List of top Mathematics and Quantitative Ecology Questions

A researcher measures the abundance of a tree species in 10 plots in each of two habitats. She tests for differences in abundance between the two habitats using an ANOVA. The results from the ANOVA are as follows: \[\begin{array}{rl} \bullet & \text{Mean abundance in habitat A = 30 trees} \\ \bullet & \text{Mean abundance in habitat B = 50 trees} \\ \bullet & \text{F-statistic (on 1 and 18 degrees of freedom) = 6.04} \\ \bullet & \text{P-value = 0.02} \\ \end{array}\] Here, a P-value of 0.02 means that:
A bird species has an annual survival probability of 0.30. While sampling the population of this species, the probability that any individual is captured in a given year is 0.40. A bird is captured, tagged, and released in Year one. The probability that it is re-captured in Year two is \(\underline{\hspace{0cm}}\) (Round off to two decimal places.)
Sex ratio at birth is biased towards females in a mongoose population. If the probability of having a daughter is 0.7 in this population, and if sex determination of each offspring is an independent event, then the probability that a female with a litter of four offspring has at least one son is \(\underline{\hspace{0cm}}\) (Round off to two decimal places.)