The spatial dimension of population ecology

Case study I The local scale: necrophagous flies and their parasitoids

Arion ater

Megaselia sp

Basalys parva

Aspilota spKleidotoma psiloides

Limosina ?sylvatica

The spatial distribution of individuals

100 boxes arranged in a regular 10x10 m grid each with a dead slug

What is the spatial distribution of flies, parasitoids, and hyperparasitoids

Does spatial distribution change with abundance?

Do parasitoids and hosts differ in spatial distribution?

Is spatial distribution linked to resource availability?

Does spatial distribution contributes to population stability?

Photo Polystyrol

Each slug was covered by a beech leaf

Arion ater

Conicera schnittmanni

Megaselia ruficornis

Megaselia ?angusta

Megaselia ?pulicaria

Gymnophora arcuata

Limosina sp. Pegomya sp.

Conicera sp.Diplonevra florea

Triphleba subcompletaMegaselia sp. Aspilota sp4 Aspilota sp1 Aspilota sp1 Kleidotoma psiloides Atractodes sp.

Sylvicola ?cinctus

Aspilota sp5 Aspilota sp2 Aspilota 5 Pentapleura sp.

Phaonia ?pallida Aspilota sp3Fannia

?immuticaOrthostigma sp.

Psychoda sp.Psychodidae sp. Basaly parva

Panorpa sp.Silphidae spp. Basalys parva Basalys abrupta

Carabidae spp. Idiotypa nigricepsTrichopria aequata

Arion ater Ceraphron sp.Gelis sp.Trichopria

evanescens

The complete food web of dead Arion snails

Aspilota sp1

Aspilota sp3 Aspilota sp1Kleidotoma

psiloides

Aspilota sp2

Orthostigma sp.

Aspilota sp4Pentapleura

sp.

Megaselia ruficornis

M. ?angusta/ ?pulicaria

Arion aterGymnophora

arcuataLimosina sp.

Necrophilus spp.

Conicera schnittmanni

Carabus spp.

?Fannia

?immutica

Psychoda sp.

Time axis

Idiotypa nigricepsBasalys parva

The sequence of colonisation

The limiting factor of colonisation was

carcass desiccation

Desiccation is dependent on

plant cover

Slug weight

(g)Conicera

schnittmaniMegaselia ruficornis

Megaselia pulicaria

Gymnophora arcuata Limosina sp Psychoda sp Fannia

immutica Panorpa sp

N weight (mg) N weight

(mg) N weight (mg) N weight

(mg) N weight (mg) N weight

(mg) N weight (mg) N weight

(mg)

2.3 1 0.000633 6 0.0066 0 0 0 0 0 0 0 0 0 0 0 0

2.5 0 0 1 0.0011 2 0.0022 0 0 3 0.0018 0 0 0 0 1 0.026

3.1 0 0 9 0.0099 0 0 1 0.00315 0 0 0 0 0 0 0 0

2.6 0 0 2 0.0022 0 0 0 0 0 0 0 0 0 0 0 02.8 0 0 7 0.0077 0 0 0 0 10 0.006 1 0.0009 1 0.0043 0 0

Coordi-nates

Slug weight

(g)Aspilota sp1 Aspilota sp2 Orthostigma

sp1 Aspilota sp4 Aspilota sp5 Kleidotoma psiloides

N parasitism rate N parasitism

rate N parasitism rate N parasitism

rate N parasitism rate N parasitism

rate9075 2.3 2 0.333 0 0.000 4 0.667 0 0.000 0 0.000 0 0.0009078 2.5 2 0.667 0 0.000 0 0.000 0 0.000 0 0.000 0 0.0009082 3.1 0 0.000 6 0.667 3 0.333 0 0.000 0 0.000 0 0.0009084 2.6 0 0.000 1 0.500 1 0.500 0 0.000 0 0.000 0 0.0008473 2.8 0 0.000 0 0.000 0 0.000 7 1.000 0 0.000 0 0.000

The raw data

Conicera schnittmanni Megaselia sp1

Aspilota sp1 Orthostigma sp1

Aspilota sp1 Orthostigma sp1

Aspilota sp1 Kleidotoma psiloides

Spatial aggregation

Coefficient of variation Morisita index

Mean crowding (Lloyd index)𝐶𝑉=𝜎𝜇 𝐼=

𝑁∑𝑖=1

𝑁

𝑛𝑖 (𝑛𝑖−1)

𝑛𝜇(𝑛𝜇−1)

𝐽=𝜎 2

𝜇2−1𝜇

+1

𝜎 2=𝜇

𝜎 2−𝜇=0𝜎2

𝜇2−1𝜇

=0

𝜎2

𝜇2−1𝜇

+1=1

Poisson random distribution

Poisson random: J = 1

Regular (segregated, overdispersed): J << 1

Clumped (aggregated, underdispersed): J >> 1

N denote the occasions in each of the N sites.

Statistical inference has to come from a Monte Carlo ranodmisation.

Lloyd index and species abundances

Parasitoids

Diptera

Necrophagous flies and their parasitoids :• Highly aggregated• Aggregation decreases with average abundance• Both guilds have the same degree of aggregation

Conicera schnittmani

Megaselia ruficornis

Megaselia pulicaria

Gymnophora arcuata Limosina sp Psychoda sp Fannia

immutica Panorpa sp

Conicera schnittmani - 0.29 0.00 0.52 0.00 0.03 0.26 0.43

Megaselia ruficornis -0.11 - 0.69 0.96 0.97 0.62 0.42 0.23

Megaselia pulicaria 0.47 -0.04 - 0.34 0.00 0.39 0.84 0.49

Gymnophora arcuata -0.07 0.00 -0.10 - 0.56 0.57 0.84 0.31

Limosina sp 0.32 0.00 0.36 -0.06 - 0.06 0.40 0.88Psychoda

sp 0.22 -0.05 0.09 -0.06 0.19 - 0.83 0.56

Fannia immutica 0.11 -0.08 -0.02 0.02 -0.09 0.02 - 0.00

Panorpa sp 0.08 0.12 0.07 -0.10 -0.01 -0.06 0.33 -

Aspilota sp1 Aspilota sp2 Orthostigma sp1 Aspilota sp4 Aspilota sp5 Kleidotoma psiloides

Aspilota sp1 - 0.18 0.51 0.58 0.64 0.08Aspilota sp2 0.14 - 0.78 0.01 0.10 0.18

Orthostigma sp1 0.07 0.03 - 0.74 0.91 0.60Aspilota sp4 -0.06 0.26 -0.03 - 0.43 0.48Aspilota sp5 0.05 0.17 0.01 0.08 - 0.33

Kleidotoma psiloides 0.18 0.13 -0.05 -0.07 -0.10 -

Spatial segregation of species?

Table of Pearson correlations (lower triangle) and the respective significance levels (upper triangle)

Aspilota sp1

Aspilota sp2

K. psiloides

C. schnittmanni

Limosina spBiplots of principal component analyses

PCA separates sphaerocerid species from C. schnittmanni and the other phorid species

PCA separates the abundant Aspilota sp1 and sp2

Necrophagous Diptera Parasitic HymenopteraLarge number of species Large number of species

Higher diversity Lower diversity

Colonization susceptible to desiccation of the carcass Parasitism fairly independent of carcass desiccationDensities of early colonizers do not depend on the weight of the carrion

Parasitism rates independent of the weight of the carrion

Densities of late colonizers correlate positively with the weight of the carrion

Parasitism in dominant species is not density dependent

Low interspecific competition Pronounced interspecific competition only at high parasitism rates

High competition between the necrophagous flies and large predators and necrophages -

High impact of large predators and necrophages on the mortality rates

Parasitism rates not influenced by the presence of larger competitors of the hosts

High degree of aggregation in the populations High degree of aggregation in the populationsNegative correlation between abundance and degree of aggregation

No marked correlation between parasitism and degree of aggregation

Aggregation of late colonizing species negatively correlated with the weight of the carrion Aggregation independent of the number of hosts

Differences in the populations of necrophages and their parasitoids

Case study II The regional scale: fragmented landscapes and meta-populations

Meta-populations refer to the spread of local populations of a single species within a fragmented landscape. Local populations are connected by dispersal

Questions:Minimum fragment sizeMinimum dispersal rate for survivalPercentage of fragments colonisedSpeed of genetic divergence within fragments

What is the influence of fragment edges?

How do corridors influence dispersal rates?

The spatial distribution of species is scattered among isolated fragments.Fragments differ in population size

The higher the population size is, the lower is the local extinction probability and the higher is the emigration rate

Distance

Case study II The regional scale: fragmented landscapes and meta-populations

)(K

NKrN

dt

dN

The Lotka – Volterra model of population growth

Levins (1969) assumed that the change in the occupancy of single spatially separated habitats

(islands) follows the same model.

Assume P being the number of islands (total K) occupied. Q= K-P is then the proportion of not

occupied islands. m is the immigration and e the local extinction probability.

Colonisations Emigration/Extinction

𝑑𝑃𝑑𝑡

=𝑚𝑃 (𝐾−𝑃𝐾 ) 𝑑𝑄𝑑𝑡

=−𝑒𝑃

𝑑𝑃𝑑𝑡

=𝑚𝑃 (𝐾−𝑃𝐾 )−𝑒𝑃The Levins model of meta-populations

Colonisation probability is exponentially dependent on the average distance I of the islands and extinction probability scales proportionally to island size.

𝑒∝1𝐴𝑚∝𝑒−𝑐𝐼

𝑑𝑝𝑑𝑡

=𝑎𝑒−𝑐𝐼𝑝 (1−𝑝 )−𝑏 1𝐴𝑝

The canonical model of metapopulation ecology

Metapopulation modelling allows for an estimation of species survival in fragmented landscapes and provides estimates on species occurrences.

If we deal with the fraction p of fragments colonized

𝑑𝑝𝑑𝑡

=𝑚𝑝 (1−𝑝 )−𝑒𝑝

The standard equation of metapopulation modeling

Extinction times

When is a metapopulation stable?

𝑑𝑝𝑑𝑡

=0=𝑚𝑝 (1−𝑝 )−𝑒𝑝

𝑝=1−𝑒𝑚

The meta-population is only stable if m > e.

𝑇 𝑅=𝑇 𝐿𝑒𝑃2

2 𝐾−2 𝑃

If we know local extinction times TL we can estimate the regional time TR to extinction

0

200

400

600

800

1000

1200

0 1 2 3 4 5 6 7

p K 0.5

Med

ian

time

to e

xtinc

tion

𝑃𝐾

=𝑝>3

√𝐾

The condition for long-term survival

𝑑𝑝𝑑𝑡

=𝑚𝑝 (1−𝑝 )−𝑒𝑝

If m and e are known p denotes the proportion of fragments colonised

Bird metapopulations

Zosterops abyssinicus

Zosterops poliogaster

The lowland Z. abyssinicus has a continuous distribution.The highland Z. poliogaster has a scattered mountain distribution.It has a meta-population structure.The highland species occurs in forest fragments

Species Region N Wing Tarsus Weight GPSZ. poligaster CH-Satellite 25 62.9 20.9 12.7 2°35´S; 37°51´EZ. poligaster CH-Simba valley 10 61.1 21.2 11.4 2°42´S; 37°55´EZ. poligaster Mount Kasigau 20 59 21 10.6 3°49´S; 38°39´EZ. poligaster Mt. Kulal 32 63.4 21.7 13.6 2°39´N; 36°56´E

Species Region Site Starting frequency

Lowest frequency

Highest frequency

Frequency range

Length of call

Z.abyssinicus Chyulu Lowands Hunters Lodge 3501 2937 3848 911 0.1733Z.abyssinicus Chyulu Lowands Hunters Lodge 3473 3191 3853 662 0.2049Z.abyssinicus Chyulu Lowands Hunters Lodge 3321 3256 4048 792 0.1952Z.abyssinicus Chyulu Lowands Hunters Lodge 3495 2865 4091 1226 0.1588Z.abyssinicus Chyulu Lowands Hunters Lodge 3703 3038 4094 1056 0.2133

Location Locus

Fragment

length

Mt. Kasiga

uTH

ChawiaTH

Mbololo

TH Mbolol

o

TH Mbolol

o

TH Nganga

o

TH Nganga

oChyulu

HillsChyulu

HillsAberda

resMt.

KulalChulu

lowlands

Cu_28 1 160 0 0 0 0 0 0 0 0 0 0 0 0Cu_28 2 162 0.4524 0.0192 0.025 0.0161 0 0.0862 0.0238 0 0 0.02 0 0Cu_28 3 164 0.5476 0.9808 0.975 0.9839 1 0.9138 0.9762 1 1 0.98 1 1Zl44 1 214 0 0 0 0 0 0 0 0 0 0.02 0 0Zl44 2 218 0 0 0 0 0 0 0 0 0 0 0 0Zl44 3 220 1 1 1 1 1 1 1 1 1 0.74 0.8667 0.9286Zl44 4 224 0 0 0 0 0 0 0 0 0 0.24 0.1333 0.0714Zl44 5 226 0 0 0 0 0 0 0 0 0 0 0 0Zl41 1 82 0.9524 0.9615 1 0.9839 1 0.9483 0.9762 1 1 0.9792 1 1

Morphological raw data

Bird call raw data

Allele frequency raw data Data collected by J. C. Habel, TH Munich

Bird call patternsSpecies P. abyssinicus P. poliogaster

Region Chyulu lowlands Taita lowlands Chyulu hills Taita hills Aberdares

Site Hunters Lodge Kibwesi Mtito

Andei Mumoni Dembwa Mwatate Satellite Simba Mt. Kasigau Mbololo Ngangao Aberdare

s

P. abyssini

cus

Chyulu lowlands

Kibwesi 0.33

Mtito Andei <0.001 0.42

Mumoni 0.49 0.99 0.31

Taita lowlands

Dembwa 0.95 0.98 0.08 0.99

Mwatate 0.99 0.21 0.03 0.93 0.99

P. poliogas

ter

Chyulu hills

Satellite 0.49 <0.001 <0.001 <0.001 <0.001 <0.001

Simba 0.98 0.62 0.06 0.99 0.99 0.99 <0.001

Taita hills

Mt. Kasigau 0.47 0.99 0.37 0.99 0.99 0.98 <0.001 0.99

Mbololo <0.001 <0.001 0.99 <0.001 <0.001 <0.001 <0.001 <0.001 0.07

Ngangao 0.13 0.99 0.63 0.99 0.79 0.12 <0.001 0.36 0.99 <0.001

Aberdares

Aberdares <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001

Mt. Kulal Mt. Kulal 0.05 <0.001 <0.001 <0.001 <0.001 0.01 0.55 <0.001 <0.001 <0.001 <0.001 0.99

Local birdcalls within Z. poliogaster are more different than between Z. poliogaster and Z. abyssinicus

Birdcall within the lowland Z. poliogaster do not significantly

differ

ANOVA probabilities for no difference

: Bird calls: Allele frequencies: Morphology

Northern and southern populations of Z. poliogaster differ considerable in bird

dialect. Soon gen flow will cease despite of occasional migration.

Bird call patterns within Z. poliogaster differ more between local populations than do genetic and morphological charcters.

Dist CH-Satellite CH-Simba_valley Mt_Kasigau Mt._Kulal ChawiaCH-Satellite 14003.55 15397.05 83023.01 13299.94CH-Simba_valley 14003.55 15701.06 70770.7 13718.35Mt_Kasigau 15397.05 15701.06 71486.18 2332.959Mt._Kulal 83023.01 70770.7 71486.18 72338.83Chawia 13299.94 13718.35 2332.959 72338.83

Geographic distances in m

Sum 10418.22 15576.44 5139.1 74321.64 10382.77Rel sum 0.125381 0.18746 0.061848 0.894447 0.124955

The average relative distance of a site to all other sites.𝐼 𝑖=

∑𝑗=1

𝑛

𝑑𝑖𝑗

𝑑𝑚𝑎𝑥

𝑝𝑡+1=𝑝𝑡+𝑑𝑝𝑑𝑡

=𝑝𝑡+𝑎𝑒−𝑐𝐼𝑝𝑡 (1−𝑝𝑡 )−𝑏 1𝐴 𝑝𝑡

Species population occupancy modelling SPOM

Site I A [ha] p0 p1 p2 p3 p4 p5 p6CH-Satellite 0.125381 0.77 0.5 0.286 0.190 0.135 0.099 0.074 0.056CH-Simba_valley 0.18746 6.99 0.5 0.568 0.629 0.681 0.722 0.754 0.777

Mt_Kasigau 0.061848 6.21 0.5 0.577 0.645 0.701 0.743 0.773 0.793Mt._Kulal 0.894447 4.05 0.5 0.489 0.480 0.472 0.465 0.458 0.452Chawia 0.124955 5.94 0.5 0.568 0.629 0.679 0.718 0.747 0.767Fururu 0.077297 9.21 0.5 0.589 0.669 0.735 0.785 0.821 0.844

=AE56+$W$53*EXP(-$Y$53*$W56)*AE56*(1-AE56)-$X$53*1/$X56*AE56a = 0.5b = 0.5c = 1

a 0.5 0.1 0.5 0.5b 0.5 0.5 0.1 0.5c 1 1 1 5Site p6 p6 p6 p6CH-Satellite 0.056 0.003 0.672 0.017CH-Simba_valley 0.777 0.424 0.909 0.565Mt_Kasigau 0.793 0.417 0.929 0.719Mt._Kulal 0.452 0.268 0.704 0.232Chawia 0.767 0.401 0.916 0.615Fururu 0.844 0.479 0.938 0.760MachaE 0.673 0.297 0.902 0.571Mbololo 0.810 0.454 0.921 0.633Mwachora 0.849 0.485 0.939 0.764Ndiwenyi 0.787 0.413 0.926 0.690Ngangao 0.450 0.139 0.845 0.307Ronge 0.214 0.037 0.764 0.099Vuria 0.841 0.481 0.934 0.720Wundanyi 0.585 0.225 0.882 0.471YaleS 0.577 0.220 0.879 0.454

Species population occupancy modelling SPOM

High dispersal increases the probability of occupancy.High local mortality decreases local colonisation.Distance between fragments has a high impact on colonisation probability.The highly isolated Mt. Kulal has low occupancy probabilities.

𝑁𝐾

=𝑝>3

√𝐾3/√15 = 0.77 For long-term stability of the meta-population

at least 77% = 12 sites have to be occupied

𝑇 𝑅=𝑇 𝐿𝑒𝑃2

2 𝐾−2 𝑃

Is the species endangered?

𝑝=1−𝑒− 1𝑇 𝑇=

1− ln (1−𝑝 )  

Sitep6 1-p6 Extinction

time

CH-Satellite 0.508251 0.492 1.478

CH-Simba_valley 0.725387 0.275 3.115

Mt_Kasigau 0.87694 0.123 7.615

Mt._Kulal 0.438394 0.562 1.213Chawia 0.794841 0.205 4.355Fururu 0.872029 0.128 7.303MachaE 0.832455 0.168 5.453Mbololo 0.769542 0.230 3.817

Mwachora 0.871579 0.128 7.275

Ndiwenyi 0.854269 0.146 6.349Ngangao 0.726755 0.273 3.133Ronge 0.595481 0.405 1.929Vuria 0.834469 0.166 5.526Wundanyi 0.802087 0.198 4.534YaleS 0.791203 0.209 4.270

TL 4.491P 11TR 16636092

Zosterops poliogaster is regionally not endangered despite of the higher local extinction probabilities

Extinction time

1.4783.1157.6151.2134.3557.3035.4533.8177.2756.3493.1331.9295.5264.5344.270

4.4916

33.18457

The loss of habitats might provide to fast extinction