Calculating rmax
The demographic potential of a species is limited. The intrinsic rate of increase \(rmax\) is the maximum increase in log population size that a species can attain in a year. According to Sinclair (2003), it is related to the body mass of adult females \(W\) by the formula:
\[ rmax = 1.375 \times W^{-0.315} \]
Body masses are found in the literature in publications such as Kingdon & Hoffman (2013), Cornelis et al. (2014), Illius & Gordon (1992), Sinclair (1996), Suraud et al. (2012), or Foley & Faust (2010). Alternatively, \(rmax\) can be obtained from specific demographic analyses. In the following table, we have listed the \(rmax\) values obtained with one or the other method giving precedence to specific analyses when available.
species_name <- c("Impala", "Tiang", "Blue wildebeest", "Roan", "Buffalo",
"Eland", "Giraffe", "Elephant")
adult_female_body_mass <- c(55, 127, 230, 250, 400, 450, 702, 2873)
species <- data.frame(adult_female_body_mass, row.names = species_name)
species$rmax <- 1.375 * adult_female_body_mass ^ (-0.315)
species["Eland", "rmax"] <- 0.150 # Sinclair (1996)
species["Elephant", "rmax"] <- 0.07 # Foley & Faust (2010)
species["Giraffe", "rmax"] <- 0.125 # Suraud et al. (2012)
species
#> adult_female_body_mass rmax
#> Impala 55 0.3891244
#> Tiang 127 0.2989541
#> Blue wildebeest 230 0.2479468
#> Roan 250 0.2415192
#> Buffalo 400 0.2082830
#> Eland 450 0.1500000
#> Giraffe 702 0.1250000
#> Elephant 2873 0.0700000Building conversion table
Aerial and ground counts are not directly comparable because some species are better detected from the ground and others from the air. It is generally considered that small light species are better detected from the ground while large dark species are better detected from the air. We took advantage of series of counts carried out in parallel using the two field methods to calculate conversion factors to be applied to aerial counts to obtain ground count equivalents. This permits reconciling the two types of counts within a mixed series. We also specify the preferred field method for each category of species.
categories <- c("Medium light and brown species (20-150kg)",
"Large light and brown species (>150kg)",
"Large dark (>150kg)", "Giraffe", "Elephant")
short_names <- c("MLB", "LLB", "LD", "Giraffe", "Elephant")
conversion_facts <- c(6.747, 2.302, 0.561, 3.011, 0.659)
pref_field_methods <- c("G", "G", "A", "A", "A")
category_info <- data.frame("category" = categories,
"acronym" = short_names,
"conversion_fact" = conversion_facts,
"pref_field_method" = pref_field_methods)
category_info
#> category acronym conversion_fact
#> 1 Medium light and brown species (20-150kg) MLB 6.747
#> 2 Large light and brown species (>150kg) LLB 2.302
#> 3 Large dark (>150kg) LD 0.561
#> 4 Giraffe Giraffe 3.011
#> 5 Elephant Elephant 0.659
#> pref_field_method
#> 1 G
#> 2 G
#> 3 A
#> 4 A
#> 5 ACategorizing species
Here we relate the species to a color/size category.
species$"category" <- c("MLB", "MLB", "LLB", "LLB", "LD", "LLB", "Giraffe",
"Elephant")
species
#> adult_female_body_mass rmax category
#> Impala 55 0.3891244 MLB
#> Tiang 127 0.2989541 MLB
#> Blue wildebeest 230 0.2479468 LLB
#> Roan 250 0.2415192 LLB
#> Buffalo 400 0.2082830 LD
#> Eland 450 0.1500000 LLB
#> Giraffe 702 0.1250000 Giraffe
#> Elephant 2873 0.0700000 ElephantReferences
Cornelis D et al. (2014) Species account: African buffalo (Syncerus caffer). In: Ecology, Evolution and Behaviour of Wild Cattle: Implications for Conservation (Eds M Melletti & J Burton). Cambridge University Press, Cambridge. DOI: 10.1017/CBO9781139568098.
Foley CAH & Faust LJ (2010) Rapid population growth in an elephant Loxodonta africana population recovering from poaching in Tarangire National Park, Tanzania. Oryx, 44, 205-212. DOI: 10.1017/S0030605309990706.
Illius AW & Gordon IJ (1992) Modelling the nutritional ecology of ungulate herbivores: evolution of body size and competitive interactions. Oecologia, 89, 428-434. DOI: 10.1017/S0030605309990706.
Kingdon J & Hoffman M (2013) Mammals of Africa. Volume VI: Pigs, Hippopotamuses, Chevrotain, Giraffes, Deer and Bovids. Bloomsbury Publishing, London, United Kingdom, 680 pp.
Sinclair ARE (1996) Mammal populations: fluctuation, regulation, life history theory, and their implications for conservation. In: Frontiers of population ecology (Eds RB Floyd & AW Sheppard), pp. 127–154. CSIRO: Melbourne, Australia.
Sinclair (2003) Mammal population regulation, keystone processes and ecosystem dynamics. Philosophical Transactions: Biological Sciences, 358, 1729-1740. DOI: 10.1098/rstb.2003.1359.
Suraud JP et al. (2012) Higher than expected growth rate of the endangered West African giraffe Giraffa camelopardalis peralta: a successful human–wildlife cohabitation. Oryx, 46, 577-583. DOI: 10.1017/S0030605311000639.