Anatomy of a population cycle: A case study using Canada lynx

Dennis MurrayTrent University

Collaborators

• S. Abele (TNC)• A. Borlestean (Trent U.)• J. Bowman (OMNR)• S. Boutin (U. Alberta)• K. Chan (Trent U.)• R. Gau (NWTG)• C. Krebs (UBC)• M. O’Donoghue (YTG)

• J. Roth (U. Manitoba)• J. Row (Trent U.)• T. Steury (Trent U.)• C. Szumski (U. Manitoba / Trent U.)• D. Thornton (Trent U.)• P. Wilson (Trent U.)• A. Wirsing (U. Washington)

The lynx-hare population cycle

More recent lynx harvest statistics

1919-20

1920-21

1921-22

1922-23

1923-24

1924-25

1925-26

1926-27

1927-28

1928-29

1929-30

1930-31

1931-32

1932-33

1933-34

1934-35

1935-36

1936-37

1937-38

1938-39

1939-40

1940-41

1941-42

1942-43

1943-44

1944-45

1945-46

1946-47

1947-48

1948-49

1949-50

1950-51

1951-52

1952-53

1953-54

1954-55

1955-56

1956-57

1957-58

1958-59

1959-60

1960-61

1961-62

1962-63

1963-64

1964-65

1965-66

1966-67

1967-68

1968-69

1969-70

1970-71

1971-72

1972-73

1973-74

1974-75

1975-76

1976-77

1977-78

1978-79

1979-80

1980-81

1981-82

1982-83

1983-84

1984-85

1985-86

1986-87

1987-88

1988-89

1989-90

1990-91

1991-92

1992-93

1993-94

1994-95

1995-96

1996-97

1997-98

1998-99

1999-2000

2000-01

0

2000

4000

6000

8000

10000

12000

14000

Years

Harvest statistics continue to be collected and reveal high spatio-temporal variability.

Differentiating between signal vs. noise remains challenging

Lynx

num

bers

Cyclic propensity in lynx harvest time series

• Most northern populations are cyclic, southern populations are less likely to cycle

• All cyclic populations exhibit 9-10 year periodicity• Population variability is higher in the southern range

Murray et al (2008)

• Northern snowshoe hare populations are cyclic• Cyclic populations exhibit 9-13 year periodicity• Southern hare populations have dampened fluctuations

Cyclic propensity in hare harvest time series

Murray et al (2008)

-3 -2 -1 0 1 2 3Ln(Hares/ha)

-1

0

1

2

3

4

Ln(L

ynx/

1 00

k m)

Lynx and hare densities are closely associated

Steury & Murray (2004)

Field studies reveal a close association between lynx and hare numbers

Lynx and hare distributions are closely matched

Snowshoe hare Canada lynx

M. M. Wehtje (unpubl) Peers et al (2012)

Trophic interactions in the boreal forest

Stenseth et al (1997)

Hare

Lynx

Do alternate prey stabilize predator-prey population cycles?

Lynx diet through a population cycleK

ills (

%)

• At increasing/high hare densities, lynx eat mainly hares• At low hare densities, almost 50% of lynx prey biomass is

red squirrel

O’Donoghue et al. (1998)B

iom

ass (

%)

Prey (mean & s.e.)

0

2

4

6

8

10

12

14

-27 -26 -25 -24 -23 -22 -21 -20

C13

N15

Snow shoe hare

Columbian ground sq

Microtus sp

Muskrat

Pocket gopherRuffed grouse Redbacked vole

Shorttail shrew

Sorex sp

Blue grouse

Deer mouse

Eutamius sp

Flying squirrel

Red squirrel

Lynx prey have distinct isotopic signatures

Roth et al. (2007)

C13 is higher in southwestern range, indicating a generalized diet

N15

C13

Lynx have distinct isotopic signatures across portions of their range

Roth et al. (2007)

Lynx diet influences cyclic amplitude

Roth et al. (2007)

Lynx populations have a higher cyclic propensity when they rely heavily on snowshoe hares

4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.40

0.1

0.2

0.3

1998

1999

2000

2001

Mean δ15N (‰)

P1-tailed = 0.04

R2 = 0.86

4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.40

0.1

0.2

0.3

1998

1999

2000

2001

Snowshoe hare in dietdrives higher lynx recruitment

P1-tailed = 0.04

R2 = 0.86

Diet specialization

C. Szumski (unpubl)

Prop

. juv

enile

s in

harv

est

dN1/dt = r1 N1 (1 – N1 / k1) – P f1 (N1) – δ1 N1 (Hare)

dN2/dt = r2 N2 (1 – N2 / k2) – P f2 (N2) - δ2 N2 (Squirrel)

dP/dt = P (Χ1 f1 (N1) + Χ2 f2 (N2) - δp ) (Lynx)

where,

N : prey numbers (1 = hare; 2 = squirrel)P : lynx numbersr : rate of increasek : carrying capacityf : functional responseδ : death rate Χ : conversion efficiency

LV model including alternate prey

Lynx-Hare functional response

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 200000

100

200

300

400

500

600

87-88

88-89

89-9090-9191-92

92-93

93-94

94-95

95-96

96-97

Hares per 100 km2

Rate

of P

reda

tion

(har

es/

year

)

K. Chan (unpubl.)

Lynx-Squirrel functional response

15000 16000 17000 18000 19000 20000 21000 22000 23000 240000

50

100

150

200

250

300

350

400

450

500

87-88

88-89 89-9090-91

91-92

92-93

93-94

94-95

95-96

96-97

Red squirrels per 100 km

Rate

of P

reda

tion

(squ

irrel

s / y

ear)

K. Chan (unpubl.)

Revised Lynx-Squirrel functional response

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 200000

50

100

150

200

250

300

350

400

450

500

87-88

88-8989-90

90-9191-92

92-93

93-94

94-95

95-96

96-97

Hares per 100 km2

Rate

of P

reda

tion

(squ

irrel

s / y

ear)

K. Chan (unpubl.)

1985 1990 1995 2000 2005 2010 20150

5000

10000

15000

20000

25000

30000

35000

40000

45000

0

500

1000

1500

2000

2500

Year

red

squi

rels

per

10

0km

2

cone

s per

tree

S. Boutin (unpubl.)

Correlation between squirrel numbers and mast crop

Squirrels Cones

time lag =1 year

dN1/dt = r1 N1 (1 – N1 / k1) – P f1 (N1) – δ1 N1 (Hare)

dN2/dt = r2 N2 (1 – N2 / k2) – P f2 (N1) - δ2 N2 + ε (Squirrel)

dP/dt = P (Χ1 f1 (N1) + Χ2 f2 (N1) - δp ) (Lynx)

Revised model

• The revised model forces the lynx-squirrel functional response to reflect change in hare rather than change in squirrel densities.

• Because squirrels are influenced by annual cone crop, stochasticity was included.

Rosenzweig-Macarthur model

As the prey isocline shifts to the left, the system becomes increasingly unstable.

Prey

Predator

-3000 2000 7000 12000 17000 220000

2

4

6

8

10

12

14

16

18

Lynx

per

100

km

2

Squirrel No Squirrel

Increased instability when squirrels are included

Hares per 100 km2K. Chan (unpubl.)

Alternate prey consistently destabilize predator-prey cycles by moving the prey isocline to the left, not right

Simulations using case studiesParameter Hanski and

Korpimaki 1995Messier et al.

(2004) Fryxell et al.

2007

r1 5.4 y-1 0.2 y-1 0.10512 y-1

k1 100 N1 2 N1 49.6 N1

c 600 N-1·P-1·y-1 12.3 N ·P-1·y-1 250.3 N-1·P-1·y-1

h 10 N1 0.47 N1 0.3 N1

a 1400 N2·N1-1·P-1·y-1 25 N2·N1

-1·P-1·y-1 1199 N2·N1-1·P-1·y-1

b -2 N2 -1 N2 -8 N2

χ1 0.0047 N1-1 0.0141N1

-1 0.0141N1-1

χ2 0.002 N2-1 0.0134 N2

-1 0.0134 N2-1

δ1 0 y-1 0.0856 y-1 0 y-1

δp 7.49 y-1 7.49 y-1 24.28 y-1

K. Chan (unpubl.)

Functional responses from case studies

0 20 40 60 80 100 1200

5

10

15

20

25

30moosebeaver

0 20 40 60 80 100 1200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Wildebeest

Gazelle

0 20 40 60 80 100 1200

100

200

300

400

500

600

700vole1vole 2

K. Chan (unpubl.)

Case studies also reveal increased instability with alternate prey

beavermoose

• Lowered capture efficiency of lynx on hare- Maybe the case in southern populations

• Increased lynx mortality rate - Likely the case in southern populations

• Increased in hare mortality rate- Likely the case in southern populations

• Reduced carrying capacity of hares- Likely the case in southern populations

Increased numerical stability of lynx is driven by

Southern snowshoe hares occupy variegated landscapes

Evidence of density-dependent predation in southern hares

0.0 0.5 1.0 1.5 2.0Hares / ha

0.0

0.2

0.4

0.6

0.8

1.0

Ann

ual p

reda

tion

rate

A. Wirsing (unpubl)

Density-dependent predation in southern hare populations

Cyclic attenuation in natural populations

Cycle attenuation in Fenoscandian voles

Population cycles are becoming attenuated

Statistical detection of cyclic attenuation is challenging given data quality

Ims et al (2006)

Are lynx cycles attenuating?

1919-20

1920-21

1921-22

1922-23

1923-24

1924-25

1925-26

1926-27

1927-28

1928-29

1929-30

1930-31

1931-32

1932-33

1933-34

1934-35

1935-36

1936-37

1937-38

1938-39

1939-40

1940-41

1941-42

1942-43

1943-44

1944-45

1945-46

1946-47

1947-48

1948-49

1949-50

1950-51

1951-52

1952-53

1953-54

1954-55

1955-56

1956-57

1957-58

1958-59

1959-60

1960-61

1961-62

1962-63

1963-64

1964-65

1965-66

1966-67

1967-68

1968-69

1969-70

1970-71

1971-72

1972-73

1973-74

1974-75

1975-76

1976-77

1977-78

1978-79

1979-80

1980-81

1981-82

1982-83

1983-84

1984-85

1985-86

1986-87

1987-88

1988-89

1989-90

1990-91

1991-92

1992-93

1993-94

1994-95

1995-96

1996-97

1997-98

1998-99

1999-2000

2000-01

0

2000

4000

6000

8000

10000

12000

14000

Years

Robust statistical methods for detecting cyclic attenuation are lacking

Lynx

num

bers

Attenuation?

Modeling cyclic attenuation in lynx

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 1010

500

1000

1500

2000

2500

• Climate change

• Competition

• Harvest regime

M. Hornseth (unpubl)

Krebs (2011)

The snowshoe hare is the keystone of the boreal forest ecosystem

Robust field data are essential for detecting attenuation

... ....

.

.

Are snowshoe hare population Are hare cycles collapsing?

Are hare populations becoming increasingly asynchronous?

Model systems for understanding cyclic attenuation

Model systems serve to develop a mechanistic understanding of density dependence and cyclic attenuation

A. Borlestean (unpubl)

20010020TID

0 5 10 15 20Days

0

100

200

300

400

500

600

700

800

Num

ber o

f cel

ls (m

illio

ns)

A. Borlestean (unpubl)

Conclusion

• Alternate prey destabilize predator-prey cycles

• Southern lynx have lower cyclic propensity likely due to latitudinal changes in the lynx-hare relationship itself

• Lynx population cycles may be attenuating due to factors like climate change, increased competition, and overharvest

Current needs & challenges in understanding population cycles

• Good long-term empirical data (experimental and observational)

• Clarity between statistical methods

• Mechanistic & modeling studies

• Methodology for detecting occurrence and underlying causes of cyclic attenuation