Coloured noise affecting single- species populations in a spatial setting Frida Lögdberg.
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Coloured noise affecting single- species populations in a spatial setting Frida Lögdberg
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Transcript of Coloured noise affecting single- species populations in a spatial setting Frida Lögdberg.
Coloured noise affecting single-species populations in a spatial setting
Frida Lögdberg
Single-patch populations
• Over compensatory: reddening of noise (increase in autocorrelation) will decrease extinction risk.
• Under compensatory:reddening of noise will increase extinction risk.
Two models
Model 1: Landscape implicit Model 2: Landscape explicit
Model 1
• Discrete population process (Ricker):
• Dispersal is a mass-action mixing process:
bdispi
K
tNr
dispii etNtN
1
1
n
ijjij
n
ijjii
dispi tNddtNtN )()1)(()(
Environmental noise
• 1/f noise in 2D:– Time, noise color– Space, synchrony
Model 1
• Noise affecting K:
• Noise affecting r (indirect):0 10 20 30 40 50 60 70 80 90 100
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
)))1(/(1(,1,
,,b
titi KNrtiti eNN
)1( ,))/(1(
,1,,
tiKNr
titi
btieNN
Model 1: Results
• Over comp., noise in K: as the single-patch system.• Undercomp ., noise in K: hump-shaped response.• Over comp., noise in r: small hump-shaped response.• No interaction effects between synchrony and colour.
0.2 0.4 0.6 0.8 1 1.20
0.2
0.4
0.6
0.8
1
Ext
. ris
k
Noise colour,
0.2 0.4 0.6 0.8 1 1.2500
600
700
800
900
1000
Den
sity
, mea
n
Noise colour,
0.2 0.4 0.6 0.8 1 1.2500
1000
1500
2000
2500
Den
sity
, var
ianc
e
Noise colour,
0.2 0.4 0.6 0.8 1 1.20
0.2
0.4
0.6
0.8
1
Ext
. ris
k
Noise colour,
0.2 0.4 0.6 0.8 1 1.2500
600
700
800
900
1000
Den
sity
, mea
n
Noise colour,
0.2 0.4 0.6 0.8 1 1.2500
1000
1500
2000
2500
Den
sity
, var
ianc
e
Noise colour,
Noise in K, under comp.
0.2 0.4 0.6 0.8 1 1.20
0.2
0.4
0.6
0.8
1
Ext
. ris
k
Noise colour,
=0.9=0.8=0.6=0.4=0.2=0.1
0.2 0.4 0.6 0.8 1 1.2500
600
700
800
900
1000
Den
sity
, mea
n
Noise colour,
0.2 0.4 0.6 0.8 1 1.2500
1000
1500
2000
2500
Den
sity
, var
ianc
e
Noise colour,
Noise in K, over comp. Noise in r, over comp.
Model 2
• Discrete population process (Ricker):
• Dispersal is distance dependent and follows a negative exponential distribution.
• Environmental noise (colour and synchrony) as in Model 1.
bdispi
K
tNr
dispii etNtN
1
1
0 0.5 10
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.80.4
0.5
0.6
0.7
0.8
0 0.5 10
0.2
0.4
0.6
0.8
1
0 0.5 10
0.2
0.4
0.6
0.8
1
0 0.5 10
0.2
0.4
0.6
0.8
1
0 0.5 10
0.2
0.4
0.6
0.8
1
0 0.5 10
0.2
0.4
0.6
0.8
1
Model 2
Contrast = 1 Contrast = 3 Contrast = 5
Conti
nuity
= 0
Conti
nuity
= 1
Conti
nuity
= 5
Landscapes:generated with spectral method.
Landscape characteristics:ContinuityContrast
0.2 0.4 0.6 0.8 1
0
0.5
10
0.5
1
Noise colour ()Sync () 0.2 0.4 0.6 0.8 1
0
0.5
10
0.5
1
Noise colour ()Sync ()
0.2 0.4 0.6 0.8 1
0
0.5
10
0.5
1
Noise colour ()Sync () 0.2 0.4 0.6 0.8 1
0
0.5
10
0.5
1
Noise colour ()Sync ()
0.2 0.4 0.6 0.8 1
0
0.5
10
0.5
1
Noise colour ()Sync () 0.2 0.4 0.6 0.8 1
0
0.5
10
0.5
1
Noise colour ()Sync () 0.2 0.4 0.6 0.8 1
0
0.5
10
0.5
1
Noise colour ()Sync ()
Model 2: Results
Contrast = 1 Contrast = 3 Contrast = 5
Conti
nuity
= 0
Conti
nuity
= 1
Conti
nuity
= 5Pop. dynamics is
over compen-satory.
Noise enters in K.
0.2 0.4 0.6 0.8 1
0
0.5
10
0.5
1
Noise colour ()Sync () 0.2 0.4 0.6 0.8 1
0
0.5
10
0.5
1
Noise colour ()Sync ()
0.2 0.4 0.6 0.8 1
0
0.5
10
0.5
1
Noise colour ()Sync () 0.2 0.4 0.6 0.8 1
0
0.5
10
0.5
1
Noise colour ()Sync ()
0.2 0.4 0.6 0.8 1
0
0.5
10
0.5
1
Noise colour ()Sync () 0.2 0.4 0.6 0.8 1
0
0.5
10
0.5
1
Noise colour ()Sync () 0.2 0.4 0.6 0.8 1
0
0.5
10
0.5
1
Noise colour ()Sync ()
Model 2: Results
Contrast = 1 Contrast = 3 Contrast = 5
Conti
nuity
= 0
Conti
nuity
= 1
Conti
nuity
= 5Pop. dynamics is
under compen-satory.
Noise enters in K.
Model 2: Results
Contrast = 1 Contrast = 3 Contrast = 5
Conti
nuity
= 0
Conti
nuity
= 1
Conti
nuity
= 5Pop. dynamics is
over compen-satory.
Noise enters in r.
0.2 0.4 0.6 0.8 1
0
0.5
10
0.5
1
Noise colour ()Sync () 0.2 0.4 0.6 0.8 1
0
0.5
10
0.5
1
Noise colour ()Sync ()
0.2 0.4 0.6 0.8 1
0
0.5
10
0.5
1
Noise colour ()Sync () 0.2 0.4 0.6 0.8 1
0
0.5
10
0.5
1
Noise colour ()Sync ()
0.2 0.4 0.6 0.8 1
0
0.5
10
0.5
1
Noise colour ()Sync () 0.2 0.4 0.6 0.8 1
0
0.5
10
0.5
1
Noise colour ()Sync () 0.2 0.4 0.6 0.8 1
0
0.5
10
0.5
1
Noise colour ()Sync ()
Conclusions
• No complex interaction effects between any of landscape, synchrony and colour.
• Aggregation versus random landscape affects the extinction risk quantitatively. Men ar du tydlig effekt/markerad effekt
• Population dynamics matter, also when increasing the complexity by adding space.
Implications• To determine extinction risk one have to consider: dynamics, colour,
synchrony, continuity, contrast. – Besides mean and varinace of resources.
• On the other hand most of these have the same effect regardless of the others
• If you want to improve the survival of the populationYou should:– Redder the noise or whiter the noise (be careful with dynamics)– Reduce synchrony– Increase contrast– Reduce continuity– (and of course increase man and reduce variance)
• I f you have to choose: Which is the best to do? Depends on what system, what parameters value you have.
