1. Analysis of ecological data: Gr
Mule deer body cond Ag N W E σ
PSN
PEN
PAN
PWTN
PWTF G Ye
Analysis of ecological data:
"ecology isn't rocket science, it's harder”
Kate Searle
(and many other stressed out ecological modellers)
Hilborn & Ludwig The limits of applied ecological research. Ecol. Appl. 3:

2. Spatial and temporal heterogeneity
Ecological processes and systems are multi-faceted and multi-scaled, such that an understanding of any individual part of the system requires recognition of drivers and constraints resulting from many interconnected processes
Behaviour
Populations
Communities and Ecosystems
Spatial and temporal heterogeneity

3. sampling or measurement error
Moreover, states and variables within ecological systems are often not able to be measured directly, but must be inferred from surrogate observations.
It is often difficult to design experiments to adhere to standard statistical assumptions
This means that ecological data typically confound simple statistical approaches due to factors such as:
detectability
sampling or measurement error
unequal and irregular sampling effort over space and time
How do we observe the animal we are interested in?
How do we measure habitat quality for the animal?
Detectability – structural zeros, design error, observer error, animal error, naughty noughts (sampled outside habitat range) (Zuur hippo diagram) – ZIP, ZINB etc
Hierarchical models – things measured at multiple scales – show a DAG
Spatial and temporal autocorrelation, or both
Example:
Mule deer – measurement model for body fat, hierarchical, surrogate measurements for vegetation, spatial correlation within home ranges
NVC Vegetation distribution models for categorical data?

4. Most common issues encountered:
Detectability – structural zeros, design error, observer error, animal error, naughty noughts (sampled outside habitat range)
Zero-inflated models, hurdle models
multi-state mark-recapture models
Hierarchical models – states and processes are measured at multiple scales
Spatial and temporal autocorrelation, or both
Yi,t
What we measured
The “true” process
Ei,t
Hierarchical path analysis of the effect of habitat phenology on deer body condition
Seasonal abundance models for Culicoides insects

5. direct link to consumer fitness
Hierarchical path analysis of the effect of habitat phenology on deer body condition
Asynchrony in vegetation phenology
spatially and temporally asynchronous pulses of plant growth
herbivores are able to prolong the period during which they have access to forage of peak nutritional value
direct link to consumer fitness

6. PREDICTIONS: Vegetation metrics:
More asynchronous phenology = longer ‘green-up’ periods prolonged access = better winter body condition
Shorter ‘green-up’ periods = compression in the time period over = poorer body condition
Vegetation metrics:
Integrative NDVI (INDVI): productivity and biomass – correlates well with ANPP. Higher INDVI = higher body condition.
Maximal or mean slope of NDVI during green-up: fastness of greening up in the Spring – e.g., how elongated or compressed is the phenological development of plants in each individual’s home range. Elongated green-up – higher body condition.
Onset of vegetation emergence: earlier vegetation onset = higher body condition.

7. Data model for Mule deer body condition (% fat)
GPS location data, home ranges
NDVI
Climate
Data model for Mule deer body condition (% fat)

8. Body fat measurement regression equation
Path analysis diagram for how performance (percent body fat) of mule deer is affected directly and indirectly by climate and plant phenology in western Colorado. All lines in diagram represent a specific linear model.
Green-up precipitation
Elevation
Aspect
Winter precipitation
Green-up temperature
PWTN
PWPN
PSN
PEN
PAN
PNF
Path coefficients for effect of e.g., N (NDVI) on F (%FAT)
NDVI indices
PWPF
σobs1
σ proc1
PWTF
PNF
Data model:
Year
Age
PAF
Mule deer body condition
(percent fat)
PYF
Body fat measurement regression equation
Capture month
PRF
PCF
σ obs2
σ proc2
Range σ
Error (exogenous independent variables) reflecting error in measurement or process variance

9. Mean slope during vegetation green-up:
Green-up precipitation
Elevation
Aspect
Winter precipitation
Green-up temperature
0.22
(0.13,0.30)
0.21
(0.14,0.30)
-0.072
(-0.15,0.0037)
-0.26
(-0.36,-0.16)
0.12
(0.013,0.22)
Mean slope
0.049
(-0.041,0.14)
-0.10
(-0.31,0.093)
Mule deer body condition
(percent fat)
Mean slope adjusted R2: 0.28
BODY CONDITION adjusted R2: 0.62
Age
Add posterior density plot for effect of mean slope on body fat
-0.036
(-0.086,0.013)
Path analysis diagram for how performance (percent fat) of adult, female mule deer is affected directly and indirectly by climate in western Colorado in 2008,2009 and Indirect linkages are manifested through a measure of the speed of vegetation green-up in the spring derived from NDVI measurements (‘mean slope’). All lines in the diagram represent a specific linear model. Thick solid lines represent strong evidence for an effect (95% credible interval does not overlap zero). Dotted lines represent no clear effect. Regression coefficient estimates are given with 95% credible intervals. ‘+’ predicted positive relationship, ‘-‘ predicted negative relationship.

10. Seasonal abundance models for Culicoides insects
We know that the European distribution of Culicoides disease vectors is driven by climatic, host and land cover variation – how can we use phenology to better understand disease risk?
Need to understand the spatial and temporal patterns of abundance
C. obsoletus
complex
C. pulicaris
C. dewulfi

11. Orders of magnitude variation in abundance
Lots of zeros
Orders of magnitude variation in abundance
Just Use this slide as example for zero-inflated and over-dispersed data? Add harmonics model and also Adam’s triangular dist model? Multi-site model that needs to include spatial and temporal correlations.
Messy

12. 6 years of weekly trapping data from the whole of Spain
Modelling seasonal dynamics of Culiciodes spp. to generate vector abundance predictions for use in a BTV-1 spread model for the 2007 outbreak
6 years of weekly trapping data from the whole of Spain
GLMM (Poisson –log link) with overdispersion, temporal autocorrelation (AR-1) and hierarchical structure for between site differences
jth trap catch for site k (yjk) collected in week tjk:
Seasonality in population with site-specific parameters
Temporal autocorrelation
Add harmonics and triangular models here – talk about spatial (multi-site) and temporal correlations (seasonal harmonics and AR(1))
overdispersion
Influence of meteorological parameters with site specific parameters
overdispersion
Corresponding meteorological variables:

13. and g is a fixed function; there appear to be two natural choices for g:
• the triangular function g(w) = max(0, |1 − w|); or
• the density function φ(w) of a standard normal distribution.
λ : background midge abundance when not in a peak
sk : width of peak (assumed to be the same for all sites, so s1 represents the
longest peak and SK the shortest peak at each site)
mik : magnitude of the k-th longest peak at site i
pik : timing of the k-th longest peak at site i
φij : impact of time-varying covariates in modifying magnitude of the peak

14. Conclusions Multi-site spatio-temporal models
extreme events – droughts and flood
detection of long-term trends in multifaceted variable times-series (sampling methods)

15. Thank you Adam Butler (BioSS) Beth Purse (CEH)
Mindy Rice (Colorado Division of Wildlife)
Tom Hobbs (Colorado State University)
Simon Carpenter (Institute of Animal Health)