Statistics in ecology
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Statistics in Ecology. Alison Johnston British Trust for Ornithology. Spatial population trends Migrant declines Spatial abundance Massimino et al. In prep. Common bird Census. Breeding Bird Survey. Common bird Census. Breeding Bird Survey. Distance sampling & Detectability.

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Statistics in Ecology

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Statistics in Ecology

Alison Johnston

British Trust for Ornithology


Spatial population trends

Migrant declines

Spatial abundance

Massimino et al. In prep


Common bird Census

Breeding Bird Survey


Common bird Census

Breeding Bird Survey


Distance sampling & Detectability

Nuthatch Sitta europaea

Curlew Numenius arquata


ln(μij) ~ sitei + yearj


Grey partridge

Lapwing

Turtle dove

Greenfinch

Yellowhammer

Whitethroat

Skylark


Arithmetic mean

Geometric mean

Species 1: t1 = 0.5

Species 2: t2 = 2.0


Grey partridge

Lapwing

Turtle dove

Greenfinch

Yellowhammer

Whitethroat

Skylark

Geometric mean


Common bird Census

Breeding Bird Survey


Modelling bird abundance - GAMs

ln(μit) ~ land coveri+ island

+ smooth (eastingi, northingi)

+ offset (detectabilityit)

2nd run

1st run

- response variable the number detected in a 1km square

- smoothed geographical differences in abundance

- non-linear changes in land-use and abundance

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01

02

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GAMs

df» 15

df» 8

df» 3


ln(μit) ~ land coveri

+ smooth (eastingi, northingi)

+ offset (detectabilityit)


Massimino et al. In prep


Newson et al. 2011. J. ApplEcol

Johnston et al. In submission

Davey et al. 2012. Glob. Ecol. Biogeog.

Pearce-Higgins et al. 2012


GAMs – pros and cons

Flexibility

- non-linear relationships

- more biologically realistic models

Flexibility

- how much?

- overfitting

- model selection

Smooths can account for effect of variables of interest

Good for descriptive models

Require more care for explanatory models


Spatial population trends

Migrant declines

Spatial abundance

Ockendon et al. 2012 Bird Study

www.xkcd.com


Afro-Palaearctic migrants


Many UK population trends of Afro-Palaearctic migrants are declining


Breeding habitat

Bioclimatic wintering zone

Wintering habitat

Median arrival date

Trend in arrival date

Median*trend interaction

north

arid

humid

south

● woodland

× general

△ wetland

○ open


POP TREND ~ breeding habitat

+ wintering habitat

+ bioclimatic zone

+ median arrival * trend arrival

weight (1/trend.se)


POP TREND ~ breeding habitat

+ wintering habitat

+ bioclimatic zone

+ median arrival * trend arrival

weight (1/trend.se)


What’s wrong with this model?


Spatial population trends

Migrant declines

Spatial abundance

Johnston et al. In submission


Motivation

  • Baseline EU target 20% of energy from renewable sources by 2020

  • This requires substantial contribution of offshore wind

  • Internationally important seabirds breeding on UK coast

  • Seabirds long-lived species with low productivity

“For the vast majority of the birds that fly in near shore and offshore areas, very little is known.

This lack of data is of particular concern,

given the large scale of proposed offshore windfarms, and the probability of cumulative effects”

Drewitt & Langston 2006


Impact Assessment

A description of the aspects of the environment likely to be significantly affected by the proposed project including, in particular, population, fauna, flora, water...

“are likely to have a significant effect on the conservation status of European protected species”

Habitat change/loss (positive or negative)

Changes in prey or predators (positive or negative)

Disturbance causing displacement or behavioural change

Collision with structures

Additional energy cost of avoiding structures


Dogger Bank Development

Slow survey

Detectability

95% ID

Visual observations

Snapshot count

All birds seen

24% ID (13% certain)

Digital images

“are likely to have a significant effect on the conservation status of European protected species”


Black-headed gull

Razorbill

Large gull (gannet/great black-backed gull/lesser black-backed gull)

Large auk (razorbill/guillemot)

Kittiwake

Small bird (lots)

razorbills

large auks

~ f(day) + behavior + latitude + longitude

Johnston et al. In prep


Black-headed gull

Black-headed gull

Razorbill

Razorbill

Large gull (gannet/great black-backed gull/lesser black-backed gull)

Large gull (gannet/great black-backed gull/lesser black-backed gull)

Large auk (razorbill/guillemot)

Large auk (razorbill/guillemot)

Kittiwake

Kittiwake

puffin

Small bird (lots)

Small bird (lots)

fulmar

Johnston et al. In prep


Black-headed gull

Black-headed gull

Black-headed gull

Black-headed gull

Razorbill

Razorbill

Razorbill

Razorbill

great black-backed gull

gannet

great black-backed gull

lesser black-backed gull

guillemot

razorbill

guillemot

guillemot

Kittiwake

Kittiwake

Kittiwake

Kittiwake

Little auk

fulmar

puffin

kittiwake


Impact Assessment

A description of the aspects of the environment likely to be significantly affected by the proposed project including, in particular, population, fauna, flora, water...

“are likely to have a significant effect on the conservation status of European protected species”


Kittiwake

kittiwake


Kittiwake

kittiwake


3


0

1

0

1

0

0

1

0

1

0

0

0

0

0

1

0

0

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3

3

0

0

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1

0

0

0

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2


Abundance modelling

abundance ~ sea_surface_temp + depth + distance_coast + distance_colonies

+ sandeel_boats + season + season interactions + f(day)

+ correlation(lat, long) + offset(effort)


No certain seen


No certain seen

No we could have seen

x 119


No certain seen

No we could have seen

No. modelled to be in whole area


Great black-backed gull

Larusmarinus

J F M A M J J A S O N D J F M A M J J A S O N D

2010 2011


Puffin

Fraterculaarctica

J F M A M J J A S O N D J F M A M J J A S O N D

2010 2011


Assumptions

  • Certain and probable species IDs are recorded accurately

  • In boat surveys all individuals on the transect line are detected and identified

  • Boat observations do not affect the proportions of species detected

  • All stages of modelling are independent to enable accurate error propogation

Conclusions

  • Many species have a high proportion of individuals not identified

  • Randomised ‘best guesses’ can vastly improve estimates of abundance

  • Now able to estimate species-specific distributions and abundances

  • Propogation of error from all stages of the process

  • Final confidence limits account for all sources of uncertainty including uncertainty in species ID.


Spatial population trends

Migrant declines

Spatial abundance

www.xkcd.com


"the sexy job in the next 10 years will be statisticians.”

Google's Chief Economist , 2009


Razorbill

Black-headed gull

lesser black-backed gull

Kittiwake

guillemot

kittiwake


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