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

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