Ecological Archives E094-258-A4

Emily V. Moran, Sharon Bewick, Christina A. Cobbold. 2013. Effects of plant genotype and insect dispersal rate on the population dynamics of a forest pest. Ecology 94:2792–2802. http://dx.doi.org/10.1890/12-1708.1

Appendix D. Figures depicting the effects on population dynamics of stochasticity in α and r, linking two patches of the same genotype, and the variation in α or r alone; phase diagrams for the other genotype combinations; the effect of changing PET or parasitoid:host dispersal ratios; and a graph showing oscillatory dynamics when parasitoid dispersal is higher than host dispersal.

In this appendix, color-coding in the phase diagrams is the same as in the main paper.

Effect of stochasticity in α vs. r:

The analyses in the paper and above assume that there is no variation in α or r over time. However, climatic variation or other environmental factors could affect caterpillar mass and/or the relationship between mass and fecundity (thereby changing r) or caterpillar development time and/or PET (thereby changing α). Therefore, we ran several simulations to explore what happens when r and α for each year of the simulation are drawn from a normal distribution with a standard deviation equal to 5%, 10%, or 20% of the mean value of each parameter. For the 10% case, we also asked what would happen if variation in the parameters were perfectly correlated between patches (eg., r1 and r2 increase or decrease by the same amount) vs. if variation were uncorrelated. The most obvious effect of stochasticity is that the regions of steady-state dynamics are replaced by regions in which dynamics are totally asynchronous between patches. As variation in the parameters increases, these asynchronous regions expand, regardless of whether the variation is correlated or uncorrelated between patches.

FigD1

Fig. D1. Genotype 216 coupled to 259, when r and α are stochastic, with SD = 5% of parameter mean. Variation uncorrelated between patches.


 

 

FigD2

Fig. D2. Genotype 216 coupled to 259, when r and α are stochastic, with SD = 10% of parameter mean. Variation uncorrelated between patches.


 

FigD3

Fig. D3. Genotype 216 coupled to 259, when r and α are stochastic, with SD = 20% of parameter mean. Variation uncorrelated between patches.


 

FigD4

Fig. D4. Genotype 216 coupled to 259, when r and α are stochastic, with SD = 10% of parameter mean. Variation perfectly correlated between patches.


Dynamics for two coupled patches of identical genotype:

Unlike the case in which two different genotypes are coupled by dispersal, the phase diagram for two patches of the same genotype is symmetric.

 

FigD5

Fig. D5. Genotype 271 coupled to 271, assuming PET = 37 and host dispersal: parasitoid dispersal = 2:1.


Effect of heterogeneity in α vs. r:

FTC growing on different aspen genotypes differ in both developmental rate (which affects parasitoid survival via parameter α) and female pupal mass (which affects the intrinsic population growth rate r of the caterpillars). The asymmetrical phase diagrams seen in Figs. 3, S2, and S3 is the result of heterogeneity between patches in both these parameters. However, the observed pattern is similar when only one of the two parameters varies between patches.

 

FigD6

Fig. D6. Genotype 216 coupled to 259, when only α varies between patches.


 

FigD7

Fig. D7. Genotype 216 coupled to 259, when only r varies between patches.

 

Dynamics for other aspen genotype combinations:

As in the text, I indicates non-synchronized dynamics, where outbreak frequencies are different in the two patches. II indicates entrainment, where patches display identical outbreak frequencies, but those outbreaks occur at different times. III indicates synchrony, IV parasitoid synchrony only, and V host synchrony only. VI indicates non-oscillating dynamics.


 

FigD8

Fig. D8. Genotype 216 coupled to 271, assuming PET = 37 and host dispersal: parasitoid dispersal = 2:1.


 

FigD9

Fig. D9. Genotype 216 coupled to 259, assuming PET = 37 and host dispersal: parasitoid dispersal = 2:1.


 

Effect of PET:

The effect of parasitoid emergence time on the synchronization of patches is fairly subtle, causing some changes in the size and shape of the regions of synchrony and asynchrony but not the basic pattern.

 

FigD10

Fig. D10. Genotype 216 coupled to 259, assuming PET = 20 and host dispersal: parasitoid dispersal = 2:1.


 

FigD11

Fig. D11. Genotype 216 coupled to 259, assuming PET = 45 and host dispersal: parasitoid dispersal = 2:1.


 

Effect of host dispersal:parasitoid dispersal ratio assumptions:

When only host disperse, the areas of parameter space in which patches are asynchronous or in which they have the same period but different phases both increase, while there is a decrease in the area of parameter space for which populations do not fluctuate or are synchronous. When both hosts and parasitoids disperse, the period-phase diagram appears similar to those shown in the main body of the paper, whether hosts or parasitoids are better dispersers. However, as the ratio of host:parasitoid dispersal decreases, the area of synchrony increases and the area of non-oscillating population sizes decreases. When only parasitoids disperse, the period-phase diagram is quite different, with a large crescent-shaped area of synchrony.

 

FigD12

Fig. D12. Genotype 216 coupled to 259, assuming PET = 37 and parasitoid dispersal = 0


 

FigD13

Fig. D13. Genotype 216 coupled to 259, assuming PET = 37 and host dispersal: parasitoid dispersal = 1:2


 

FigD14

Fig. D14. Genotype 216 coupled to 259, assuming PET = 37 and host dispersal = 0


 

FigD15

Fig. D15. Comparison of outbreak dynamics on clones 271 (‘L’) and 259 (‘H’) in isolation vs. when patches of the two genotypes are linked by dispersal, parasitoid dispersal is twice as high as host dispersal, and the L patch is 20% the size of the H patch.

Outbreak frequency for the mixed genotype stand is higher than for either genotype alone.


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