)(R-1)

15. N t+1 = (N t R) / {1 + [N t.(R-1)/K]} The expression [(R-1)/K] is often written as a N t+1 = (N t R) / [1 + (N t.a)] N t+1 / Nt = R = R / {1 + [N t.(R-1)/K]} Reproductive rate not constant! Rearrange

16. Using Constant R Using Variable R Stock – Recruit Curve

17. Shape of Growth Curve depends on R and K K = 796 The higher the R, the faster the population reaches K R=1.12 The higher the K, the bigger the N for a given t AND the slower it takes to reach K for a given R

18. Model is realistic for EXACTLY compensating density-dependence N t+1 = (N t R) / [1 + (N t.a)] Is this realistic? 0.00 0.50 1.00 1.50 2.00 2.50 0.000.501.001.502.002.50 Log Density K K1:1 Under-compensating Over-compensating

19. In the absence of competition, Potential recruitment can be calculated from N t+1 = N t.R The difference between N t+1 and N t is due to net recruitment (+ or -) Actual recruitment is calculated from N t+1 = (N t R) / [1 + (N t.a)] k = log 10 (Produced) – log 10 (Surviving) k = log 10 (N t R) – log 10 {(N t R) / [1 + (N t.a)]} k = log 10 N t + log 10 R – {log 10 N t +log 10 R – log 10 (1 + aN t )} k = log 10 (1 + aN t ) = b The difference between Potential and Actual = k Substituting or Substituting N t+1 = (N t R) / {1 + [N t.(R-1)/K]} b

20. Models assume instantaneous responses of N t+1 to N t Population lags What if the amount of resources available to a population at time t (which, after all, determines the size of the population at time t+1 – through R) is determined by the size of the population at time t-1 i.e. R is dependent NOT on N t but on N t-1 N t+1 = (N t R) / [1 + (N t-1.a)] R = 2.8 Time lags promote fluctuations in population size WHY? Fluctuations common in models of DISCRETE breeding because the population still responding at the end of a time interval to the density at its start

21. R = 1.15 R = 2.8 R = 1.55 R = 2.0 R = 1.25 Magnitude of fluctuations dependent on R