In ecology and fisheries science it is common to calculate the rates of growth, natural mortality, fishing mortality, immigration, emigration, etc. using 'instantaneous' rates. I understand instantaneous rates in the context of finance and banking better than in ecology. There is likely something basic I'm missing here but I'm stumped to figure this out.
To calculate the number of individuals alive at time t, I am given the following equation: $$ N_{t+1} = N_{t}e^{-M_{0}-(C_{t}+Q_{t})/B_{t}} $$ where N is the number of individuals, M0 is 'base instantaneous natural mortality', Ct is 'catch in year t', Qt is consumption in year t (by a specific natural predator), and Bt is a proportion of total biomass (not numbers) vulnerable to predation and fishing.
I'm given little information about units. From what I understand, M0 is a mortality rate that is instantaneous with year-1 units. Bt is actual biomass, not a rate. Ct and Qt are likewise absolute biomass. Thus we are summing instantaneous mortality rate with a proportion. Why?
To be more specific about why I'm confused, M0 to me is a number that is same as ln(m) where m is an annual (or time step t) proportion of the population that dies from natural mortality. Then, why would $(C_{t}+Q_{t})/B_{t}$ appear in the exponent? This is a proportion of total at a time-step t - it doesn't make sense to me why it would be treated as 'instantaneous'.