Linking parasite populations in hosts to parasite populations in space through Taylor's law and the negative binomial distribution

Abstract

The spatial distribution of individuals of any species is a basic concern of ecology. The spatial distribution of parasites matters to control and conservation of parasites that affect human and nonhuman populations. This paper develops a quantitative theory to predict the spatial distribution of parasites based on the distribution of parasites in hosts and the spatial distribution of hosts. Four models are tested against observations of metazoan hosts and their parasites in littoral zones of four lakes in Otago, New Zealand. These models differ in two dichotomous assumptions, constituting a 2 × 2 theoretical design. One assumption specifies whether the variance function of the number of parasites per host individual is described by Taylor's law (TL) or the negative binomial distribution (NBD). The other assumption specifies whether the numbers of parasite individuals within each host in a square meter of habitat are independent or perfectly correlated among host individuals. We find empirically that the variance–mean relationship of the numbers of parasites per square meter is very well described by TL but is not well described by NBD. Two models that posit perfect correlation of the parasite loads of hosts in a square meter of habitat approximate observations much better than two models that posit independence of parasite loads of hosts in a square meter, regardless of whether the variance–mean relationship of parasites per host individual obeys TL or NBD. We infer that high local interhost correlations in parasite load strongly influence the spatial distribution of parasites. Local hotspots could influence control and conservation of parasites.

Metabolic theory of ecology successfully predicts distinct scaling of ectoparasite load on hosts

“…variation due to host resistance, exposure levels and phylogeny). This variation itself can be informed by scaling theory [38][39][40][41][42], further highlighting the possibility of generating a unified, thorough and efficient [43] scaling theory for parasitism.…”

Chagas disease vector control and Taylor's law

“…If the number of bugs per site of a habitat were described by the negative binomial distribution, then the mean and variance would imply a fraction of sites with zero bugs. Efforts have been made to link TL with the mean and the variance of the negative binomial distribution [ 8 , 52 – 57 ], but it has recently been recognized that TL cannot hold with constant parameters at the same time that the negative binomial distribution holds with a constant scale parameter and a changing probability parameter ([ 9 ], p. E50) (see S1 Text for further details). A practically important topic for further research is finding a useful way to estimate the fraction of sites of a habitat with no bugs, when the mean and variance of bug abundance obey TL, as here.…”

“…Although Taylor was not the first to publish empirical examples of the above linear relationship, he made it widely known [ 4 , 5 ], and it is usually called Taylor's law (TL) among ecologists, or fluctuation scaling or large-number scaling among physicists [ 6 ]. More than 1000 papers have been published on TL and its applications to hundreds of species and many fields besides ecology [ 6 ], including weekly cases of measles in 366 communities in England and Wales pre- and post-vaccination [ 7 ], the aggregation of parasite individuals within host individuals (not including any parasites, vectors, or hosts related to the transmission of Chagas disease) [ 8 , 9 ], human population densities [ 10 ], crop yields [ 11 ], prime numbers [ 12 ] and tornado outbreaks [ 13 ]. TL can be generated by many different models (e.g., [ 6 , 7 , 14 – 16 ]).…”

Biological and statistical processes jointly drive population aggregation: using host–parasite interactions to understand Taylor's power law

“…For over five decades scientists have debated the driving forces underlying the macroecological scaling relationship known as Taylor's power law (TPL), which is often used to study the degree of aggregation within or among populations [1][2][3][4][5][6][7]. Originally outlined in a short paper to show that variance in population density increases as a power function of its mean [1], TPL has become one of the most widely verified scaling 'rules' in ecology, with empirical support from over 500 species of viruses, protists, arthropods, plants, birds, mammals and even humans [8][9][10][11][12].…”