Ecological Archives E093-141-A3
Jennifer C. Geib and Candace Galen. 2012. Tracing impacts of partner abundance in facultative pollination mutualisms: from individuals to populations. Ecology 93:1581–1592. http://dx.doi.org/10.1890/11-1271.1
Appendix C. ANOVA and ANCOVA tables discussed in Results testing the relationships between Bombus balteatus density and clover visitation rates, B. balteatus visits and pollination, and pollination and seed set; testing how seed set responded to pollination treatments; and testing the effects of bumble bee addition on cumulative seed germination two years after planting, the effects of bumble bee addition on cumulative germination in 2008 and 2009, and the effects of bumble bee addition on seedling survival in T. parryi and T. dasyphyllum.
Table C1. ANCOVA testing the relationship between B. balteatus density and visitation rates for (A) early-flowering plants of Trifolium dasyphyllum and T. parryi and (B) for early and late-flowering T. parryi. Bees = bee density treatment (0, 1, 2, 3 bees added); Time = time of season (early or late: before or after emergence of worker bees, respectively).
Source | Num df | Den df | F | Pr > F | |
(A) Type III tests of fixed effects: Interspecific differences | |||||
Whole model |
bees | 1 | 18 | 20.15 | 0.0003 |
bees2 | 1 | 18 | 7.66 | 0.0127 | |
species | 1 | 18 | 0.01 | 0.9361 | |
bees × species | 1 | 18 | 3.05 | 0.0977 | |
bees2 × species | 1 | 18 | 1.98 | 0.1768 | |
T. dasyphyllum |
bees | 1 | 10 | 13.24 | 0.0045 |
T. parryi |
bees | 1 | 9 | 18.69 | 0.0019 |
bees2 | 1 | 9 | 8.37 | 0.0178 | |
(B) Type III tests of fixed effects: Interseasonal differences | |||||
Whole model |
bees | 1 | 10 | 8.55 | 0.0152 |
bees2 | 1 | 10 | 3.06 | 0.1109 | |
time | 1 | 10 | 0.14 | 0.7152 | |
bees × time | 1 | 10 | 0.65 | 0.4377 | |
bees2 × time | 1 | 10 | 0.56 | 0.4712 |
Table C2. ANCOVA testing the relationship between B. balteatus visits and pollination in (A) early-flowering plants of each Trifolium species and (B) for early and late-flowering T. parryi. Time = time of season (early or late: before or after emergence of worker bees, respectively).
Source | Num df | Den df | F | Pr > F | |
(A) Type III tests of fixed effects: Interspecific differences | |||||
Whole model |
visits | 1 | 69.8 | 12.66 | 0.0007 |
species | 1 | 103.0 | 4.76 | 0.0315 | |
visits × species | 1 | 106.0 | 4.89 | 0.0291 | |
T. dasyphyllum |
visits | 1 | 42.0 | 0.50 | 0.4832 |
T. parryi | visits | 1 | 23.3 | 31.83 | <.0001 |
(B) Type III tests of fixed effects: Intraseasonal differences | |||||
Whole model |
visits | 1 | 21.3 | 0.01 | 0.9144 |
time | 1 | 15.7 | 55.74 | <.0001 | |
visits × time | 1 | 21.3 | 15.52 | 0.0007 | |
T. parryi early |
visits | 1 | 23.3 | 31.83 | <.0001 |
T. parryi late |
visits | 1 | 5.3 | 0.82 | 0.4030 |
Table C3. ANCOVA testing the relationship between pollination and seed set for (A) early-flowering plants of T. dasyphyllum and T. parryi and (B) for early and late-flowering T. parryi. Pollination = number of stylar pollen tubes, HP seed set = seed set of hand-pollinated plant near each patch; used as an index of resource limitation. Time = time of season (early or late).
Source | Num df | Den df | F | Pr > F | |
(A) Type III tests of fixed effects: Interspecies differences | |||||
Whole model |
pollination | 1 | 100.0 | 12.89 | 0.0005 |
species | 1 | 89.0 | 3.81 | 0.0541 | |
pollination × species | 1 | 101.0 | 0.51 | 0.4748 | |
HP seed set | 1 | 24.4 | 9.55 | 0.0049 | |
HP seed set × species | 1 | 59.8 | 0.64 | 0.4273 | |
(B) Type III tests of fixed effects: Intraseason differences | |||||
Whole model |
pollination | 1 | 65.3 | 1.93 | 0.1698 |
time | 1 | 22.5 | 0.16 | 0.6931 | |
pollination × time | 1 | 65.3 | 4.62 | 0.0354 | |
HP seed set | 1 | 14.6 | 18.74 | 0.0006 | |
HP seed set × time | 1 | 14.6 | 3.03 | 0.1029 | |
T. parryi early |
pollination | 1 | 44.4 | 11.20 | 0.0017 |
HP seed set | 1 | 12.7 | 4.14 | 0.0634 | |
T. parryi late |
pollination | 1 | 6.86 | 0.12 | 0.7346 |
HP seed set | 1 | 2.45 | 18.5 | 0.0345 |
Table C4. ANOVA testing how seed set responded to pollination treatments (HP, - B. balteatus, natural pollination) in T. dasyphyllum and T. parryi. HP = saturated with pollen by hand, - B. balteatus = B. balteatus queens and workers excluded from plants. Time = time of season (early or late).
Source | df | Type III SS | F | Pr > F |
pollination treatment | 2 | 1.053 | 4.50 | 0.0137 |
time | 1 | 1.976 | 16.88 | <.0001 |
species | 1 | 0.031 | 0.26 | 0.6083 |
pollination treatment × time | 2 | 1.221 | 5.21 | 0.0072 |
pollination treatment × species | 2 | 0.093 | 0.40 | 0.6733 |
time × species | 1 | 1.022 | 8.73 | 0.0040 |
pollination treatment × time × species | 2 | 0.073 | 0.31 | 0.7334 |
error | 91 | 10.652 |
Table C5. ANOVA testing the effects of bumble bee addition on cumulative seed germination two years after planting. Bees = bee density treatment (0, 1, 2, 3 bees added).
Source | df | Type III SS | F | Pr > F | |
(A) Whole model |
block | 4 | 0.201 | 3.28 | 0.0280 |
species | 1 | 0.006 | 0.38 | 0.5433 | |
bees | 3 | 0.081 | 1.77 | 0.1804 | |
species × bees | 3 | 0.092 | 2.00 | 0.1412 | |
block × species | 4 | 0.112 | 1.83 | 0.1564 | |
error | 24 | 0.368 | |||
(B) Planned contrasts |
T. parryi 0 vs. 1,2,3 | 1 | 0.951 | 62.01 | <.0001 |
T. dasyphyllum 3 vs. 0,1,2 | 1 | 0.811 | 52.89 | <.0001 |
Table C6. Repeated-measures ANOVA testing for the effects of bumble bee addition on cumulative germination in 2008 and 2009. Bees = bee density treatment (0, 1, 2, 3 bees added).
Source | df | Type III SS | F | Pr > F | |
Tests of hypotheses for between subjects effects | |||||
species | 1 | 0.092 | 2.91 | 0.0979 | |
bees | 2 | 0.194 | 2.05 | 0.1270 | |
species × bees | 2 | 0.267 | 2.81 | 0.0549 | |
error | 32 | 1.011 | |||
Tests of hypotheses for within subjects effects | |||||
time | 1 | 0.231 | 43.34 | <.0001 | |
time × species | 1 | 0.039 | 7.28 | 0.0110 | |
time × bees | 2 | 0.031 | 1.92 | 0.1464 | |
time × species × bees | 2 | 0.039 | 2.46 | 0.0807 | |
error(time) | 32 | 0.171 |
Table C7. ANOVA testing the effects of bumble bee addition on seedling survival in T. parryi and T. dasyphyllum. Bees = bee density treatment (0, 1, 2, 3 bees added).
Source | df | Type III SS | F | Pr > F |
block | 4 | 3.129 | 1.70 | 0.1838 |
species | 1 | 0.942 | 2.05 | 0.1656 |
bees | 3 | 0.372 | 0.20 | 0.9344 |
species × bees | 3 | 1.231 | 0.54 | 0.7471 |
block × species | 4 | 0.502 | 0.22 | 0.9509 |
error | 23 | 10.570 |