2. Monday 3.10 Pop Quiz #8 Last Day to Drop Semester Classes
See and Hear MO Frogs and Toads
Ch 10 – 11 Math
For Friday:

3. Missouri Toads and Frogs
Most pictures from MDC

4. Frogs and Toads Phylum Chordata Class Amphibia
Order Anura (frogs and toads)
Family Bufonidae (toads)
Family Hylidae (tree frogs)
Family Ranidae (“true” frogs)

5. Frogs vs Toads Frogs Wet Smooth/slimy Hop/Jump Bulgy eyes
Long sticky tongues
Egg masses
Toads
Dry
Rough/warty
Walk/Dig
Flat eyes
Short drier tongues
Strands of eggs

6. Plains Spadefoot Toad 2 Spea bombifrons

7. American Toad 4 Bufo americanus

8. Cricket Frog 7 Acris creptians

9. Northern Spring Peeper 9 Pseudacris crucifer

10. Gray Treefrog 10 Hyla versicolor

11. Western Chorus Frog 12 Pseudacris triseriata

12. Eastern Narrow-mouth Toad 13 Gastrophryne carolinensis

13. Northern Crawfish Frog 15 Rana areolata

14. Bullfrog 17 Rana catesbeiana

15. Southern Leopard Frog 20 Rana sphenocephala

16. Ch 10 – 11 Mathbonanza
Starting only with observed age classes, offspring prodcued, and age at death, we can calculate survival rates, death rates, birth rates.
We can determine type of growth curve.
We can predict Nt and K.

17. In a pulsed population Phlox drummondii observations – p 233
X (age in days)
nx (number surviving to end of age class)
mx (number of offspring produced per parents during pulse)
0-299
996
158
0.3352
154
0.7963
151
2.3995
147
3.1904
136
2.5411
105
3.1589 74
8.6625 22
4.3072

18. R0, net reproductive rate
Per season! Pulsed population!! Sum total of all seeds produced per individuals who survived through each age class. We need lx, survivorship rate and offspring/survivor/class (lxmx) R0 = Σ lxmx

19. R0, net reproductive rate
lx = nx/ n0 l2 = 158/996 = l3 = 154/996 = l4 = 151/996 = Calculate for all nx

20. R0, net reproductive rate
R0 = Σ lxmx New column = lxmx Add all of those for R0 = Σ lxmx

21. Total # of offspring per season?
R0 x N x 996 =

22. Geometric rate of increase
At what rate does the total population grow from one pulse to the next?
λ = N(t + 1)/Nt
This plant is an annual, so t = 1 year.
(All previous age classes were in the same pulse/year!)
Nt = 996, Nt+1 = 2408

23. Same pop, Ch 11, p 242
So, by rearranging, N2 = N1 x λ, and N3 = N2 x λ Because N1 = N0 x λ, by substitution, N2 = N0 x λ x λ = N0 x λ2 By extension, N3 = N0 x λ x λ x λ = N0 x λ3

24. Geometric Growth model
We can model this population at any year in time by: Nt = N0λt Practice: Calculate N25