Presentation on theme: "Analysis of ecological data:"— Presentation transcript:
1 Analysis of ecological data: GrMule deer body condAgNWEσPSNPENPANPWTNPWTFGYeAnalysis 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 processesBehaviourPopulationsCommunities and EcosystemsSpatial 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 assumptionsThis means that ecological data typically confound simple statistical approaches due to factors such as:detectabilitysampling or measurement errorunequal and irregular sampling effort over space and timeHow 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 etcHierarchical models – things measured at multiple scales – show a DAGSpatial and temporal autocorrelation, or bothExample:Mule deer – measurement model for body fat, hierarchical, surrogate measurements for vegetation, spatial correlation within home rangesNVC 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 modelsmulti-state mark-recapture modelsHierarchical models – states and processes are measured at multiple scalesSpatial and temporal autocorrelation, or bothYi,tWhat we measuredThe “true” processEi,tHierarchical path analysis of the effect of habitat phenology on deer body conditionSeasonal abundance models for Culicoides insects
5 direct link to consumer fitness Hierarchical path analysis of the effect of habitat phenology on deer body conditionAsynchrony in vegetation phenologyspatially and temporally asynchronous pulses of plant growthherbivores are able to prolong the period during which they have access to forage of peak nutritional valuedirect link to consumer fitness
6 PREDICTIONS: Vegetation metrics: More asynchronous phenology = longer ‘green-up’ periods prolonged access = better winter body conditionShorter ‘green-up’ periods = compression in the time period over = poorer body conditionVegetation 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 rangesNDVIClimateData 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 precipitationElevationAspectWinter precipitationGreen-up temperaturePWTNPWPNPSNPENPANPNFPath coefficients for effect of e.g., N (NDVI) on F (%FAT)NDVI indicesPWPFσobs1σ proc1PWTFPNFData model:YearAgePAFMule deer body condition(percent fat)PYFBody fat measurement regression equationCapture monthPRFPCFσ obs2σ proc2RangeσError (exogenous independent variables) reflecting error in measurement or process variance
9 Mean slope during vegetation green-up: Green-up precipitationElevationAspectWinter precipitationGreen-up temperature0.22(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 slope0.049(-0.041,0.14)-0.10(-0.31,0.093)Mule deer body condition(percent fat)Mean slope adjusted R2: 0.28BODY CONDITION adjusted R2: 0.62AgeAdd 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 abundanceC. obsoletuscomplexC. pulicarisC. dewulfi
11 Orders of magnitude variation in abundance Lots of zerosOrders of magnitude variation in abundanceJust 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 outbreak6 years of weekly trapping data from the whole of SpainGLMM (Poisson –log link) with overdispersion, temporal autocorrelation (AR-1) and hierarchical structure for between site differencesjth trap catch for site k (yjk) collected in week tjk:Seasonality in population with site-specific parametersTemporal autocorrelationAdd harmonics and triangular models here – talk about spatial (multi-site) and temporal correlations (seasonal harmonics and AR(1))overdispersionInfluence of meteorological parameters with site specific parametersoverdispersionCorresponding 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 peaksk : width of peak (assumed to be the same for all sites, so s1 represents thelongest peak and SK the shortest peak at each site)mik : magnitude of the k-th longest peak at site ipik : timing of the k-th longest peak at site iφij : impact of time-varying covariates in modifying magnitude of the peak
14 Conclusions Multi-site spatio-temporal models extreme events – droughts and flooddetection 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)