Population dynamics of Apis mellifera -

Population dynamics of Apis mellifera - an application of N-Mixture Models Adam Schneider State University of New York at Geneseo Eco-Informatics Summer Institute 2016

Apis mellifera 2015 Lookout Outcrop plant-pollinator network Apis mellifera Eriophyllum lanatum Gilia capitata Rumex acetosella 1

Research Question #1: How is the Apis mellifera population distributed spatially in the meadows and how is the population changing over time? Research Question #2: How is meadow fragmentation affecting the abundance of Apis mellifera in the meadows? 4

Field Methods - Exhaustive flower survey - 15 minute interaction watch per plot Lookout Main 5 4 3 2 1 6 7 8 9 10 3 Complexes 4 Meadows per Complex R = 120 plots T = 5 watches 2

Field Methods Lookout Main - 15 minute interaction watch per plot - Interaction count = Pollinator visit PLOT Watch 1 Watch 2 Watch 3 Watch 4 Watch 5 1 0 10 9 6 1 2 0 3 1 0 0 3 8 0 0 0 0 4 2 0 0 0 0 5 2 1 1 1 0 6 1 4 0 0 0 7 1 9 3 0 1 8 2 2 0 0 0 9 6 6 6 1 0 10 4 2 6 0 1 3

Generalized N-mixture model Hierarchical Model: State Model: N i ~ Negative Binomial(λ i, α) Observation Model: y i t ~ Binomial(N i, p i ) Covariates: log(λ i ) = 0 + 1 x i,1 logit(p i ) = β 0 + β 1 x i,1 + + β T x i,t Open Population: Survivors: S i,t N i,t 1 ~ Binomial( N i,t 1, ω ) Recruits: G i,t N i,t 1 ~ Binomial γ N i,t 1 5

Generalized N-mixture model Hierarchical Model: State Model: N i ~ Negative Binomial(λ i, α) Observation Model: y i t ~ Binomial(N i, p i ) Covariates: Open Population: log(λ i ) = 0 + 1 x i,1 logit(p i ) = β 0 + β 1 x i,1 + + β T x i,t Survivors: S i,t N i,t 1 ~ Binomial( N i,t 1, ω ) Recruits: G i,t N i,t 1 ~ Binomial γ N i,t 1 Population Estimate: N 1 = R λ N t = ω N t 1 + R γ 5

Model Selection Observational Covariates (OC): Total Flower Abundance (FLOW) Gilia Abundance (GIL) Eriophyllum Abundance (ERIO) Site Covariates (SC): Meadow (MEAD) AIC = 2 (# of Parameters) 2 ln L ln(l) = Log Likelihood of Model 2012 MODEL # Parameters AIC SCORE OC = ERIO & GIL 7 2487.6 OC = GIL 6 2507.85 OC = FLOW 6 2876.79 SC = MEAD 16 2954.02 NULL_DIST = NB 5 3030.76 OC = ERIO 6 3960.56 NULL_DIST = POIS 4 4578.44 6

Population Count RQ #1 Results: How is the interacting Apis mellifera population in the HJ Andrews Forest changing over time? 3500 3000 2011 2012 2013 2014 2015 Interaction Count 2500 2000 2012 Estimated Population 1500 1000 500 0 0 1 2 3 4 5 1 2 3 4 10 5 1 2 3 4 15 5 1 2 3 4 20 5 1 2 3 4 25 5 YEAR 7

Estimated Apis Population RQ #2 Results: How is meadow fragmentation affecting the abundance of Apis mellifera in the meadows? 300 250 R² = 0.5102 300 250 - LS, LO, M2, RP1, RP2 High Apis mellifera abundance - Low Apis mellifera abundance R² = 0.4473 200 200 150 150 100 R² = 0.6115 100 R² = 0.2302 50 50 0 2.5 3.5 4.5 5.5 Distance to Meadows (km) 0 0 0.01 0.02 0.03 0.04 MPI (at 1000 m) 8

Conclusions and Further Research 1. Interaction counts are an appropriate approximation for interacting population 2. Habitat fragmentation and loss of meadow habitat will have a negative effect on Apis mellifera 3. What contributes to the two distinct meadow groups? 4. Year-to-Year model with sub-watches would be very informative 9

Thank You, for all the Help and Support! Rebecca Hutchinson Julia Jones Kate Jones Andy Moldenke EISI PP TEAM and ( Dan & the RT ) Photo Credits: Slide 1 Carolyn Slide 2 http://entnemdept.ufl.edu/creatures/misc/bees/euro_honey_bee.htm Slide 3 Eddie Helderop Slide 4 Carolyn Slide 5 Carolyn & Emily 10

Population Parameters 2011 2012 2013 2014 2015 Mean λ 19.74 9.15 27.91 30.88 12.68 Dispersion α 0.19 0.21 0.21 0.38 0.56 Recruitment γ 1.27 4.78 0.63 0.82 0.87 Survival ω 0.98 0.45 0.80 0.52 0.19 11