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

Statistics in Ecology

Alison Johnston

British Trust for Ornithology


Statistics in ecology

Spatial population trends

Migrant declines

Spatial abundance

Massimino et al. In prep


Statistics in ecology

Common bird Census

Breeding Bird Survey


Statistics in ecology

Common bird Census

Breeding Bird Survey


Distance sampling detectability

Distance sampling & Detectability

Nuthatch Sitta europaea

Curlew Numenius arquata


Statistics in ecology

ln(μij) ~ sitei + yearj


Statistics in ecology

Grey partridge

Lapwing

Turtle dove

Greenfinch

Yellowhammer

Whitethroat

Skylark


Statistics in ecology

Arithmetic mean

Geometric mean

Species 1: t1 = 0.5

Species 2: t2 = 2.0


Statistics in ecology

Grey partridge

Lapwing

Turtle dove

Greenfinch

Yellowhammer

Whitethroat

Skylark

Geometric mean


Statistics in ecology

Common bird Census

Breeding Bird Survey


Statistics in ecology

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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Statistics in ecology

GAMs

df» 15

df» 8

df» 3


Statistics in ecology

ln(μit) ~ land coveri

+ smooth (eastingi, northingi)

+ offset (detectabilityit)


Statistics in ecology

Massimino et al. In prep


Statistics in ecology

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

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


Statistics in ecology

Spatial population trends

Migrant declines

Spatial abundance

Ockendon et al. 2012 Bird Study

www.xkcd.com


Statistics in ecology

Afro-Palaearctic migrants


Statistics in ecology

Many UK population trends of Afro-Palaearctic migrants are declining


Statistics in ecology

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


Statistics in ecology

POP TREND ~ breeding habitat

+ wintering habitat

+ bioclimatic zone

+ median arrival * trend arrival

weight (1/trend.se)


Statistics in ecology

POP TREND ~ breeding habitat

+ wintering habitat

+ bioclimatic zone

+ median arrival * trend arrival

weight (1/trend.se)


Statistics in ecology

What’s wrong with this model?


Statistics in ecology

Spatial population trends

Migrant declines

Spatial abundance

Johnston et al. In submission


Motivation

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

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

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”


Statistics in ecology

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


Statistics in ecology

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


Statistics in ecology

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 assessment1

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”


Statistics in ecology

Kittiwake

kittiwake


Statistics in ecology

Kittiwake

kittiwake


Statistics in ecology

3


Statistics in ecology

0

1

0

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0

0

1

0

1

0

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0

0

0

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0

0

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1

0

0

0

2

3

2


Abundance modelling

Abundance modelling

abundance ~ sea_surface_temp + depth + distance_coast + distance_colonies

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

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


Statistics in ecology

No certain seen


Statistics in ecology

No certain seen

No we could have seen

x 119


Statistics in ecology

No certain seen

No we could have seen

No. modelled to be in whole area


Statistics in ecology

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


Statistics in ecology

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

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.


Statistics in ecology

Spatial population trends

Migrant declines

Spatial abundance

www.xkcd.com


Statistics in ecology

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

Google's Chief Economist , 2009


Statistics in ecology

Razorbill

Black-headed gull

lesser black-backed gull

Kittiwake

guillemot

kittiwake


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